Finite Group DatabasebetaFinite Group Databasebeta| order | 33734 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D16867 |
| unambiguous semidirect product | C101⋊D167 |
| unambiguous semidirect product | C167⋊D101 |
| Fitting, socle, derived, Hall | C101×C167 ⋊ C2 |
| Sylow | C167 ⋊ D101 |
| Sylow | C101 ⋊ D167 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C101×C167 | C2 |
| LCS | G ▷ C101×C167 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 268 |
| transitive degree | μt(G) = 16867 |
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);(2,101)(3,100)(4,99)(5,98)(6,97)(7,96)(8,95)(9,94)(10,93)(11,92)(12,91)(13,90)(14,89)(15,88)(16,87)(17,86)(18,85)(19,84)(20,83)(21,82)(22,81)(23,80)(24,79)(25,78)(26,77)(27,76)(28,75)(29,74)(30,73)(31,72)(32,71)(33,70)(34,69)(35,68)(36,67)(37,66)(38,65)(39,64)(40,63)(41,62)(42,61)(43,60)(44,59)(45,58)(46,57)(47,56)(48,55)(49,54)(50,53)(51,52)(103,268)(104,267)(105,266)(106,265)(107,264)(108,263)(109,262)(110,261)(111,260)(112,259)(113,258)(114,257)(115,256)(116,255)(117,254)(118,253)(119,252)(120,251)(121,250)(122,249)(123,248)(124,247)(125,246)(126,245)(127,244)(128,243)(129,242)(130,241)(131,240)(132,239)(133,238)(134,237)(135,236)(136,235)(137,234)(138,233)(139,232)(140,231)(141,230)(142,229)(143,228)(144,227)(145,226)(146,225)(147,224)(148,223)(149,222)(150,221)(151,220)(152,219)(153,218)(154,217)(155,216)(156,215)(157,214)(158,213)(159,212)(160,211)(161,210)(162,209)(163,208)(164,207)(165,206)(166,205)(167,204)(168,203)(169,202)(170,201)(171,200)(172,199)(173,198)(174,197)(175,196)(176,195)(177,194)(178,193)(179,192)(180,191)(181,190)(182,189)(183,188)(184,187)(185,186)Polycyclic presentation:
2,101,167|b^a=b^100,c^a=c^1668435 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(33734, 3);