Finite Group DatabasebetaFinite Group Databasebeta| order | 23756 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic5939 |
| unambiguous semidirect product | C5939⋊C4 |
| derived, Sylow | C5939 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D5939 |
| commutator, hypocenter | C5939 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C5939 | C2 |
| LCS | G ▷ C5939 | |
| UCS | C1 ◁ C2 | |
6 conjugacy classes of subgroups.
| minimal degree | μ(G) = 5943 |
| transitive degree | μt(G) = 23756 |
A minimal faithful permutation representation — 2 generators on 5943 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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3,3446)(2504,3445)(2505,3444)(2506,3443)(2507,3442)(2508,3441)(2509,3440)(2510,3439)(2511,3438)(2512,3437)(2513,3436)(2514,3435)(2515,3434)(2516,3433)(2517,3432)(2518,3431)(2519,3430)(2520,3429)(2521,3428)(2522,3427)(2523,3426)(2524,3425)(2525,3424)(2526,3423)(2527,3422)(2528,3421)(2529,3420)(2530,3419)(2531,3418)(2532,3417)(2533,3416)(2534,3415)(2535,3414)(2536,3413)(2537,3412)(2538,3411)(2539,3410)(2540,3409)(2541,3408)(2542,3407)(2543,3406)(2544,3405)(2545,3404)(2546,3403)(2547,3402)(2548,3401)(2549,3400)(2550,3399)(2551,3398)(2552,3397)(2553,3396)(2554,3395)(2555,3394)(2556,3393)(2557,3392)(2558,3391)(2559,3390)(2560,3389)(2561,3388)(2562,3387)(2563,3386)(2564,3385)(2565,3384)(2566,3383)(2567,3382)(2568,3381)(2569,3380)(2570,3379)(2571,3378)(2572,3377)(2573,3376)(2574,3375)(2575,3374)(2576,3373)(2577,3372)(2578,3371)(2579,3370)(2580,3369)(2581,3368)(2582,3367)(2583,3366)(2584,3365)(2585,3364)(2586,3363)(2587,3362)(2588,3361)(2589,3360)(2590,3359)(2591,3358)(2592,3357)(2593,3356)(2594,3355)(2595,3354)(2596,3353)(2597,3352)(2598,3351)(2599,3350)(2600,3349)(2601,3348)(2602,3347)(2603,3346)(2604,3345)(2605,3344)(2606,3343)(2607,3342)(2608,3341)(2609,3340)(2610,3339)(2611,3338)(2612,3337)(2613,3336)(2614,3335)(2615,3334)(2616,3333)(2617,3332)(2618,3331)(2619,3330)(2620,3329)(2621,3328)(2622,3327)(2623,3326)(2624,3325)(2625,3324)(2626,3323)(2627,3322)(2628,3321)(2629,3320)(2630,3319)(2631,3318)(2632,3317)(2633,3316)(2634,3315)(2635,3314)(2636,3313)(2637,3312)(2638,3311)(2639,3310)(2640,3309)(2641,3308)(2642,3307)(2643,3306)(2644,3305)(2645,3304)(2646,3303)(2647,3302)(2648,3301)(2649,3300)(2650,3299)(2651,3298)(2652,3297)(2653,3296)(2654,3295)(2655,3294)(2656,3293)(2657,3292)(2658,3291)(2659,3290)(2660,3289)(2661,3288)(2662,3287)(2663,3286)(2664,3285)(2665,3284)(2666,3283)(2667,3282)(2668,3281)(2669,3280)(2670,3279)(2671,3278)(2672,3277)(2673,3276)(2674,3275)(2675,3274)(2676,3273)(2677,3272)(2678,3271)(2679,3270)(2680,3269)(2681,3268)(2682,3267)(2683,3266)(2684,3265)(2685,3264)(2686,3263)(2687,3262)(2688,3261)(2689,3260)(2690,3259)(2691,3258)(2692,3257)(2693,3256)(2694,3255)(2695,3254)(2696,3253)(2697,3252)(2698,3251)(2699,3250)(2700,3249)(2701,3248)(2702,3247)(2703,3246)(2704,3245)(2705,3244)(2706,3243)(2707,3242)(2708,3241)(2709,3240)(2710,3239)(2711,3238)(2712,3237)(2713,3