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Aliases
Splittings
Subgroups
4 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 3851 points:
(2,3,5,9,17)(4,7,13,25,48)(6,11,21,40,33)(8,15,29,56,105)(10,19,36,18,34)(12,23,44,82,90)(14,27,52,97,64)(16,31,60,113,204)(20,38,71,49,91)(22,42,78,75,65)(24,46,86,155,189)(26,50,93,35,66)(28,54,101,181,163)(30,58,109,196,121)(32,62,117,212,365)(37,69,41,76,68)(39,73,133,106,190)(43,80,144,148,164)(45,84,151,174,122)(47,88,159,274,350)(51,95,170,92,165)(53,99,177,137,123)(55,103,185,316,324)(57,107,192,67,124)(59,111,200,342,282)(61,115,208,357,220)(63,119,216,373,608)(70,128,83,149,167)(72,131,98,175,126)(74,135,238,205,351)(77,139,130,94,168)(79,142,141,138,127)(81,146,252,267,325)(85,153,263,309,283)(87,157,270,335,221)(89,161,278,456,593)(96,172,294,191,326)(100,179,305,256,284)(102,183,312,298,222)(104,187,320,517,567)(108,194,331,166,285)(110,198,338,241,223)(112,202,346,559,525)(114,206,353,125,224)(116,210,361,585,463)(118,214,369,600,380)(120,218,376,612,938)(129,229,156,268,328)(132,233,182,310,287)(134,236,197,336,226)(136,240,403,366,594)(140,244,235,193,329)(143,247,249,257,288)(145,250,260,299,227)(147,254,420,449,568)(150,258,291,169,289)(152,261,302,242,228)(154,265,434,510,526)(158,272,445,552,464)(160,276,452,578,381)(162,280,459,714,933)(171,292,176,300,231)(173,296,481,352,569)(178,303,246,243,232)(180,307,495,438,527)(184,314,506,499,465)(186,318,513,541,382)(188,322,521,797,908)(195,333,537,327,528)(199,340,548,423,466)(201,344,555,484,383)(203,348,563,858,866)(207,355,574,286,467)(209,359,581,405,384)(211,363,589,900,804)(213,367,596,225,385)(215,371,604,925,721)(217,374,609,934,619)(219,378,615,942,1356)(230,390,275,450,571)(234,394,317,511,530)(237,398,343,553,469)(239,401,358,579,386)(245,409,400,354,572)(248,412,417,439,531)(251,415,431,500,470)(253,418,442,542,387)(255,422,664,710,909)(259,426,478,330,532)(262,429,492,424,471)(264,432,503,485,388)(266,436,681,790,867)(269,440,534,290,472)(271,443,545,406,389)(273,447,695,851,805)(277,454,706,893,722)(279,457,711,918,620)(281,461,717,1053,1351)(293,476,311,501,474)(295,479,337,543,391)(297,483,744,595,910)(301,487,396,332,535)(304,490,414,425,475)(306,493,428,486,392)(308,497,761,699,868)(313,504,489,407,393)(315,508,775,779,806)(319,515,786,840,723)(321,519,793,882,621)(323,523,800,1155,1345)(334,539,822,570,869)(339,546,411,408,397)(341,550,836,684,807)(345,557,847,764,724)(347,561,854,825,622)(349,565,862,1238,1307)(356,576,878,529,808)(360,583,889,666,725)(362,587,896,746,623)(364,591,904,1299,1245)(368,598,914,468,726)(370,602,921,647,624)(372,606,929,1337,1162)(375,610,935,1347,1060)(377,613,939,1352,949)(379,617,945,1360,1838)(395,634,518,791,871)(399,638,560,852,810)(402,642,586,894,727)(404,645,601,919,625)(410,652,644,597,912)(413,654,661,700,872)(416,656,678,780,811)(419,659,692,841,728)(421,662,703,883,626)(427,670,741,573,873)(430,673,758,685,812)(433,676,772,765,729)(435,679,783,826,627)(437,683,1010,1151,1308)(441,687,819,533,813)(444,690,833,667,730)(446,693,844,747,628)(448,697,1027,1231,1246)(451,701,875,473,731)(453,704,886