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D14961 #44471663
Aliases
Splittings
Subgroups
8 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 4990 points:
(1,2,3)(4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,640,641,642,643,644,645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,660,661,662,663,664,665,666,667,668,669,670,671,672,673,674,675,676,677,678,679,680,681,682,683,684,685,686,687,688,689,690,691,692,693,694,695,696,697,698,699,700,701,702,703,704,705,706,707,708,709,710,711,712,713,714,715,716,717,718,719,720,721,722,723,724,725,726,727,728,729,730,731,732,733,734,735,736,737,738,739,740,741,742,743,744,745,746,747,748,749,750,751,752,753,754,755,756,757,758,759,760,761,762,763,764,765,766,767,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,784,785,786,787,788,789,790,791,792,793,794,795,796,797,798,799,800,801,802,803,804,805,806,807,808,809,810,811,812,813,814,815,816,817,818,819,820,821,822,823,824,825,826,827,828,829,830,831,832,833,834,835,836,837,838,839,840,841,842,843,844,845,846,847,848,849,850,851,852,853,854,855,856,857,858,859,860,861,862,863,864,865,866,867,868,869,870,871,872,873,874,875,876,877,878,879,880,881,882,883,884,885,886,887,888,889,890,891,892,893,894,895,896,897,898,899,900,901,902,903,904,905,906,907,908,909,910,911,912,913,914,915,916,917,918,919,920,921,922,923,924,925,926,927,928,929,930,931,932,933,934,935,936,937,938,939,940,941,942,943,944,945,946,947,948,949,950,951,952,953,954,955,956,957,958,959,960,961,962,963,964,965,966,967,968,969,970,971,972,973,974,975,976,977,978,979,980,981,982,983,984,985,986,987,988,989,990,991,992,993,994,995,996,997,998,999,1000,1001,1002,1003,1004,1005,1006,1007,1008,1009,1010,1011,1012,1013,1014,1015,1016,1017,1018,1019,1020,1021,1022,1023,1024,1025,1026,1027,1028,1029,1030,1031,1032,1033,1034,1035,1036,1037,1038,1039,1040,1041,1042,1043,1044,1045,1046,1047,1048,1049,1050,1051,1052,1053,1054,1055,1056,1057,1058,1059,1060,1061,1062,1063,1064,1065,1066,1067,1068,1069,1070,1071,1072,1073,1074,1075,1076,1077,1078,1079,1080,1081,1082,1083,1084,1085,1086,1087,1088,1089,1090,1091,1092,1093,1094,1095,1096,1097,1098,1099,1100,1101,1102,1103,1104,1105,1106,1107,1108,1109,1110,1111,1112,1113,1114,1115,1116,1117,1118,1119,1120,1121,1122,1123,1124,1125,1126,1127,1128,1129,1130,1131,1132,1133,1134,1135,1136,1137,1138,1139,1140,1141,1142,1143,1144,1145,1146,1147,1148,1149,1150,1151,1152,1153,1154,1155,1156,1157,1158,1159,1160,1161,1162,1163,1164,1165,1166,1167,1168,1169,1170,1171,1172,1173,1174,1175,1176,1177,1178,1179,1180,1181,1182,1183,1184,1185,1186,1187,1188,1189,1190,1191,1192,1193,1194,1195,1196,1197,1198,1199,1200,1201,1202,1203,1204,1205,1206,1207,1208,1209,1210,1211,1212,1213,