........................................................................... Below is a list of the largest orders of a group of automorphisms of a compact non-orientable surface of given genus p, for p between 3 and 302. For each genus p, the signatures are given for the NEC groups from which the corresponding surface actions can be obtained. Abbreviations/notation: Type (p,q,r)* stands for the NEC group signature (0; +; [-]; {(p,q,r)}) Type (p,q,r,s)* stands for the NEC group signature (0; +; [-]; {(p,q,r,s)}) Marston Conder September 2012 [plus one correction made for genus 302 on 16 February 2013, after Primoz Potocnik discovered a small bug in the LowIndexNormalSubgroups routine that meant quotients isomorphic to the wreath product A_5 \wr S_2 (and covers of this group) had been omitted] ........................................................................... Some observations can be made about this list: (a) An upper bound for these largest orders is 84(p-2), occurring for type (2,3,7)*, but this bound is attained for very few genera, namely p = 8, 15 and 147 only (b) A lower bound for these largest orders is 4p, and this is also attained for very few genera, namely p = 3, 87 and 207, with type (2,2,2,p)* in each case (c) The "next best" after 84(p-2) is 48(p-2), occurring for type (2,3,8)*, and this is attained for seven genera, namely p = 9, 17, 23, 47, 86, 236 and 255 only (d) The "next best" after (2,3,7)* and (2,3,8)* are (2,4,5)*, (2,3,9)*, (2,3,10)*, (2,3,11)*, (2,3,12)*, (2,4,6)* and (3,3,4)*, giving orders 40(p-2), 36(p-2), 30(p-2), (132/5)(p-2), 24(p-2), 24(p-2) and 24(p-2), occurring for 7, 3, 8, 1, 5, 25 and 0 values of p, respectively [Note: In some cases, more than one of the last three types occur] (e) The cases in (a), (c) and (d) above, which give order 24(p-2) or more, account for 56 values of p -- that is, about one fifth of all genera in the given range (f) The order 12(p-2) is exceeded for 84 genera in the given range (g) The order 12(p-2) is met or exceeded for 104 genera in the given range (h) The order 8(p-2) is exceeded for 198 genera in the given range -- that is, about two thirds of all genera in the given range (i) The order 8(p-2) is met or exceeded for 263 genera in the given range -- that is, almost 88% of all genera in the given range (j) The order 6(p-2) is exceeded for 284 genera in the given range (k) The order 6(p-2) is met or exceeded for 297 genera in the given range -- that is, for all but the genera 87, 207 and 267 (l) The most frequent signature types giving the maximum order are the type (2,2,2,4)* and the signature (0; +; [2]; {(2,4)}), occurring 40 and 38 times respectively (m) If M_p denotes the maximum group order, then the average value of the ratio M_p/(p-2) across the given range is approx. 13.75. Also the results of the Magma computation used to obtained the above maxima show that the most frequent types that occur among all "large" group actions on non-orientable surfaces with genus p in the given range are as follows: Type (2,2,2,4)* ... 164 genera Type (2,2,2,6)* ... 149 genera Signature (0; +; [2]; {(2,6)}) ... 121 genera Signature (0; +; [2,3]; {(1)}) ... 120 genera Signature (0; +; [2]; {(2,4)}) ... 111 genera Type (2,2,2,3)* ... 58 genera Signature (0; +; [3]; {(2,2)}) ... 54 genera Signature (0; +; [2]; {(3,3)}) ... 41 genera Type (2,2,2,3)* ... 