Finite Group DatabasebetaFinite Group Databasebeta| order | 35738 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D17869 |
| unambiguous semidirect product | C107⋊D167 |
| unambiguous semidirect product | C167⋊D107 |
| Fitting, socle, derived, Hall | C107×C167 ⋊ C2 |
| Sylow | C167 ⋊ D107 |
| Sylow | C107 ⋊ D167 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C107×C167 | C2 |
| LCS | G ▷ C107×C167 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 274 |
| transitive degree | μt(G) = 17869 |
A minimal faithful permutation representation — 2 generators on 274 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);(2,107)(3,106)(4,105)(5,104)(6,103)(7,102)(8,101)(9,100)(10,99)(11,98)(12,97)(13,96)(14,95)(15,94)(16,93)(17,92)(18,91)(19,90)(20,89)(21,88)(22,87)(23,86)(24,85)(25,84)(26,83)(27,82)(28,81)(29,80)(30,79)(31,78)(32,77)(33,76)(34,75)(35,74)(36,73)(37,72)(38,71)(39,70)(40,69)(41,68)(42,67)(43,66)(44,65)(45,64)(46,63)(47,62)(48,61)(49,60)(50,59)(51,58)(52,57)(53,56)(54,55)(109,274)(110,273)(111,272)(112,271)(113,270)(114,269)(115,268)(116,267)(117,266)(118,265)(119,264)(120,263)(121,262)(122,261)(123,260)(124,259)(125,258)(126,257)(127,256)(128,255)(129,254)(130,253)(131,252)(132,251)(133,250)(134,249)(135,248)(136,247)(137,246)(138,245)(139,244)(140,243)(141,242)(142,241)(143,240)(144,239)(145,238)(146,237)(147,236)(148,235)(149,234)(150,233)(151,232)(152,231)(153,230)(154,229)(155,228)(156,227)(157,226)(158,225)(159,224)(160,223)(161,222)(162,221)(163,220)(164,219)(165,218)(166,217)(167,216)(168,215)(169,214)(170,213)(171,212)(172,211)(173,210)(174,209)(175,208)(176,207)(177,206)(178,205)(179,204)(180,203)(181,202)(182,201)(183,200)(184,199)(185,198)(186,197)(187,196)(188,195)(189,194)(190,193)(191,192)Polycyclic presentation:
2,107,167|b^a=b^106,c^a=c^1668936 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(35738, 3);