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D7829 #30627809
Aliases
Splittings
Subgroups
4 conjugacy classes of subgroups.
Full subgroup data →
Presentation
A minimal faithful permutation representation — 2 generators on 7829 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290,291,292,293,294,295,296,297,298,299,300,301,302,303,304,305,306,307,308,309,310,311,312,313,314,315,316,317,318,319,320,321,322,323,324,325,326,327,328,329,330,331,332,333,334,335,336,337,338,339,340,341,342,343,344,345,346,347,348,349,350,351,352,353,354,355,356,357,358,359,360,361,362,363,364,365,366,367,368,369,370,371,372,373,374,375,376,377,378,379,380,381,382,383,384,385,386,387,388,389,390,391,392,393,394,395,396,397,398,399,400,401,402,403,404,405,406,407,408,409,410,411,412,413,414,415,416,417,418,419,420,421,422,423,424,425,426,427,428,429,430,431,432,433,434,435,436,437,438,439,440,441,442,443,444,445,446,447,448,449,450,451,452,453,454,455,456,457,458,459,460,461,462,463,464,465,466,467,468,469,470,471,472,473,474,475,476,477,478,479,480,481,482,483,484,485,486,487,488,489,490,491,492,493,494,495,496,497,498,499,500,501,502,503,504,505,506,507,508,509,510,511,512,513,514,515,516,517,518,519,520,521,522,523,524,525,526,527,528,529,530,531,532,533,534,535,536,537,538,539,540,541,542,543,544,545,546,547,548,549,550,551,552,553,554,555,556,557,558,559,560,561,562,563,564,565,566,567,568,569,570,571,572,573,574,575,576,577,578,579,580,581,582,583,584,585,586,587,588,589,590,591,592,593,594,595,596,597,598,599,600,601,602,603,604,605,606,607,608,609,610,611,612,613,614,615,616,617,618,619,620,621,622,623,624,625,626,627,628,629,630,631,632,633,634,635,636,637,638,639,640,641,642,643,644,645,646,647,648,649,650,651,652,653,654,655,656,657,658,659,660,661,662,663,664,665,666,667,668,669,670,671,672,673,674,675,676,677,678,679,680,681,682,683,684,685,686,687,688,689,690,691,692,693,694,695,696,697,698,699,700,701,702,703,704,705,706,707,708,709,710,711,712,713,714,715,716,717,718,719,720,721,722,723,724,725,726,727,728,729,730,731,732,733,734,735,736,737,738,739,740,741,742,743,744,745,746,747,748,749,750,751,752,753,754,755,756,757,758,759,760,761,762,763,764,765,766,767,768,769,770,771,772,773,774,775,776,777,778,779,780,781,782,783,784,785,786,787,788,789,790,791,792,793,794,795,796,797,798,799,800,801,802,803,804,805,806,807,808,809,810,811,812,813,814,815,816,817,818,819,820,821,822,823,824,825,826,827,828,829,830,831,832,833,834,835,836,837,838,839,840,841,842,843,844,845,846,847,848,849,850,851,852,853,854,855,856,857,858,859,860,861,862,863,864,865,866,867,868,869,870,871,872,873,874,875,876,877,878,879,880,881,882,883,884,885,886,887,888,889,890,891,892,893,894,895,896,897,898,899,900,901,902,903,904,905,906,907,908,909,910,911,912,913,914,915,916,917,918,919,920,921,922,923,924,925,926,927,928,929,930,931,932,933,934,935,936,937,938,939,940,941,942,943,944,945,946,947,948,949,950,951,952,953,954,955,956,957,958,959,960,961,962,963,964,965,966,967,968,969,970,971,972,973,974,975,976,977,978,979,980,981,982,983,984,985,986,987,988,989,990,991,992,993,994,995,996,997,998,999,1000,1001,1002,1003,1004,1005,1006,1007,1008,1009,1