Finite Group DatabasebetaFinite Group Databasebeta| order | 34138 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D17069 |
| unambiguous semidirect product | C101⋊D169 |
| unambiguous semidirect product | C169⋊D101 |
| Fitting, derived, Hall | C101×C169 ⋊ C2 |
| Sylow | C169 ⋊ D101 |
| Sylow | C101 ⋊ D169 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C101×C169 | C2 |
| Frattini | C13 | D1313 |
| socle | C13×C101 | D13 |
| LCS | G ▷ C101×C169 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| minimal degree | μ(G) = 270 |
| transitive degree | μt(G) = 17069 |
A minimal faithful permutation representation — 2 generators on 270 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);(2,169)(3,168)(4,167)(5,166)(6,165)(7,164)(8,163)(9,162)(10,161)(11,160)(12,159)(13,158)(14,157)(15,156)(16,155)(17,154)(18,153)(19,152)(20,151)(21,150)(22,149)(23,148)(24,147)(25,146)(26,145)(27,144)(28,143)(29,142)(30,141)(31,140)(32,139)(33,138)(34,137)(35,136)(36,135)(37,134)(38,133)(39,132)(40,131)(41,130)(42,129)(43,128)(44,127)(45,126)(46,125)(47,124)(48,123)(49,122)(50,121)(51,120)(52,119)(53,118)(54,117)(55,116)(56,115)(57,114)(58,113)(59,112)(60,111)(61,110)(62,109)(63,108)(64,107)(65,106)(66,105)(67,104)(68,103)(69,102)(70,101)(71,100)(72,99)(73,98)(74,97)(75,96)(76,95)(77,94)(78,93)(79,92)(80,91)(81,90)(82,89)(83,88)(84,87)(85,86)(171,270)(172,269)(173,268)(174,267)(175,266)(176,265)(177,264)(178,263)(179,262)(180,261)(181,260)(182,259)(183,258)(184,257)(185,256)(186,255)(187,254)(188,253)(189,252)(190,251)(191,250)(192,249)(193,248)(194,247)(195,246)(196,245)(197,244)(198,243)(199,242)(200,241)(201,240)(202,239)(203,238)(204,237)(205,236)(206,235)(207,234)(208,233)(209,232)(210,231)(211,230)(212,229)(213,228)(214,227)(215,226)(216,225)(217,224)(218,223)(219,222)(220,221)Polycyclic presentation:
2,13,101,13|b^13=d^12,b^a=b^12d,c^a=c^100,d^a=d^128536 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34138, 4);