38 genera ........................................................................... Maximum numbers of automorphisms of non-orientable surfaces Genus 3 Maximum order 12 occurring for type(s) { (2,2,2,3)* } Genus 4 Maximum order 48 occurring for type(s) { (2,4,6)* } Genus 5 Maximum order 120 occurring for type(s) { (2,4,5)* } Genus 6 Maximum order 160 occurring for type(s) { (2,4,5)* } Genus 7 Maximum order 120 occurring for type(s) { (2,4,6)* } Genus 8 Maximum order 504 occurring for type(s) { (2,3,7)* } Genus 9 Maximum order 336 occurring for type(s) { (2,3,8)* } Genus 10 Maximum order 192 occurring for type(s) { (2,4,6)* } Genus 11 Maximum order 216 occurring for type(s) { (2,4,6)* } Genus 12 Maximum order 240 occurring for type(s) { (2,4,6)* } Genus 13 Maximum order 120 occurring for type(s) { (2,4,15)* } Genus 14 Maximum order 360 occurring for type(s) { (2,3,10)* } Genus 15 Maximum order 1092 occurring for type(s) { (2,3,7)* } Genus 16 Maximum order 504 occurring for type(s) { (2,3,9)* } Genus 17 Maximum order 720 occurring for type(s) { (2,3,8)* } Genus 18 Maximum order 192 occurring for type(s) { (2,2,2,3)* } Genus 19 Maximum order 168 occurring for type(s) { (2,4,21)* } Genus 20 Maximum order 240 occurring for type(s) { (2,4,10)* } Genus 21 Maximum order 132 occurring for type(s) { (2,6,22)* } Genus 22 Maximum order 240 occurring for type(s) { (2,6,6)*, (2,2,2,3)* } Genus 23 Maximum order 1008 occurring for type(s) { (2,3,8)* } Genus 24 Maximum order 176 occurring for type(s) { (2,2,2,4)* } Genus 25 Maximum order 216 occurring for type(s) { (2,4,27)* } Genus 26 Maximum order 720 occurring for type(s) { (2,3,10)* } Genus 27 Maximum order 300 occurring for type(s) { (2,2,2,3)* } Genus 28 Maximum order 240 occurring for type(s) { (2,4,30)* } Genus 29 Maximum order 648 occurring for type(s) { (2,3,12)* } Genus 30 Maximum order 672 occurring for type(s) { (2,4,6)* } Genus 31 Maximum order 264 occurring for type(s) { (2,4,33)* } Genus 32 Maximum order 720 occurring for type(s) { (2,4,6)* } Genus 33 Maximum order 204 occurring for type(s) { (2,6,34)* } Genus 34 Maximum order 384 occurring for type(s) { (2,2,2,3)*, (2,4,12)* } Genus 35 Maximum order 1320 occurring for type(s) { (2,4,5)* } Genus 36 Maximum order 272 occurring for type(s) { (2,2,2,4)* } Genus 37 Maximum order 392 occurring for type(s) { (2,4,14)* } Genus 38 Maximum order 480 occurring for type(s) { (2,4,10)* } Genus 39 Maximum order 222 occurring for type(s) { (0; +; [2,3]; {(1)}) } Genus 40 Maximum order 336 occurring for type(s) { (2,4,42)* } Genus 41 Maximum order 360 occurring for type(s) { (3,4,5)* } Genus 42 Maximum order 600 occurring for type(s) { (2,5,6)* } Genus 43 Maximum order 360 occurring for type(s) { (2,4,45)* } Genus 44 Maximum order 672 occurring for type(s) { (2,4,8)* } Genus 45 Maximum order 276 occurring for type(s) { (2,6,46)* } Genus 46 Maximum order 1320 occurring for type(s) { (2,3,10)* } Genus 47 Maximum order 2160 occurring for type(s) { (2,3,8)* } Genus 48 Maximum order 368 occurring for type(s) { (2,2,2,4)* } Genus 49 Maximum order 408 occurring for type(s) { (2,4,51)* } Genus 50 Maximum order 1920 occurring for type(s) { (2,4,5)* } Genus 51 Maximum order 1092 occurring for type(s) { (2,3,13)* } Genus 52 Maximum order 480 occurring for type(s) { (2,6,8)* } Genus 53 Maximum order 408 occurring for type(s) { (0; +; [2]; {(2,4)}) } Genus 54 Maximum order 416 occurring for