010,1011,1012,1013,1014,1015,1016,1017,1018,1019,1020,1021,1022,1023,1024,1025,1026,1027,1028,1029,1030,1031,1032,1033,1034,1035,1036,1037,1038,1039,1040,1041,1042,1043,1044,1045,1046,1047,1048,1049,1050,1051,1052,1053,1054,1055,1056,1057,1058,1059,1060,1061,1062,1063,1064,1065,1066,1067,1068,1069,1070,1071,1072,1073,1074,1075,1076,1077,1078,1079,1080,1081,1082,1083,1084,1085,1086,1087,1088,1089,1090,1091,1092,1093,1094,1095,1096,1097,1098,1099,1100,1101,1102,1103,1104,1105,1106,1107,1108,1109,1110,1111,1112,1113,1114,1115,1116,1117,1118,1119,1120,1121,1122,1123,1124,1125,1126,1127,1128,1129,1130,1131,1132,1133,1134,1135,1136,1137,1138,1139,1140,1141,1142,1143,1144,1145,1146,1147,1148,1149,1150,1151,1152,1153,1154,1155,1156,1157,1158,1159,1160,1161,1162,1163,1164,1165,1166,1167,1168,1169,1170,1171,1172,1173,1174,1175,1176,1177,1178,1179,1180,1181,1182,1183,1184,1185,1186,1187,1188,1189,1190,1191,1192,1193,1194,1195,1196,1197,1198,1199,1200,1201,1202,1203,1204,1205,1206,1207,1208,1209,1210,1211,1212,1213,1214,1215,1216,1217,1218,1219,1220,1221,1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2,4369)(3463,4368)(3464,4367)(3465,4366)(3466,4365)(3467,4364)(3468,4363)(3469,4362)(3470,4361)(3471,4360)(3472,4359)(3473,4358)(3474,4357)(3475,4356)(3476,4355)(3477,4354)(3478,4353)(3479,4352)(3480,4351)(3481,4350)(3482,4349)(3483,4348)(3484,4347)(3485,4346)(3486,4345)(3487,4344)(3488,4343)(3489,4342)(3490,4341)(3491,4340)(3492,4339)(3493,4338)(3494,4337)(3495,4336)(3496,4335)(3497,4334)(3498,4333)(3499,4332)(3500,4331)(3501,4330)(3502,4329)(3503,4328)(3504,4327)(3505,4326)(3506,4325)(3507,4324)(3508,4323)(3509,4322)(3510,4321)(3511,4320)(3512,4319)(3513,4318)(3514,4317)(3515,4316)(3516,4315)(3517,4314)(3518,4313)(3519,4312)(3520,4311)(3521,4310)(3522,4309)(3523,4308)(3524,4307)(3525,4306)(3526,4305)(3527,4304)(3528,4303)(3529,4302)(3530,4301)(3531,4300)(3532,4299)(3533,4298)(3534,4297)(3535,4296)(3536,4295)(3537,4294)(3538,4293)(3539,4292)(3540,4291)(3541,4290)(3542,4289)(3543,4288)(3544,4287)(3545,4286)(3546,4285)(3547,4284)(3548,4283)(3549,4282)(3550,4281)(3551,4280)(3552,4279)(3553,4278)(3554,4277)(3555,4276)(3556,4275)(3557,4274)(3558,4273)(3559,4272)(3560,4271)(3561,4270)(3562,4269)(3563,4268)(3564,4267)(3565,4266)(3566,4265)(3567,4264)(3568,4263)(3569,4262)(3570,4261)(3571,4260)(3572,4259)(3573,4258)(3574,4257)(3575,4256)(3576,4255)(3577,4254)(3578,4253)(3579,4252)(3580,4251)(3581,4250)(3582,4249)(3583,4248)(3584,4247)(3585,4246)(3586,4245)(3587,4244)(3588,4243)(3589,4242)(3590,4241)(3591,4240)(3592,4239)(3593,4238)(3594,4237)(3595,4236)(3596,4235)(3597,4234)(3598,4233)(3599,4232)(3600,4231)(3601,4230)(3602,4229)(3603,4228)(3604,4227)(3605,4226)(3606,4225)(3607,4224)(3608,4223)(3609,4222)(3610,4221)(3611,4220)(3612,4219)(3613,4218)(3614,4217)(3615,4216)(3616,4215)(3617,4214)(3618,4213)(3619,4212)(3620,4211)(3621,4210)(3622,4209)(3623,4208)(3624,4207)(3625,4206)(3626,4205)(3627,4204)(3628,4203)(3629,4202)(3630,4201)(3631,4200)(3632,4199)(3633,4198)(3634,4197)(3635,4196)(3636,4195)(3637,4194)(3638,4193)(3639,4192)(3640,4191)(3641,4190)(3642,4189)(3643,4188)(3644,4187)(3645,4186)(3646,4185)(3647,4184)(3648,4183)(3649,4182)(3650