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Aliases
Splittings
Subgroups
4 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 3821 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)(32,62,117,212,366)(37,69,41,76,68)(39,73,133,106,190)(43,80,144,148,164)(45,84,151,174,122)(47,88,159,275,351)(51,95,170,92,165)(53,99,177,137,123)(55,103,185,317,325)(57,107,192,67,124)(59,111,200,343,283)(61,115,208,358,220)(63,119,216,374,616)(70,128,83,149,167)(72,131,98,175,126)(74,135,238,205,352)(77,139,130,94,168)(79,142,141,138,127)(81,146,253,268,326)(85,153,264,310,284)(87,157,271,336,221)(89,161,279,463,601)(96,172,295,191,327)(100,179,306,257,285)(102,183,313,299,222)(104,187,321,525,575)(108,194,332,166,286)(110,198,339,242,223)(112,202,347,567,533)(114,206,354,125,224)(116,210,362,593,471)(118,214,370,608,382)(120,218,378,624,978)(129,229,156,269,329)(132,233,182,311,288)(134,236,197,337,226)(136,240,407,367,602)(140,245,235,193,330)(143,248,250,258,289)(145,251,261,300,227)(147,255,426,456,576)(150,259,292,169,290)(152,262,303,243,228)(154,266,441,519,534)(158,273,452,560,472)(160,277,459,586,383)(162,281,467,743,963)(171,293,176,301,231)(173,297,489,353,577)(178,304,247,244,232)(180,308,504,445,535)(184,315,515,508,473)(186,319,379,549,384)(188,323,529,829,938)(195,334,545,328,536)(199,341,556,430,474)(201,345,563,493,385)(203,349,571,891,898)(207,356,582,287,475)(209,360,589,411,386)(211,364,597,930,837)(213,368,604,225,387)(215,372,612,955,751)(217,376,620,970,631)(219,380,627,983,1461)(230,393,276,457,579)(234,398,318,520,538)(237,402,344,561,477)(239,405,359,587,389)(241,409,664,617,964)(246,415,404,355,580)(249,418,423,446,539)(252,421,438,509,478)(254,424,449,550,390)(256,428,687,736,939)(260,433,486,331,540)(263,436,501,431,479)(265,439,512,494,391)(267,443,706,822,899)(270,447,542,291,480)(272,450,553,412,392)(274,454,721,884,838)(278,461,732,923,752)(280,465,739,948,632)(282,469,747,1134,1453)(294,484,312,510,482)(296,487,338,551,395)(298,491,776,603,940)(302,496,400,333,543)(305,499,420,432,483)(307,502,435,495,396)(309,506,795,725,900)(314,513,498,413,397)(316,517,810,814,839)(320,523,748,873,753)(322,527,825,912,633)(324,531,833,1249,1428)(335,547,656,578,892)(340,554,417,414,401)(342,558,869,710,840)(346,565,880,799,754)(348,569,887,858,634)(350,573,894,1330,1390)(357,584,909,537,841)(361,591,919,691,755)(363,595,926,780,635)(365,599,934,1384,1337)(369,606,945,476,756)(371,610,951,668,636)(373,614,959,1420,1256)(375,618,966,388,637)(377,622,974,1445,1141)(381,629,985,1465,2051)(394,644,464,737,942)(399,650,526,823,902)(403,655,568,885,843)(406,659,594,924,758)(408,662,609,949,639)(410,666,1029,979,1454)(416,673,661,605,943)(419,676,684,726,903)(422,679,703,815,844)(425,682,718,874,759)(427,685,729,913,640)(429,689,1055,1127,1429)(434,695,773,581,904)(437,698,792,711,845)(440,701,807,800,760)(442,704,626,859,641)(444,708,1078,1242,1391)(448,713,852,541,846)(451,716,866,692,761)(453,719,877,781,642)(455,723,1097,1326,1338)(458,727,906,481,762)(460,730,916,669,643)(462,734,1112,1377,1257)(466,741,1123,1413,1142)(468,745,1130,1438,989)(470,749,1137,1638,2045)(485,767,521,816,848)(488,771,562,875,764)(490,774,588,914,646)(492,778,1174,965,1430)(497,784,657,583,907)(500,787,681,712,849)(503,790,700,801,765)(505,793,715,860,647)(507,797,1197,1116,1392)(511,802,769,544,850)(514,805,789,693,766)(516,808,804,782,648)(518,812,1216,1231,1339)(522,628,863,670,