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Aliases
Splittings
Subgroups
10 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 5941 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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42)(2504,3441)(2505,3440)(2506,3439)(2507,3438)(2508,3437)(2509,3436)(2510,3435)(2511,3434)(2512,3433)(2513,3432)(2514,3431)(2515,3430)(2516,3429)(2517,3428)(2518,3427)(2519,3426)(2520,3425)(2521,3424)(2522,3423)(2523,3422)(2524,3421)(2525,3420)(2526,3419)(2527,3418)(2528,3417)(2529,3416)(2530,3415)(2531,3414)(2532,3413)(2533,3412)(2534,3411)(2535,3410)(2536,3409)(2537,3408)(2538,3407)(2539,3406)(2540,3405)(2541,3404)(2542,3403)(2543,3402)(2544,3401)(2545,3400)(2546,3399)(2547,3398)(2548,3397)(2549,3396)(2550,3395)(2551,3394)(2552,3393)(2553,3392)(2554,3391)(2555,3390)(2556,3389)(2557,3388)(2558,3387)(2559,3386)(2560,3385)(2561,3384)(2562,3383)(2563,3382)(2564,3381)(2565,3380)(2566,3379)(2567,3378)(2568,3377)(2569,3376)(2570,3375)(2571,3374)(2572,3373)(2573,3372)(2574,3371)(2575,3370)(2576,3369)(2577,3368)(2578,3367)(2579,3366)(2580,3365)(2581,3364)(2582,3363)(2583,3362)(2584,3361)(2585,3360)(2586,3359)(2587,3358)(2588,3357)(2589,3356)(2590,3355)(2591,3354)(2592,3353)(2593,3352)(2594,3351)(2595,3350)(2596,3349)(2597,3348)(2598,3347)(2599,3346)(2600,3345)(2601,3344)(2602,3343)(2603,3342)(2604,3341)(2605,3340)(2606,3339)(2607,3338)(2608,3337)(2609,3336)(2610,3335)(2611,3334)(2612,3333)(2613,3332)(2614,3331)(2615,3330)(2616,3329)(2617,3328)(2618,3327)(2619,3326)(2620,3325)(2621,3324)(2622,3323)(2623,3322)(2624,3321)(2625,3320)(2626,3319)(2627,3318)(2628,3317)(2629,3316)(2630,3315)(2631,3314)(2632,3313)(2633,3312)(2634,3311)(2635,3310)(2636,3309)(2637,3308)(2638,3307)(2639,3306)(2640,3305)(2641,3304)(2642,3303)(2643,3302)(2644,3301)(2645,3300)(2646,3299)(2647,3298)(2648,3297)(2649,3296)(2650,3295)(2651,3294)(2652,3293)(2653,3292)(2654,3291)(2655,3290)(2656,3289)(2657,3288)(2658,3287)(2659,3286)(2660,3285)(2661,3284)(2662,3283)(2663,3282)(2664,3281)(2665,3280)(2666,3279)(2667,3278)(2668,3277)(2669,3276)(2670,3275)(2671,3274)(2672,3273)(2673,3272)(2674,3271)(2675,3270)(2676,3269)(2677,3268)(2678,3267)(2679,3266)(2680,3265)(2681,3264)(2682,3263)(2683,3262)(2684,3261)(2685,3260)(2686,3259)(2687,3258)(2688,3257)(2689,3256)(2690,3255)(2691,3254)(2692,3253)(2693,3252)(2694,3251)(2695,3250)(2696,3249)(2697,3248)(2698,3247)(2699,3246)(2700,3245)(2701,3244)(2702,3243)(2703,3242)(2704,3241)(2705,3240)(2706,3239)(2707,3238)(2708,3237)(2709,3236)(2710,3235)(2711,3234)(2712,3233)(2713,3232)(2714,3231)(2715,3230)(2716,3229)(2717,3228)(2718,3227)(2719,3226)(2720,3225)(2721,3224)(2722,3223)(2723,3222)(2724,3221)(2725,3220)(2726,3219)(2727,3218)(2728,3217)(2729,3216)(2730,3215)(2731,3214)(2732,3213)(2733,3212)(2734,3211)(2735,3210