1214,1215,1216,1217,1218,1219,1220,1221,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027,2968)(2028,2967)(2029,2966)(2030,2965)(2031,2964)(2032,2963)(2033,2962)(2034,2961)(2035,2960)(2036,2959)(2037,2958)(2038,2957)(2039,2956)(2040,2955)(2041,2954)(2042,2953)(2043,2952)(2044,2951)(2045,2950)(2046,2949)(2047,2948)(2048,2947)(2049,2946)(2050,2945)(2051,2944)(2052,2943)(2053,2942)(2054,2941)(2055,2940)(2056,2939)(2057,2938)(2058,2937)(2059,2936)(2060,2935)(2061,2934)(2062,2933)(2063,2932)(2064,2931)(2065,2930)(2066,2929)(2067,2928)(2068,2927)(2069,2926)(2070,2925)(2071,2924)(2072,2923)(2073,2922)(2074,2921)(2075,2920)(2076,2919)(2077,2918)(2078,2917)(2079,2916)(2080,2915)(2081,2914)(2082,2913)(2083,2912)(2084,2911)(2085,2910)(2086,2909)(2087,2908)(2088,2907)(2089,2906)(2090,2905)(2091,2904)(2092,2903)(2093,2902)(2094,2901)(2095,2900)(2096,2899)(2097,2898)(2098,2897)(2099,2896)(2100,2895)(2101,2894)(2102,2893)(2103,2892)(2104,2891)(2105,2890)(2106,2889)(2107,2888)(2108,2887)(2109,2886)(2110,2885)(2111,2884)(2112,2883)(2113,2882)(2114,2881)(2115,2880)(2116,2879)(2117,2878)(2118,2877)(2119,2876)(2120,2875)(2121,2874)(2122,2873)(2123,2872)(2124,2871)(2125,2870)(2126,2869)(2127,2868)(2128,2867)(2129,2866)(2130,2865)(2131,2864)(2132,2863)(2133,2862)(2134,2861)(2135,2860)(2136,2859)(2137,2858)(2138,2857)(2139,2856)(2140,2855)(2141,2854)(2142,2853)(2143,2852)(2144,2851)(2145,2850)(2146,2849)(2147,2848)(2148,2847)(2149,2846)(2150,2845)(2151,2844)(2152,2843)(2153,2842)(2154,2841)(2155,2840)(2156,2839)(2157,2838)(2158,2837)(2159,2836)(2160,2835)(2161,2834)(2162,2833)(2163,2832)(2164,2831)(2165,2830)(2166,2829)(2167,2828)(2168,2827)(2169,2826)(2170,2825)(2171,2824)(2172,2823)(2173,2822)(2174,2821)(2175,2820)(2176,2819)(2177,2818)(2178,2817)(2179,2816)(2180,2815)(2181,2814)(2182,2813)(2183,2812)(2184,2811)(2185,2810)(2186,2809)(2187,2808)(2188,2807)(2189,2806)(2190,2805)(2191,2804)(2192,2803)(2193,2802)(2194,2801)(2195,2800)(2196,2799)(2197,2798)(2198,2797)(2199,2796)(2200,2795)(2201,2794)(2202,2793)(2203,2792)(2204,2791)(2205,2790)(2206,2789)(2207,2788)(2208,2787)(2209,2786)(2210,2785)(2211,2784)(2212,2783)(2213,2782)(2214,2781)(2215,2780)(2216,2779)(2217,2778)(2218,2777)(2219,2776)(2220,2775)(2221,2774)(2222,2773)(2223,2772)(2224,2771)(2225,2770)(2226,2769)(2227,2768)(2228,2767)(2229,2766)(2230,2765)(2231,2764)(2232,2763)(2233,2762)(2234,2761)(2235,2760)(2236,2759)(2237,2758)(2238,2757)(2239,2756)(2240,2755)(2241,2754)(2242,2753)(2243,2752)(2244,2751)(2245,2750)(2246,2749)(2247,2748)(2248,2747)(2249,2746)(2250,2745)(2251,2744)(2252,2743)(2253,2742)(2254,2741)(2255,2740)(2256,2739)(2257,2738)(2258,2737)(2259,2736)(2260,2735)(2261,2734)(2262,2733)(2263,2732)(2264,2731)(2265,2730)(2266,2729