type(s) { (2,2,2,4)* } Genus 55 Maximum order 456 occurring for type(s) { (2,4,57)* } Genus 56 Maximum order 1296 occurring for type(s) { (2,4,6)* } Genus 57 Maximum order 1320 occurring for type(s) { (2,3,12)*, (2,4,6)* } Genus 58 Maximum order 1008 occurring for type(s) { (2,3,18)* } Genus 59 Maximum order 456 occurring for type(s) { (0; +; [2]; {(2,4)}) } Genus 60 Maximum order 464 occurring for type(s) { (2,2,2,4)* } Genus 61 Maximum order 504 occurring for type(s) { (2,4,63)* } Genus 62 Maximum order 1440 occurring for type(s) { (2,4,6)* } Genus 63 Maximum order 366 occurring for type(s) { (0; +; [2,3]; {(1)}) } Genus 64 Maximum order 528 occurring for type(s) { (2,4,66)* } Genus 65 Maximum order 720 occurring for type(s) { (2,5,8)* } Genus 66 Maximum order 960 occurring for type(s) { (2,5,6)* } Genus 67 Maximum order 552 occurring for type(s) { (2,4,69)* } Genus 68 Maximum order 528 occurring for type(s) { (0; +; [2]; {(2,4)}), (2,2,2,4)* } Genus 69 Maximum order 420 occurring for type(s) { (2,6,70)* } Genus 70 Maximum order 2448 occurring for type(s) { (2,3,9)* } Genus 71 Maximum order 552 occurring for type(s) { (0; +; [2]; {(2,4)}) } Genus 72 Maximum order 672 occurring for type(s) { (2,6,8)* } Genus 73 Maximum order 600 occurring for type(s) { (2,4,75)* } Genus 74 Maximum order 2160 occurring for type(s) { (2,3,10)* } Genus 75 Maximum order 438 occurring for type(s) { (0; +; [2,3]; {(1)}) } Genus 76 Maximum order 624 occurring for type(s) { (2,4,78)* } Genus 77 Maximum order 1000 occurring for type(s) { (2,4,10)* } Genus 78 Maximum order 608 occurring for type(s) { (2,2,2,4)* } Genus 79 Maximum order 648 occurring for type(s) { (2,4,81)* } Genus 80 Maximum order 624 occurring for type(s) { (0; +; [2]; {(2,4)}), (2,2,2,4)* } Genus 81 Maximum order 492 occurring for type(s) { (2,6,82)* } Genus 82 Maximum order 1152 occurring for type(s) { (2,4,9)* } Genus 83 Maximum order 1944 occurring for type(s) { (2,4,6)* } Genus 84 Maximum order 656 occurring for type(s) { (2,2,2,4)* } Genus 85 Maximum order 696 occurring for type(s) { (2,4,87)* } Genus 86 Maximum order 4032 occurring for type(s) { (2,3,8)* } Genus 87 Maximum order 348 occurring for type(s) { (2,2,2,87)* } Genus 88 Maximum order 720 occurring for type(s) { (2,4,90)* } Genus 89 Maximum order 696 occurring for type(s) { (0; +; [2]; {(2,4)}) } Genus 90 Maximum order 1320 occurring for type(s) { (2,5,6)* } Genus 91 Maximum order 744 occurring for type(s) { (2,4,93)* } Genus 92 Maximum order 1440 occurring for type(s) { (2,4,8)* } Genus 93 Maximum order 2184 occurring for type(s) { (2,3,12)*, (2,4,6)* } Genus 94 Maximum order 768 occurring for type(s) { (2,4,96)* } Genus 95 Maximum order 744 occurring for type(s) { (0; +; [2]; {(2,4)}) } Genus 96 Maximum order 752 occurring for type(s) { (2,2,2,4)* } Genus 97 Maximum order 3420 occurring for type(s) { (2,3,9)* } Genus 98 Maximum order 1920 occurring for type(s) { (2,5,5)* } Genus 99 Maximum order 582 occurring for type(s) { (0; +; [2,3]; {(1)}) } Genus 100 Maximum order 816 occurring for type(s) { (2,4,102)* } Genus 101 Maximum order 1320 occurring for type(s) { (2,4,10)* } Genus 102 Maximum order 1200 occurring for type(s) { (2,2,2,3)* } Genus 103 Maximum order 840 occurring for type(s) { (2,4,105)* } Genus 104 Maximum order 816 occurring for type(s) { (0; +; [2]; {(2,4)}), (2,2,2,4)* } Genus 105 Maximum order 636 occurring for