)(2736,3209)(2737,3208)(2738,3207)(2739,3206)(2740,3205)(2741,3204)(2742,3203)(2743,3202)(2744,3201)(2745,3200)(2746,3199)(2747,3198)(2748,3197)(2749,3196)(2750,3195)(2751,3194)(2752,3193)(2753,3192)(2754,3191)(2755,3190)(2756,3189)(2757,3188)(2758,3187)(2759,3186)(2760,3185)(2761,3184)(2762,3183)(2763,3182)(2764,3181)(2765,3180)(2766,3179)(2767,3178)(2768,3177)(2769,3176)(2770,3175)(2771,3174)(2772,3173)(2773,3172)(2774,3171)(2775,3170)(2776,3169)(2777,3168)(2778,3167)(2779,3166)(2780,3165)(2781,3164)(2782,3163)(2783,3162)(2784,3161)(2785,3160)(2786,3159)(2787,3158)(2788,3157)(2789,3156)(2790,3155)(2791,3154)(2792,3153)(2793,3152)(2794,3151)(2795,3150)(2796,3149)(2797,3148)(2798,3147)(2799,3146)(2800,3145)(2801,3144)(2802,3143)(2803,3142)(2804,3141)(2805,3140)(2806,3139)(2807,3138)(2808,3137)(2809,3136)(2810,3135)(2811,3134)(2812,3133)(2813,3132)(2814,3131)(2815,3130)(2816,3129)(2817,3128)(2818,3127)(2819,3126)(2820,3125)(2821,3124)(2822,3123)(2823,3122)(2824,3121)(2825,3120)(2826,3119)(2827,3118)(2828,3117)(2829,3116)(2830,3115)(2831,3114)(2832,3113)(2833,3112)(2834,3111)(2835,3110)(2836,3109)(2837,3108)(2838,3107)(2839,3106)(2840,3105)(2841,3104)(2842,3103)(2843,3102)(2844,3101)(2845,3100)(2846,3099)(2847,3098)(2848,3097)(2849,3096)(2850,3095)(2851,3094)(2852,3093)(2853,3092)(2854,3091)(2855,3090)(2856,3089)(2857,3088)(2858,3087)(2859,3086)(2860,3085)(2861,3084)(2862,3083)(2863,3082)(2864,3081)(2865,3080)(2866,3079)(2867,3078)(2868,3077)(2869,3076)(2870,3075)(2871,3074)(2872,3073)(2873,3072)(2874,3071)(2875,3070)(2876,3069)(2877,3068)(2878,3067)(2879,3066)(2880,3065)(2881,3064)(2882,3063)(2883,3062)(2884,3061)(2885,3060)(2886,3059)(2887,3058)(2888,3057)(2889,3056)(2890,3055)(2891,3054)(2892,3053)(2893,3052)(2894,3051)(2895,3050)(2896,3049)(2897,3048)(2898,3047)(2899,3046)(2900,3045)(2901,3044)(2902,3043)(2903,3042)(2904,3041)(2905,3040)(2906,3039)(2907,3038)(2908,3037)(2909,3036)(2910,3035)(2911,3034)(2912,3033)(2913,3032)(2914,3031)(2915,3030)(2916,3029)(2917,3028)(2918,3027)(2919,3026)(2920,3025)(2921,3024)(2922,3023)(2923,3022)(2924,3021)(2925,3020)(2926,3019)(2927,3018)(2928,3017)(2929,3016)(2930,3015)(2931,3014)(2932,3013)(2933,3012)(2934,3011)(2935,3010)(2936,3009)(2937,3008)(2938,3007)(2939,3006)(2940,3005)(2941,3004)(2942,3003)(2943,3002)(2944,3001)(2945,3000)(2946,2999)(2947,2998)(2948,2997)(2949,2996)(2950,2995)(2951,2994)(2952,2993)(2953,2992)(2954,2991)(2955,2990)(2956,2989)(2957,2988)(2958,2987)(2959,2986)(2960,2985)(2961,2984)(2962,2983)(2963,2982)(2964,2981)(2965,2980)(2966,2979)(2967,2978)(2968,2977)(2969,2976)(2970,2975)(2971,2974)(2972,2973)
Conjugacy classes & character table
5942 conjugacy classes. The character table is too large to display.
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23756, 3);
Finite Group Databasebeta