)(2267,2728)(2268,2727)(2269,2726)(2270,2725)(2271,2724)(2272,2723)(2273,2722)(2274,2721)(2275,2720)(2276,2719)(2277,2718)(2278,2717)(2279,2716)(2280,2715)(2281,2714)(2282,2713)(2283,2712)(2284,2711)(2285,2710)(2286,2709)(2287,2708)(2288,2707)(2289,2706)(2290,2705)(2291,2704)(2292,2703)(2293,2702)(2294,2701)(2295,2700)(2296,2699)(2297,2698)(2298,2697)(2299,2696)(2300,2695)(2301,2694)(2302,2693)(2303,2692)(2304,2691)(2305,2690)(2306,2689)(2307,2688)(2308,2687)(2309,2686)(2310,2685)(2311,2684)(2312,2683)(2313,2682)(2314,2681)(2315,2680)(2316,2679)(2317,2678)(2318,2677)(2319,2676)(2320,2675)(2321,2674)(2322,2673)(2323,2672)(2324,2671)(2325,2670)(2326,2669)(2327,2668)(2328,2667)(2329,2666)(2330,2665)(2331,2664)(2332,2663)(2333,2662)(2334,2661)(2335,2660)(2336,2659)(2337,2658)(2338,2657)(2339,2656)(2340,2655)(2341,2654)(2342,2653)(2343,2652)(2344,2651)(2345,2650)(2346,2649)(2347,2648)(2348,2647)(2349,2646)(2350,2645)(2351,2644)(2352,2643)(2353,2642)(2354,2641)(2355,2640)(2356,2639)(2357,2638)(2358,2637)(2359,2636)(2360,2635)(2361,2634)(2362,2633)(2363,2632)(2364,2631)(2365,2630)(2366,2629)(2367,2628)(2368,2627)(2369,2626)(2370,2625)(2371,2624)(2372,2623)(2373,2622)(2374,2621)(2375,2620)(2376,2619)(2377,2618)(2378,2617)(2379,2616)(2380,2615)(2381,2614)(2382,2613)(2383,2612)(2384,2611)(2385,2610)(2386,2609)(2387,2608)(2388,2607)(2389,2606)(2390,2605)(2391,2604)(2392,2603)(2393,2602)(2394,2601)(2395,2600)(2396,2599)(2397,2598)(2398,2597)(2399,2596)(2400,2595)(2401,2594)(2402,2593)(2403,2592)(2404,2591)(2405,2590)(2406,2589)(2407,2588)(2408,2587)(2409,2586)(2410,2585)(2411,2584)(2412,2583)(2413,2582)(2414,2581)(2415,2580)(2416,2579)(2417,2578)(2418,2577)(2419,2576)(2420,2575)(2421,2574)(2422,2573)(2423,2572)(2424,2571)(2425,2570)(2426,2569)(2427,2568)(2428,2567)(2429,2566)(2430,2565)(2431,2564)(2432,2563)(2433,2562)(2434,2561)(2435,2560)(2436,2559)(2437,2558)(2438,2557)(2439,2556)(2440,2555)(2441,2554)(2442,2553)(2443,2552)(2444,2551)(2445,2550)(2446,2549)(2447,2548)(2448,2547)(2449,2546)(2450,2545)(2451,2544)(2452,2543)(2453,2542)(2454,2541)(2455,2540)(2456,2539)(2457,2538)(2458,2537)(2459,2536)(2460,2535)(2461,2534)(2462,2533)(2463,2532)(2464,2531)(2465,2530)(2466,2529)(2467,2528)(2468,2527)(2469,2526)(2470,2525)(2471,2524)(2472,2523)(2473,2522)(2474,2521)(2475,2520)(2476,2519)(2477,2518)(2478,2517)(2479,2516)(2480,2515)(2481,2514)(2482,2513)(2483,2512)(2484,2511)(2485,2510)(2486,2509)(2487,2508)(2488,2507)(2489,2506)(2490,2505)(2491,2504)(2492,2503)(2493,2502)(2494,2501)(2495,2500)(2496,2499)(2497,2498)
Polycyclic presentation:
2,3,4987|b^a=b^2,c^a=c^4986
Conjugacy classes & character table
7482 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29922, 5);
Finite Group Databasebeta