type(s) { (2,6,106)* } Genus 106 Maximum order 2184 occurring for type(s) { (2,3,14)* } Genus 107 Maximum order 1320 occurring for type(s) { (2,4,11)* } Genus 108 Maximum order 848 occurring for type(s) { (2,2,2,4)* } Genus 109 Maximum order 888 occurring for type(s) { (2,4,111)* } Genus 110 Maximum order 1440 occurring for type(s) { (2,4,10)* } Genus 111 Maximum order 654 occurring for type(s) { (0; +; [2,3]; {(1)}) } Genus 112 Maximum order 2640 occurring for type(s) { (2,4,6)* } Genus 113 Maximum order 888 occurring for type(s) { (0; +; [2]; {(2,4)}) } Genus 114 Maximum order 1344 occurring for type(s) { (2,2,2,3)*, (2,4,12)*, (3,4,4)* } Genus 115 Maximum order 936 occurring for type(s) { (2,4,117)* } Genus 116 Maximum order 3420 occurring for type(s) { (2,3,10)* } Genus 117 Maximum order 708 occurring for type(s) { (2,6,118)* } Genus 118 Maximum order 960 occurring for type(s) { (2,4,120)* } Genus 119 Maximum order 2184 occurring for type(s) { (2,4,7)* } Genus 120 Maximum order 944 occurring for type(s) { (2,2,2,4)* } Genus 121 Maximum order 984 occurring for type(s) { (2,4,123)* } Genus 122 Maximum order 2880 occurring for type(s) { (2,4,6)* } Genus 123 Maximum order 1452 occurring for type(s) { (2,2,2,3)* } Genus 124 Maximum order 1008 occurring for type(s) { (2,4,126)* } Genus 125 Maximum order 984 occurring for type(s) { (0; +; [2]; {(2,4)}) } Genus 126 Maximum order 1120 occurring for type(s) { (2,4,35)* } Genus 127 Maximum order 1500 occurring for type(s) { (2,2,2,3)* } Genus 128 Maximum order 1296 occurring for type(s) { (2,4,18)* } Genus 129 Maximum order 780 occurring for type(s) { (2,6,130)* } Genus 130 Maximum order 1920 occurring for type(s) { (2,5,6)* } Genus 131 Maximum order 1032 occurring for type(s) { (0; +; [2]; {(2,4)}) } Genus 132 Maximum order 1200 occurring for type(s) { (2,4,30)* } Genus 133 Maximum order 1080 occurring for type(s) { (2,4,135)* } Genus 134 Maximum order 3960 occurring for type(s) { (2,3,10)* } Genus 135 Maximum order 798 occurring for type(s) { (0; +; [2,3]; {(1)}) } Genus 136 Maximum order 1104 occurring for type(s) { (2,4,138)* } Genus 137 Maximum order 2160 occurring for type(s) { (2,4,8)* } Genus 138 Maximum order 1088 occurring for type(s) { (2,2,2,4)* } Genus 139 Maximum order 1128 occurring for type(s) { (2,4,141)* } Genus 140 Maximum order 1104 occurring for type(s) { (0; +; [2]; {(2,4)}), (2,2,2,4)* } Genus 141 Maximum order 852 occurring for type(s) { (2,6,142)* } Genus 142 Maximum order 2184 occurring for type(s) { (2,3,26)* } Genus 143 Maximum order 1128 occurring for type(s) { (0; +; [2]; {(2,4)}) } Genus 144 Maximum order 1136 occurring for type(s) { (2,2,2,4)* } Genus 145 Maximum order 1352 occurring for type(s) { (2,4,26)* } Genus 146 Maximum order 3456 occurring for type(s) { (2,4,6)* } Genus 147 Maximum order 12180 occurring for type(s) { (2,3,7)* } Genus 148 Maximum order 1200 occurring for type(s) { (2,4,150)* } Genus 149 Maximum order 1764 occurring for type(s) { (2,2,2,3)* } Genus 150 Maximum order 1184 occurring for type(s) { (2,2,2,4)* } Genus 151 Maximum order 1224 occurring for type(s) { (2,4,153)* } Genus 152 Maximum order 1440 occurring for type(s) { (2,6,8)* } Genus 153 Maximum order 924 occurring for type(s) { (2,6,154)* } Genus 154 Maximum order 1344 occurring for type(s) { (2,4,42)* } Genus 155 Maximum order 1224 occurring for type(s) { (0; +; [2]; {(2,4)}) } Genus 156 Maximum