,648,629)(455,708,1041,1292,1163)(458,712,1047,1330,1061)(460,715,1050,1346,950)(462,719,1056,1470,1833)(477,735,512,781,815)(480,739,554,842,732)(482,742,580,884,630)(488,750,640,575,876)(491,753,658,686,816)(494,756,675,766,733)(496,759,689,827,631)(498,763,1105,1045,1309)(502,767,737,536,817)(505,770,755,668,734)(507,773,769,748,632)(509,777,1122,1140,1247)(514,784,830,649,633)(516,788,1136,1220,1164)(520,795,1147,1281,1062)(522,798,1152,1320,951)(524,802,1158,1580,1827)(538,820,544,828,635)(540,824,1185,911,1310)(547,831,655,669,738)(549,834,672,749,636)(551,838,1202,1030,1248)(556,845,752,650,637)(558,849,1216,1125,1165)(562,856,1227,1205,1063)(564,860,1234,1266,952)(566,864,1241,1681,1821)(577,880,1263,870,1249)(582,887,653,651,641)(584,891,1277,1012,1166)(588,898,1288,1107,1064)(590,902,1295,1187,953)(592,906,1303,1763,1770)(599,916,1316,809,1167)(603,923,1326,993,1065)(605,927,1333,1088,954)(607,931,1341,932,1343)(611,936,1348,948,1365)(614,940,1353,1829,1476)(616,943,1357,1834,1367)(618,947,1363,1044,1457)(639,968,859,1232,1251)(643,972,901,1293,1168)(646,976,926,1331,1066)(657,984,1007,1141,1252)(660,986,1024,1221,1169)(663,989,1038,1282,1067)(665,991,1046,1321,955)(671,998,1085,913,1312)(674,1000,1102,1031,1253)(677,1002,1119,1126,1170)(680,1005,1133,1206,1068)(682,1008,1144,1267,956)(688,1016,1182,874,1254)(691,1019,1199,1013,1171)(694,1022,1213,1108,1069)(696,1025,1224,1188,957)(698,1029,1438,1677,1771)(702,1033,1260,814,1172)(705,1036,1274,994,1070)(707,1039,1285,1089,958)(709,1043,1455,1756,1688)(713,1048,1461,1808,1587)(716,1051,1464,1823,1477)(718,1054,1467,1828,1368)(720,1058,1473,1938,2336)(736,1075,792,1142,1256)(740,1079,853,1222,1173)(743,1083,895,1283,1071)(745,1086,920,1322,959)(751,1093,974,915,1314)(754,1095,988,1032,1257)(757,1097,1004,1127,1174)(760,1100,1021,1207,1072)(762,1103,1035,1268,960)(768,1111,1081,877,1258)(771,1114,1099,1014,1175)(774,1117,1116,1109,1073)(776,1120,1130,1189,961)(778,1124,1537,1572,1772)(782,1128,1178,818,1176)(785,1131,1196,995,1074)(787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2275,2736,3134,3439,3239,3437,2256,2721,3122,3430,3638,3760,3086,1214,177,302,489,752,1094,1509,797,1151,1572,2034,2496,2920,2997,3328,3568,3718,3802,3716,2459,659,27,53,100,180,308,498,359,582,888,1273,1720,1241,1333,483,745,1087,1504,1970,1462,1774,2260,2725,3126,2810,3175,3473,3667,3778,3830,3762,3773,2671,834,93,167,287,469,727,1066,517,790,1140,1557,2016,2478,2572,2980,3316,3560,3714,3558,1978,398,637,966,1382,1859,2355,1450,198,339,547,832,1195,800,921,240,404,646,977,1394,931,1342,1817,2312,2779,3176,2709,3109,3419,3630,3755,3586,3651,2197,535,816,1174,1598,2061,2522,1671,316,510,779,1125,1539,1997,2099,2555,2968,3308,3556,3306,1499,1964,2438,2878,3249,3522,2914,1022,99,178,304,491,754,459,596,62,118,215,372,607,932,1344,1820,2316,2784,3182,2144,2602,3008,3337,3574,3285,3442,1705,2176,2634,3038,3361,3492,3103,1225,181,309,499,764,1107,1520,1619,2082,2543,2960,3304,2958,3303,3555,3713,3801,3841,3721,2471,676,42,79,143,248,413,216,367,597,913,1313,1777,1303,1337,1808,2299,2762,3156,2801,1570,2032,2494,2918,3273,2861,3129,