649)(524,820,1227,1315,1258)(528,827,1238,1366,1143)(530,831,1245,1403,990)(532,835,1253,1784,2034)(546,853,552,861,652)(548,856,1048,941,1393)(555,864,678,694,770)(557,867,697,783,653)(559,871,1166,1101,1327)(564,878,786,671,654)(566,882,1311,1220,1259)(570,889,1322,1300,1144)(572,893,1328,1352,991)(574,896,1333,1881,1996)(585,911,1350,901,1329)(590,917,675,672,658)(592,921,1363,1082,1260)(596,928,1373,1201,1145)(598,932,1380,1282,992)(600,936,1386,1941,1947)(607,947,1401,842,1261)(611,953,1410,1059,1146)(613,957,1416,1178,993)(615,961,1424,1990,1886)(619,968,1435,757,1147)(621,972,1441,1032,994)(623,976,1449,2026,1789)(625,980,1456,638,995)(630,987,1467,2055,2682)(645,1003,744,1128,1432)(651,1010,830,1243,1394)(660,1020,931,1378,1263)(663,1024,956,1414,1149)(665,1027,971,1439,997)(667,1030,1514,1462,2046)(674,1038,1026,967,1433)(677,1041,1052,1117,1395)(680,1044,1075,1232,1340)(683,1047,1094,1316,1264)(686,1050,1109,1367,1150)(688,1053,1120,1404,998)(690,1057,1540,1634,2035)(696,1064,1171,944,1396)(699,1067,1194,1102,1341)(702,1070,1213,1221,1265)(705,1073,1136,1301,1151)(707,1076,1235,1353,999)(709,1080,1566,1777,1997)(714,1086,1016,905,1331)(717,1089,1294,1083,1266)(720,1092,1308,1202,1152)(722,1095,1319,1283,1000)(724,1099,1587,1877,1948)(728,1104,1347,847,1267)(731,1107,1360,1060,1153)(733,1110,1370,1179,1001)(735,1114,1605,1939,1887)(738,1118,1398,763,1154)(740,1121,1407,1033,1002)(742,1125,1619,1983,1790)(746,1132,1630,2019,1644)(750,1139,1640,2225,2676)(768,1160,824,1233,1343)(772,1165,886,1317,1269)(77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0,3788,2184,2573,577,900,1339,1888,2500,3074,3501,3033,790,69,127,227,390,640,998,1478,827,1239,1761,2353,2933,1768,2363,2943,3400,1664,2248,2837,3327,2024,2642,3193,3573,1607,2185,2014,366,601,938,1390,1947,2556,3118,2531,556,866,1291,1830,2433,3009,2555,2920,706,1075,1560,2137,2743,1330,1877,2487,3063,1272,1807,2409,2989,1630,2210,2802,3300,1532,111,201,346,566,883,1314,1857,2463,2823,3319,3640,3650,2788,591,920,1362,1909,2515,2662,3213,3589,3479,3717,3802,3818,3639,3134,907,1344,1890,1298,1837,2440,3015,3455,1195,133,235,400,652,1012,1494,2080,1251,1781,2380,2960,2297,2369,459,729,1106,1596,2175,2048,2673,2651,3100,3513,3731,2215,2809,2632,3182,3263,3391,1089,95,171,294,485,768,1161,1665,2250,2840,3330,3207,3385,3561,3749,3643,3781,2130,240,408,663,1025,1508,2092,2714,3254,3612,2593,3146,3539,2117,214,371,611,954,380,628,82,148,257,430,691,1059,1543,932,1381,1934,2541,3102,3220,3595,3767,3722,1721,245,414,671,1035,1350,1897,2504,1871,2480,2026,2644,3196,1709,2293,2874,3347,2864,637,994,1475,1786,2388,2971,3425,2923,2953,3187,3570,3754,2855,3340,3648,3782,3205,3515,1306,175,300,494,781,1179,1687,2273,1584,183,314,514,806,1209,1722,2309,2889,2431,475,755,1145,1646,618,967,1434,2003,443,707,1077,1562,2139,2744,3267,3617,3432,3152,926,1370,1919,378,625,981,1459,835,1227,1744,2335,2917,3382,3665,3785,3626,1386,1905,327,535,839,1258,1791,2392,2974,2314,421,11,22,43,81,147,256,429,690,1058,1542,2122,2733,1118,1611,2189,2785,1010,1491,2076,2701,3246,3609,3773,3410,3678,3572,1408,204,351,575,898,1337,1886,2498,1853,306,501,789,1188,1697,2282,2865,2166,321,526,824,1234,1755,829,1242,1766,2361,767,1159,1662,2246,974,1446,2021,2637,734,1113,1604,2182,2779,1754,2346,2927,3388,2055,2683,3233,3262,1982,2590,3144,3538,1388,1944,2002,2614,3168,2913,3378,3663,3777,3231,2517,543,849,1270,1805,2407,2987,3434,2899,685,29,57,108,