236)(2714,3235)(2715,3234)(2716,3233)(2717,3232)(2718,3231)(2719,3230)(2720,3229)(2721,3228)(2722,3227)(2723,3226)(2724,3225)(2725,3224)(2726,3223)(2727,3222)(2728,3221)(2729,3220)(2730,3219)(2731,3218)(2732,3217)(2733,3216)(2734,3215)(2735,3214)(2736,3213)(2737,3212)(2738,3211)(2739,3210)(2740,3209)(2741,3208)(2742,3207)(2743,3206)(2744,3205)(2745,3204)(2746,3203)(2747,3202)(2748,3201)(2749,3200)(2750,3199)(2751,3198)(2752,3197)(2753,3196)(2754,3195)(2755,3194)(2756,3193)(2757,3192)(2758,3191)(2759,3190)(2760,3189)(2761,3188)(2762,3187)(2763,3186)(2764,3185)(2765,3184)(2766,3183)(2767,3182)(2768,3181)(2769,3180)(2770,3179)(2771,3178)(2772,3177)(2773,3176)(2774,3175)(2775,3174)(2776,3173)(2777,3172)(2778,3171)(2779,3170)(2780,3169)(2781,3168)(2782,3167)(2783,3166)(2784,3165)(2785,3164)(2786,3163)(2787,3162)(2788,3161)(2789,3160)(2790,3159)(2791,3158)(2792,3157)(2793,3156)(2794,3155)(2795,3154)(2796,3153)(2797,3152)(2798,3151)(2799,3150)(2800,3149)(2801,3148)(2802,3147)(2803,3146)(2804,3145)(2805,3144)(2806,3143)(2807,3142)(2808,3141)(2809,3140)(2810,3139)(2811,3138)(2812,3137)(2813,3136)(2814,3135)(2815,3134)(2816,3133)(2817,3132)(2818,3131)(2819,3130)(2820,3129)(2821,3128)(2822,3127)(2823,3126)(2824,3125)(2825,3124)(2826,3123)(2827,3122)(2828,3121)(2829,3120)(2830,3119)(2831,3118)(2832,3117)(2833,3116)(2834,3115)(2835,3114)(2836,3113)(2837,3112)(2838,3111)(2839,3110)(2840,3109)(2841,3108)(2842,3107)(2843,3106)(2844,3105)(2845,3104)(2846,3103)(2847,3102)(2848,3101)(2849,3100)(2850,3099)(2851,3098)(2852,3097)(2853,3096)(2854,3095)(2855,3094)(2856,3093)(2857,3092)(2858,3091)(2859,3090)(2860,3089)(2861,3088)(2862,3087)(2863,3086)(2864,3085)(2865,3084)(2866,3083)(2867,3082)(2868,3081)(2869,3080)(2870,3079)(2871,3078)(2872,3077)(2873,3076)(2874,3075)(2875,3074)(2876,3073)(2877,3072)(2878,3071)(2879,3070)(2880,3069)(2881,3068)(2882,3067)(2883,3066)(2884,3065)(2885,3064)(2886,3063)(2887,3062)(2888,3061)(2889,3060)(2890,3059)(2891,3058)(2892,3057)(2893,3056)(2894,3055)(2895,3054)(2896,3053)(2897,3052)(2898,3051)(2899,3050)(2900,3049)(2901,3048)(2902,3047)(2903,3046)(2904,3045)(2905,3044)(2906,3043)(2907,3042)(2908,3041)(2909,3040)(2910,3039)(2911,3038)(2912,3037)(2913,3036)(2914,3035)(2915,3034)(2916,3033)(2917,3032)(2918,3031)(2919,3030)(2920,3029)(2921,3028)(2922,3027)(2923,3026)(2924,3025)(2925,3024)(2926,3023)(2927,3022)(2928,3021)(2929,3020)(2930,3019)(2931,3018)(2932,3017)(2933,3016)(2934,3015)(2935,3014)(2936,3013)(2937,3012)(2938,3011)(2939,3010)(2940,3009)(2941,3008)(2942,3007)(2943,3006)(2944,3005)(2945,3004)(2946,3003)(2947,3002)(2948,3001)(2949,3000)(2950,2999)(2951,2998)(2952,2997)(2953,2996)(2954,2995)(2955,2994)(2956,2993)(2957,2992)(2958,2991)(2959,2990)(2960,2989)(2961,2988)(2962,2987)(2963,2986)(2964,2985)(2965,2984)(2966,2983)(2967,2982)(2968,2981)(2969,2980)(2970,2979)(2971,2978)(2972,2977)(2973,2976)(2974,2975)Polycyclic presentation:
2^2,5939|a^2=b,c^a=c^59385942 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(23756, 1);