1686,2158,2618,3024,3351,3584,2688,845,97,174,298,484,746,1088,1167,1591,2055,2518,2939,3197,3491,3680,3786,3835,3806,3563,1990,415,11,22,43,81,147,255,206,354,573,874,1255,862,925,1330,1798,2286,2747,2327,1043,1456,1921,2400,2849,2339,2773,3169,3466,3662,3774,3637,3659,2214,546,48,90,163,282,463,721,1060,1476,1943,2420,2865,2800,3196,3490,3679,3785,3726,3311,1513,233,393,632,961,1377,1855,1036,107,193,330,533,814,521,600,918,1320,1785,2271,1824,591,905,1302,1762,2247,2710,2235,2694,3090,3400,3615,3350,3450,1722,329,531,811,1169,1593,2056,1232,1667,2132,2587,2993,2584,2332,2799,3195,3489,3678,3580,2963,1079,1494,1959,2433,2874,3246,2487,690,50,94,169,290,473,278,365,593,908,1307,1770,1341,1815,2309,2775,3171,3469,2807,1664,2129,2583,2989,3322,2931,3137,1258,1700,2171,2629,3034,3191,2702,852,1221,1652,2114,2568,2111,1834,2331,2798,3194,3488,3344,2535,2953,3298,3551,3710,3799,3571,2006,429,19,37,70,129,230,117,213,368,599,917,1319,904,1300,1758,2240,2700,3098,2333,1138,1555,2013,2475,2903,2413,2728,1160,1584,2048,2510,2932,3283,2228,553,841,1206,1634,2095,1631,1356,1833,2330,2797,3193,3014,3343,3579,3725,3805,3842,3728,3319,1529,247,3,6,12,24,47,89,162,281,462,720,1059,563,859,1233,1669,2135,2591,1830,697,1028,1437,1902,2385,1836,2297,2760,3153,3453,3652,3426,3461,1736,336,542,826,1188,1615,1185,1611,2075,2536,2954,3299,2601,3006,3335,3572,3720,3803,3582,2971,1097,128,228,388,627,956,1373,701,1032,1442,1907,2388,1903,320,518,792,1143,1561,2021,1348,348,564,861,1237,1676,2145,1743,2220,2675,3072,3386,3020,3148,1272,190,325,526,805,1163,1587,1845,2344,2813,3209,3502,2128,2581,2987,3320,3562,3715,3346,2546,735,1074,1489,1954,2429,2871,2023,440,686,1014,1423,1890,1419,159,275,451,702,1034,1445,929,1338,1810,2302,2766,3161,2338,1218,1649,2110,2564,2974,2506,2739,873,1253,1695,2166,2625,2788,2239,2698,3095,3405,3618,3401,1648,2108,2562,2972,3310,3557,3016,2069,2530,2948,3294,3548,3708,3331,1546,258,425,668,995,1406,991,60,114,207,356,577,881,589,901,1294,1748,2226,2683,1835,777,1123,1536,1994,2460,1933,2263,719,1057,1472,1937,2414,2859,1747,2224,2680,3076,3389,3073,1202,1628,2089,2547,2962,3305,2607,3013,3342,3578,3724,3804,3585,2983,1114,139,243,407,649,978,645,975,1391,1868,2363,2827,1920,346,560,853,1223,1655,2118,1353,436,682,1009,1418,1887,1354,1796,2284,2744,3140,3443,3115,3162,1283,1732,2206,2661,3061,2658,822,1182,1607,2070,2531,2949,2142,2598,3003,3332,3570,3719,3349,2558,753,66,123,222,382,621,951,1369,1849,2349,2818,3214,1436,185,317,512,782,1129,1544,935,187,321,520,796,1150,1571,1279,1728,2201,2657,3058,2611,2753,884,1268,1714,2187,2646,2184,2643,3047,3369,3596,3688,3418,1662,2125,2578,2984,3318,3561,3019,2085,472,730,1069,1484,1950,2426,1560,2019,2481,2907,3265,2904,1008,86,156,269,441,688,1017,604,926,1332,1801,2290,2752,1839,838,1203,1630,2091,2549,2041,2277,569,868,1247,1689,2161,2315,2782,3179,3477,3670,3780,3089,1216,1645,2105,2559,2970,3309,2610,1601,2064,2525,2944,3291,3546,2999,1128,1542,2000,2464,2895,2461,662,29,57,108,195,334,540,361,586,895,1284,1734,2209,1357,497,762,1104,1517,1979,1465,1776,378,616,944,1359,1837,2335,2803,3199,3493,3682,3775,2674,836