,4181)(3651,4180)(3652,4179)(3653,4178)(3654,4177)(3655,4176)(3656,4175)(3657,4174)(3658,4173)(3659,4172)(3660,4171)(3661,4170)(3662,4169)(3663,4168)(3664,4167)(3665,4166)(3666,4165)(3667,4164)(3668,4163)(3669,4162)(3670,4161)(3671,4160)(3672,4159)(3673,4158)(3674,4157)(3675,4156)(3676,4155)(3677,4154)(3678,4153)(3679,4152)(3680,4151)(3681,4150)(3682,4149)(3683,4148)(3684,4147)(3685,4146)(3686,4145)(3687,4144)(3688,4143)(3689,4142)(3690,4141)(3691,4140)(3692,4139)(3693,4138)(3694,4137)(3695,4136)(3696,4135)(3697,4134)(3698,4133)(3699,4132)(3700,4131)(3701,4130)(3702,4129)(3703,4128)(3704,4127)(3705,4126)(3706,4125)(3707,4124)(3708,4123)(3709,4122)(3710,4121)(3711,4120)(3712,4119)(3713,4118)(3714,4117)(3715,4116)(3716,4115)(3717,4114)(3718,4113)(3719,4112)(3720,4111)(3721,4110)(3722,4109)(3723,4108)(3724,4107)(3725,4106)(3726,4105)(3727,4104)(3728,4103)(3729,4102)(3730,4101)(3731,4100)(3732,4099)(3733,4098)(3734,4097)(3735,4096)(3736,4095)(3737,4094)(3738,4093)(3739,4092)(3740,4091)(3741,4090)(3742,4089)(3743,4088)(3744,4087)(3745,4086)(3746,4085)(3747,4084)(3748,4083)(3749,4082)(3750,4081)(3751,4080)(3752,4079)(3753,4078)(3754,4077)(3755,4076)(3756,4075)(3757,4074)(3758,4073)(3759,4072)(3760,4071)(3761,4070)(3762,4069)(3763,4068)(3764,4067)(3765,4066)(3766,4065)(3767,4064)(3768,4063)(3769,4062)(3770,4061)(3771,4060)(3772,4059)(3773,4058)(3774,4057)(3775,4056)(3776,4055)(3777,4054)(3778,4053)(3779,4052)(3780,4051)(3781,4050)(3782,4049)(3783,4048)(3784,4047)(3785,4046)(3786,4045)(3787,4044)(3788,4043)(3789,4042)(3790,4041)(3791,4040)(3792,4039)(3793,4038)(3794,4037)(3795,4036)(3796,4035)(3797,4034)(3798,4033)(3799,4032)(3800,4031)(3801,4030)(3802,4029)(3803,4028)(3804,4027)(3805,4026)(3806,4025)(3807,4024)(3808,4023)(3809,4022)(3810,4021)(3811,4020)(3812,4019)(3813,4018)(3814,4017)(3815,4016)(3816,4015)(3817,4014)(3818,4013)(3819,4012)(3820,4011)(3821,4010)(3822,4009)(3823,4008)(3824,4007)(3825,4006)(3826,4005)(3827,4004)(3828,4003)(3829,4002)(3830,4001)(3831,4000)(3832,3999)(3833,3998)(3834,3997)(3835,3996)(3836,3995)(3837,3994)(3838,3993)(3839,3992)(3840,3991)(3841,3990)(3842,3989)(3843,3988)(3844,3987)(3845,3986)(3846,3985)(3847,3984)(3848,3983)(3849,3982)(3850,3981)(3851,3980)(3852,3979)(3853,3978)(3854,3977)(3855,3976)(3856,3975)(3857,3974)(3858,3973)(3859,3972)(3860,3971)(3861,3970)(3862,3969)(3863,3968)(3864,3967)(3865,3966)(3866,3965)(3867,3964)(3868,3963)(3869,3962)(3870,3961)(3871,3960)(3872,3959)(3873,3958)(3874,3957)(3875,3956)(3876,3955)(3877,3954)(3878,3953)(3879,3952)(3880,3951)(3881,3950)(3882,3949)(3883,3948)(3884,3947)(3885,3946)(3886,3945)(3887,3944)(3888,3943)(3889,3942)(3890,3941)(3891,3940)(3892,3939)(3893,3938)(3894,3937)(3895,3936)(3896,3935)(3897,3934)(3898,3933)(3899,3932)(3900,3931)(3901,3930)(3902,3929)(3903,3928)(3904,3927)(3905,3926)(3906,3925)(3907,3924)(3908,3923)(3909,3922)(3910,3921)(3911,3920)(3912,3919)(3913,3918)(3914,3917)(3915,3916)
Polycyclic presentation:
2,7829|b^a=b^7828
Conjugacy classes & character table
3916 conjugacy classes. The character table is too large to display.
Relationships
GAP
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15658, 1);
Finite Group Databasebeta