195,335,548,857,1281,1819,2422,3001,3447,1617,208,359,588,915,1356,1456,2038,2660,2468,3043,3477,3715,2821,1971,2577,3133,2776,558,870,1296,1835,2438,3013,3454,3701,3462,3159,3550,3744,2770,3127,3529,3736,3622,1199,1710,2295,2876,3349,1169,1673,2258,2847,3334,1930,2536,3098,1132,1631,2212,2804,2121,2352,450,25,49,92,166,287,476,757,1148,1650,2235,2032,2653,2620,3172,2826,3322,1067,73,134,237,403,656,1016,1498,2084,2708,1420,1983,2591,1055,1537,2116,2727,2105,119,217,377,623,977,1452,2033,2655,2199,2582,3137,3534,2096,2717,3256,3613,3242,3050,805,76,138,243,412,669,1033,1517,889,1323,1868,2475,3051,3486,3723,3805,3707,1695,224,386,635,992,1473,2061,2689,1749,2340,2020,2635,3185,1681,2266,2853,3338,2832,2543,563,877,1305,1846,2451,3026,2771,2937,721,1094,1583,2163,2767,3282,3623,3161,3507,1289,165,285,473,753,1143,1645,2231,1558,153,265,440,702,1071,1556,2134,2740,2404,2983,3431,3659,2801,606,946,1400,1957,323,530,832,1248,1776,2374,2956,3411,3680,3140,917,105,189,325,533,837,1256,1789,1214,144,250,420,678,1043,1526,2106,1332,1880,2490,3065,2421,2379,463,736,1116,1609,398,649,1008,1489,2074,2699,3244,2373,2954,2641,3191,3343,2270,1104,1594,2173,2773,3109,3224,3598,2227,2824,3321,3641,3296,3396,3566,1396,1952,2560,2155,2759,3277,3553,3730,1834,293,483,765,1157,1660,2244,2834,2141,277,460,731,1108,1598,823,1232,1752,2344,2925,2677,3227,3303,957,1417,1979,2585,599,935,966,1432,2000,1740,2330,2911,3376,2053,1363,1910,2516,1927,2534,3097,3511,3725,1732,2319,2898,3364,2886,2551,3113,3521,1884,2496,3071,3499,3038,2964,3416,3682,3791,2872,659,1019,1501,2086,2709,1317,1860,2466,3041,3475,3714,3660,3675,1600,198,340,555,865,1290,1829,2432,3008,2449,3023,3460,3704,2818,1959,2566,3125,2765,506,796,1196,1705,2289,489,773,1167,1671,2256,930,1377,1928,467,744,1129,1626,1057,1238,1759,2351,2931,3390,3230,3601,3632,1424,1917,2523,3087,976,1450,2029,2649,1642,2228,436,19,37,70,129,230,394,645,1004,1485,2071,2697,3243,3607,3772,3816,3359,1041,31,61,116,211,365,600,937,1389,1946,1414,1974,2580,1027,1510,2094,2715,2070,1867,313,512,804,1207,1720,2307,2887,2183,347,568,886,1318,1862,2469,3045,3480,3030,787,66,123,222,384,633,990,1471,820,1228,1746,2337,2919,3383,3666,3786,3700,1657,2240,2831,3273,2018,2633,3184,3568,1589,2168,2011,2624,3177,3564,3751,3809,3779,3807,2528,554,48,90,163,283,471,751,1141,704,44,83,150,260,434,696,1065,1550,1267,1801,2402,2981,1628,212,367,603,941,103,186,320,524,821,1230,1750,2342,2924,1980,2586,3139,1514,584,910,1349,1896,2479,2659,3211,3588,3763,3160,3551,3745,2781,3132,904,1341,1889,1280,1817,2420,3000,3446,1192,131,232,396,647,1006,1487,2072,1247,1774,2370,2949,2271,2366,457,726,1102,1592,2171,2046,2670,2648,3201,3581,3760,2201,2794,2630,604,942,1394,1086,1574,2153,2757,3096,869,1294,1833,2436,3012,3453,3163,3384,1078,1563,2140,2745,2128,1879,2489,3064,3494,1813,2416,2997,3444,2213,2805,3302,3630,2114,210,363,596,929,1376,816,1222,1738,2328,2909,3375,3661,3292,928,1374,1924,2529,3091,3217,3592,3765,3719,1718,2304,2884,3355,2049,1348,1894,2502,1856,2461,3036,3471,3711,1707,238,404,657,1017,1499,567,884,1315,1858,2464,3039,2905,2951,732,1109,1599,2177,2775,2674,3225,3204,3514,1303,1843,2447,30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Polycyclic presentation:
5,3821|b^a=b^1753
Conjugacy classes & character table
769 conjugacy classes — view the full character table.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19105, 1);
Finite Group Databasebeta