Finite Group DatabasebetaFinite Group Databasebeta| order | 35894 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D17947 |
| unambiguous semidirect product | C131⋊D137 |
| unambiguous semidirect product | C137⋊D131 |
| Fitting, socle, derived, Hall | C131×C137 ⋊ C2 |
| Sylow | C137 ⋊ D131 |
| Sylow | C131 ⋊ D137 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C131×C137 | C2 |
| LCS | G ▷ C131×C137 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 268 |
| transitive degree | μt(G) = 17947 |
A minimal faithful permutation representation — 2 generators on 268 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);(2,131)(3,130)(4,129)(5,128)(6,127)(7,126)(8,125)(9,124)(10,123)(11,122)(12,121)(13,120)(14,119)(15,118)(16,117)(17,116)(18,115)(19,114)(20,113)(21,112)(22,111)(23,110)(24,109)(25,108)(26,107)(27,106)(28,105)(29,104)(30,103)(31,102)(32,101)(33,100)(34,99)(35,98)(36,97)(37,96)(38,95)(39,94)(40,93)(41,92)(42,91)(43,90)(44,89)(45,88)(46,87)(47,86)(48,85)(49,84)(50,83)(51,82)(52,81)(53,80)(54,79)(55,78)(56,77)(57,76)(58,75)(59,74)(60,73)(61,72)(62,71)(63,70)(64,69)(65,68)(66,67)(133,268)(134,267)(135,266)(136,265)(137,264)(138,263)(139,262)(140,261)(141,260)(142,259)(143,258)(144,257)(145,256)(146,255)(147,254)(148,253)(149,252)(150,251)(151,250)(152,249)(153,248)(154,247)(155,246)(156,245)(157,244)(158,243)(159,242)(160,241)(161,240)(162,239)(163,238)(164,237)(165,236)(166,235)(167,234)(168,233)(169,232)(170,231)(171,230)(172,229)(173,228)(174,227)(175,226)(176,225)(177,224)(178,223)(179,222)(180,221)(181,220)(182,219)(183,218)(184,217)(185,216)(186,215)(187,214)(188,213)(189,212)(190,211)(191,210)(192,209)(193,208)(194,207)(195,206)(196,205)(197,204)(198,203)(199,202)(200,201)Polycyclic presentation:
2,131,137|b^a=b^130,c^a=c^1368975 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35894, 3);