,1199,1625,2086,2545,2961,2148,2606,3012,3341,3577,3723,3352,2574,767,1110,1523,1983,2452,1980,401,641,970,1386,1863,2358,1453,200,343,554,843,1209,1638,939,254,421,663,990,1403,936,1318,1783,2268,2731,3130,2712,2765,3159,3457,3655,3588,3653,2200,537,819,1178,1602,2065,2526,1673,2139,2595,3000,3330,3569,3022,2101,487,749,1091,1506,1971,1503,1968,2442,2882,3252,3524,2917,1025,101,182,311,502,768,1112,609,88,160,277,455,709,1044,880,1264,1709,2182,2641,2149,2289,2750,3144,3446,3287,3444,1708,2180,2638,3042,3364,3498,3106,1227,1659,2122,2575,2982,3317,2613,1621,285,466,724,1063,1479,1946,2423,2868,3243,3519,3696,2474,679,44,83,150,259,427,671,369,601,920,1323,1789,2276,1360,539,823,1184,1610,2074,1575,1788,2274,2735,3133,2863,3131,1768,2255,2719,3119,3427,3635,2691,847,1213,1642,2102,2557,2969,2151,1172,1596,2059,2521,2941,3289,2590,2996,3327,3567,3717,3564,1993,418,13,26,51,96,173,297,208,358,580,885,1270,1717,942,296,482,743,1084,1500,1048,1310,1773,2259,2724,2341,2778,3174,3472,3666,3777,3640,3661,2217,548,833,1196,1622,2084,2544,1678,2147,2605,3011,3340,3576,3025,2117,2571,2979,3315,3559,3312,1516,236,397,636,965,1381,1858,1039,109,197,337,544,829,1192,612,135,239,402,643,973,606,930,1340,1814,2308,2774,2246,2708,3107,3416,3627,3353,3452,1725,331,534,815,1173,1597,2060,1234,1670,2136,2592,2998,3329,2616,1637,2098,2554,2967,3307,2964,1083,1498,1963,2437,2877,3248,2490,693,52,98,176,301,488,751,373,31,61,116,211,364,592,907,1306,1769,2257,2723,1675,2143,2600,3005,3334,2934,3139,1261,1704,2175,2633,3037,3198,2705,854,1224,1656,2119,2573,2981,2154,1191,1618,2081,2542,2959,2539,2957,3302,3554,3712,3800,3573,2009,432,21,41,77,140,245,410,212,366,595,911,1311,1775,1910,2391,2843,3227,3511,3225,1149,1569,2030,2491,2915,2416,2730,1243,1685,2156,2615,3021,3348,2231,555,844,1210,1639,2100,2556,1681,808,1166,1590,2054,2517,2938,3212,3505,3692,3795,3840,3321,1532,250,5,10,20,39,74,136,113,205,352,570,870,1250,1426,1893,2379,2835,3223,2833,708,1042,1454,1918,2397,1840,2307,2772,3167,3464,3660,3429,3463,1739,338,545,830,1193,1620,2083,1238,1677,2146,2604,3010,3339,3408,3621,3749,3815,3844,3813,2973,1100,131,232,392,631,960,1376,704,56,106,191,327,529,809,998,1409,1881,2371,2831,2369,363,590,903,1298,1755,2236,1754,2234,2692,3087,3397,3023,3150,1275,192,328,530,810,1168,1592,858,1231,1666,2131,2586,2992,3079,3392,3610,3742,3812,3740,2548,739,1078,1493,1958,2432,2873,2026,443,25,49,92,166,286,468,652,981,1397,1873,2367,1871,2366,2830,3222,3510,3694,3230,1229,1663,2127,2580,2986,2509,2741,876,1257,1699,2170,2628,2795,2242,559,851,1220,1651,2113,2567,2664,3064,3381,3603,3739,3601,2073,2534,2952,3297,3550,3709,3333,1549,261,9,18,35,67,125,225,385,624,954,1372,1852,2320,2787,3184,3481,3674,3515,2838,788,1137,1553,2010,2472,1936,2265,802,1159,1582,2045,2507,2929,1750,342,552,840,1205,1633,2094,2190,2649,3053,3374,3600,3372,3599,3738,3811,3843,3851,3818,2985,1117,142)
Polycyclic presentation:
5,3851|b^a=b^2809
Conjugacy classes & character table
775 conjugacy classes — view the full character table.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19255, 1);
Finite Group Databasebeta