order 1320 occurring for type(s) { (2,6,10)* } Genus 157 Maximum order 1272 occurring for type(s) { (2,4,159)* } Genus 158 Maximum order 1248 occurring for type(s) { (0; +; [2]; {(2,4)}), (2,2,2,4)* } Genus 159 Maximum order 942 occurring for type(s) { (0; +; [2,3]; {(1)}) } Genus 160 Maximum order 1296 occurring for type(s) { (2,4,162)* } Genus 161 Maximum order 1272 occurring for type(s) { (0; +; [2]; {(2,4)}) } Genus 162 Maximum order 3840 occurring for type(s) { (2,4,6)* } Genus 163 Maximum order 1320 occurring for type(s) { (2,4,165)* } Genus 164 Maximum order 2160 occurring for type(s) { (2,4,10)* } Genus 165 Maximum order 996 occurring for type(s) { (2,6,166)* } Genus 166 Maximum order 1440 occurring for type(s) { (2,4,45)* } Genus 167 Maximum order 6600 occurring for type(s) { (2,4,5)* } Genus 168 Maximum order 1328 occurring for type(s) { (2,2,2,4)* } Genus 169 Maximum order 1368 occurring for type(s) { (2,4,171)* } Genus 170 Maximum order 5040 occurring for type(s) { (2,3,10)* } Genus 171 Maximum order 2028 occurring for type(s) { (2,2,2,3)* } Genus 172 Maximum order 2448 occurring for type(s) { (2,4,9)* } Genus 173 Maximum order 6840 occurring for type(s) { (2,4,5)* } Genus 174 Maximum order 1376 occurring for type(s) { (2,2,2,4)* } Genus 175 Maximum order 1416 occurring for type(s) { (2,4,177)* } Genus 176 Maximum order 1392 occurring for type(s) { (0; +; [2]; {(2,4)}), (2,2,2,4)* } Genus 177 Maximum order 3000 occurring for type(s) { (2,3,20)* } Genus 178 Maximum order 1920 occurring for type(s) { (2,4,15)* } Genus 179 Maximum order 1416 occurring for type(s) { (0; +; [2]; {(2,4)}) } Genus 180 Maximum order 1424 occurring for type(s) { (2,2,2,4)* } Genus 181 Maximum order 1464 occurring for type(s) { (2,4,183)* } Genus 182 Maximum order 4320 occurring for type(s) { (2,4,6)* } Genus 183 Maximum order 1086 occurring for type(s) { (0; +; [2,3]; {(1)}) } Genus 184 Maximum order 4368 occurring for type(s) { (2,4,6)* } Genus 185 Maximum order 1464 occurring for type(s) { (0; +; [2]; {(2,4)}) } Genus 186 Maximum order 1600 occurring for type(s) { (2,4,50)* } Genus 187 Maximum order 1512 occurring for type(s) { (2,4,189)* } Genus 188 Maximum order 1488 occurring for type(s) { (0; +; [2]; {(2,4)}), (2,2,2,4)* } Genus 189 Maximum order 1140 occurring for type(s) { (2,6,190)* } Genus 190 Maximum order 1536 occurring for type(s) { (2,4,192)* } Genus 191 Maximum order 2184 occurring for type(s) { (2,4,13)* } Genus 192 Maximum order 1680 occurring for type(s) { (2,4,42)* } Genus 193 Maximum order 1560 occurring for type(s) { (2,4,195)* } Genus 194 Maximum order 2304 occurring for type(s) { (2,6,6)*, (2,2,2,3)* } Genus 195 Maximum order 1158 occurring for type(s) { (0; +; [2,3]; {(1)}) } Genus 196 Maximum order 1584 occurring for type(s) { (2,4,198)* } Genus 197 Maximum order 2184 occurring for type(s) { (2,4,14)* } Genus 198 Maximum order 2352 occurring for type(s) { (2,2,2,3)* } Genus 199 Maximum order 1608 occurring for type(s) { (2,4,201)* } Genus 200 Maximum order 2640 occurring for type(s) { (2,4,10)* } Genus 201 Maximum order 1212 occurring for type(s) { (2,6,202)* } Genus 202 Maximum order 2400 occurring for type(s) { (2,2,2,3)* } Genus 203 Maximum order 1608 occurring for type(s) { (0; +; [2]; {(2,4)}) } Genus 204 Maximum order 1616 occurring for type(s) { (2,2,2,4)* } Genus 205 Maximum order 1656 occurring for type(s) { (2,4,207)* } Genus 