Finite Group DatabasebetaFinite Group Databasebeta| order | 34882 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D17441 |
| unambiguous semidirect product | C107⋊D163 |
| unambiguous semidirect product | C163⋊D107 |
| Fitting, socle, derived, Hall | C107×C163 ⋊ C2 |
| Sylow | C163 ⋊ D107 |
| Sylow | C107 ⋊ D163 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C107×C163 | C2 |
| LCS | G ▷ C107×C163 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 270 |
| transitive degree | μt(G) = 17441 |
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);(2,107)(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)(109,270)(110,269)(111,268)(112,267)(113,266)(114,265)(115,264)(116,263)(117,262)(118,261)(119,260)(120,259)(121,258)(122,257)(123,256)(124,255)(125,254)(126,253)(127,252)(128,251)(129,250)(130,249)(131,248)(132,247)(133,246)(134,245)(135,244)(136,243)(137,242)(138,241)(139,240)(140,239)(141,238)(142,237)(143,236)(144,235)(145,234)(146,233)(147,232)(148,231)(149,230)(150,229)(151,228)(152,227)(153,226)(154,225)(155,224)(156,223)(157,222)(158,221)(159,220)(160,219)(161,218)(162,217)(163,216)(164,215)(165,214)(166,213)(167,212)(168,211)(169,210)(170,209)(171,208)(172,207)(173,206)(174,205)(175,204)(176,203)(177,202)(178,201)(179,200)(180,199)(181,198)(182,197)(183,196)(184,195)(185,194)(186,193)(187,192)(188,191)(189,190)Polycyclic presentation:
2,107,163|b^a=b^106,c^a=c^1628722 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34882, 3);