206 Maximum order 4896 occurring for type(s) { (2,4,6)* } Genus 207 Maximum order 828 occurring for type(s) { (2,2,2,207)* } Genus 208 Maximum order 1680 occurring for type(s) { (2,4,210)* } Genus 209 Maximum order 1656 occurring for type(s) { (0; +; [2]; {(2,4)}) } Genus 210 Maximum order 2184 occurring for type(s) { (2,6,7)* } Genus 211 Maximum order 1704 occurring for type(s) { (2,4,213)* } Genus 212 Maximum order 5040 occurring for type(s) { (2,3,12)* } Genus 213 Maximum order 1284 occurring for type(s) { (2,6,214)* } Genus 214 Maximum order 1728 occurring for type(s) { (2,4,216)* } Genus 215 Maximum order 1704 occurring for type(s) { (0; +; [2]; {(2,4)}) } Genus 216 Maximum order 1712 occurring for type(s) { (2,2,2,4)* } Genus 217 Maximum order 1752 occurring for type(s) { (2,4,219)* } Genus 218 Maximum order 5184 occurring for type(s) { (2,4,6)* } Genus 219 Maximum order 1302 occurring for type(s) { (0; +; [2,3]; {(1)}) } Genus 220 Maximum order 1776 occurring for type(s) { (2,4,222)* } Genus 221 Maximum order 1752 occurring for type(s) { (0; +; [2]; {(2,4)}) } Genus 222 Maximum order 5280 occurring for type(s) { (2,4,6)* } Genus 223 Maximum order 1800 occurring for type(s) { (2,4,225)* } Genus 224 Maximum order 1776 occurring for type(s) { (0; +; [2]; {(2,4)}), (2,2,2,4)* } Genus 225 Maximum order 1356 occurring for type(s) { (2,6,226)* } Genus 226 Maximum order 2688 occurring for type(s) { (3,4,4)* } Genus 227 Maximum order 2700 occurring for type(s) { (2,2,2,3)* } Genus 228 Maximum order 1808 occurring for type(s) { (2,2,2,4)* } Genus 229 Maximum order 1848 occurring for type(s) { (2,4,231)* } Genus 230 Maximum order 6840 occurring for type(s) { (2,3,10)* } Genus 231 Maximum order 1374 occurring for type(s) { (0; +; [2,3]; {(1)}) } Genus 232 Maximum order 6072 occurring for type(s) { (2,3,11)* } Genus 233 Maximum order 1848 occurring for type(s) { (0; +; [2]; {(2,4)}) } Genus 234 Maximum order 1856 occurring for type(s) { (2,2,2,4)* } Genus 235 Maximum order 1896 occurring for type(s) { (2,4,237)* } Genus 236 Maximum order 11232 occurring for type(s) { (2,3,8)* } Genus 237 Maximum order 1428 occurring for type(s) { (2,6,238)* } Genus 238 Maximum order 1920 occurring for type(s) { (2,4,240)* } Genus 239 Maximum order 1896 occurring for type(s) { (0; +; [2]; {(2,4)}) } Genus 240 Maximum order 1904 occurring for type(s) { (2,2,2,4)* } Genus 241 Maximum order 1944 occurring for type(s) { (2,4,243)* } Genus 242 Maximum order 2880 occurring for type(s) { (0; +; [2]; {(2,3)})*, (2,2,2,3)* } Genus 243 Maximum order 1446 occurring for type(s) { (0; +; [2,3]; {(1)}) } Genus 244 Maximum order 1968 occurring for type(s) { (2,4,246)* } Genus 245 Maximum order 9720 occurring for type(s) { (2,4,5)* } Genus 246 Maximum order 2080 occurring for type(s) { (2,4,65)* } Genus 247 Maximum order 2744 occurring for type(s) { (2,4,14)* } Genus 248 Maximum order 1968 occurring for type(s) { (0; +; [2]; {(2,4)}), (2,2,2,4)* } Genus 249 Maximum order 1500 occurring for type(s) { (2,6,250)* } Genus 250 Maximum order 2112 occurring for type(s) { (2,4,66)* } Genus 251 Maximum order 1992 occurring for type(s) { (0; +; [2]; {(2,4)}) } Genus 252 Maximum order 6000 occurring for type(s) { (2,4,6)* } Genus 253 Maximum order 2040 occurring for type(s) { (2,4,255)* } Genus 254 Maximum order 3024 occurring for type(s) { (0; +; [2]; {(2,3)})*, (2,2,2,3)* } Genus 255 Maximum order 12144 occurring for type(s) { (2,3,8)* } Genus 256 Maximum order 2064 occurring for type(s) { (2,4,258)* } Genus 257 Maximum order 4896 occurring for type(s) { (2,3,16)* } Genus 258 Maximum order 3072 occurring for type(s) { (2,2,2,3)*, (2,4,12)* } Genus 259 Maximum order 2088 occurring for type(s) { (2,4,261)* } Genus 260 Maximum order 2064 occurring for type(s) { (0; +; [2]; {(2,4)}), (2,2,2,4)* } Genus 261 Maximum order 1680 occurring for type(s) { (2,8,15)* } Genus 262 Maximum order 2112 occurring for type(s) { (2,4,264)* } Genus 263 Maximum order 2088 occurring for type(s) { (0; +; [2]; {(2,4)}) } Genus 264 Maximum order 2096 occurring for type(s) { (2,2,2,4)* } Genus 265 Maximum order 2136 occurring for type(s) { (2,4,267)* } Genus 266 Maximum order 2240 occurring for type(s) { (2,4,70)* } Genus 267 Maximum order 1100 occurring for type(s) { (2,2,2,55)* } Genus 268 Maximum order 2160 occurring for type(s) { (2,4,270)* } Genus 269 Maximum order 2136 occurring for type(s) { (0; +; [2]; {(2,4)}) } Genus 270 Maximum order 2144 occurring for type(s) { (2,2,2,4)* } Genus 271 Maximum order 2184 occurring for type(s) { (2,4,273)* } Genus 272 Maximum order 5040 occurring for type(s) { (2,4,7)* } Genus 273 Maximum order 1644 occurring for type(s) { (2,6,274)* } Genus 274 Maximum order 4896 occurring for type(s) { (2,3,18)* } Genus 275 Maximum order 6552 occurring for type(s) { (2,3,12)*, (2,4,6)* } Genus 276 Maximum order 2192 occurring for type(s) { (2,2,2,4)* } Genus 277 Maximum order 3000 occurring for type(s) { (2,4,15)* } Genus 278 Maximum order 2208 occurring for type(s) { (0; +; [2]; {(2,4)}), (2,2,2,4)* } Genus 279 Maximum order 1662 occurring for type(s) { (0; +; [2,3]; {(1)}) } Genus 280 Maximum order 2256 occurring for type(s) { (2,4,282)* } Genus 281 Maximum order 2232 occurring for type(s) { (0; +; [2]; {(2,4)}) } Genus 282 Maximum order 2688 occurring for type(s) { (2,4,24)*, (2,6,8)* } Genus 283 Maximum order 2280 occurring for type(s) { (2,4,285)* } Genus 284 Maximum order 2256 occurring for type(s) { (0; +; [2]; {(2,4)}), (2,2,2,4)* } Genus 285 Maximum order 1716 occurring for type(s) { (2,6,286)* } Genus 286 Maximum order 2400 occurring for type(s) { (2,4,75)* } Genus 287 Maximum order 6840 occurring for type(s) { (2,4,6)* } Genus 288 Maximum order 2288 occurring for type(s) { (2,2,2,4)* } Genus 289 Maximum order 2328 occurring for type(s) { (2,4,291)* } Genus 290 Maximum order 3840 occurring for type(s) { (2,4,10)* } Genus 291 Maximum order 3468 occurring for type(s) { (2,2,2,3)* } Genus 292 Maximum order 2352 occurring for type(s) { (2,4,294)* } Genus 293 Maximum order 2328 occurring for type(s) { (0; +; [2]; {(2,4)}) } Genus 294 Maximum order 2336 occurring for type(s) { (2,2,2,4)* } Genus 295 Maximum order 2376 occurring for type(s) { (2,4,297)* } Genus 296 Maximum order 2352 occurring for type(s) { (0; +; [2]; {(2,4)}), (2,2,2,4)* } Genus 297 Maximum order 1788 occurring for type(s) { (2,6,298)* } Genus 298 Maximum order 2496 occurring for type(s) { (2,4,78)* } Genus 299 Maximum order 2376 occurring for type(s) { (0; +; [2]; {(2,4)}) } Genus 300 Maximum order 2384 occurring for type(s) { (2,2,2,4)* } Genus 301 Maximum order 2424 occurring for type(s) { (2,4,303)* } Genus 302 Maximum order 7200 occurring for type(s) { (2,4,6)* } ...........................................................................