Finite Group DatabasebetaFinite Group Databasebeta| order | 36406 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D18203 |
| unambiguous semidirect product | C109⋊D167 |
| unambiguous semidirect product | C167⋊D109 |
| Fitting, socle, derived, Hall | C109×C167 ⋊ C2 |
| Sylow | C167 ⋊ D109 |
| Sylow | C109 ⋊ D167 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C109×C167 | C2 |
| LCS | G ▷ C109×C167 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 276 |
| transitive degree | μt(G) = 18203 |
A minimal faithful permutation representation — 2 generators on 276 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)(110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276);(2,109)(3,108)(4,107)(5,106)(6,105)(7,104)(8,103)(9,102)(10,101)(11,100)(12,99)(13,98)(14,97)(15,96)(16,95)(17,94)(18,93)(19,92)(20,91)(21,90)(22,89)(23,88)(24,87)(25,86)(26,85)(27,84)(28,83)(29,82)(30,81)(31,80)(32,79)(33,78)(34,77)(35,76)(36,75)(37,74)(38,73)(39,72)(40,71)(41,70)(42,69)(43,68)(44,67)(45,66)(46,65)(47,64)(48,63)(49,62)(50,61)(51,60)(52,59)(53,58)(54,57)(55,56)(111,276)(112,275)(113,274)(114,273)(115,272)(116,271)(117,270)(118,269)(119,268)(120,267)(121,266)(122,265)(123,264)(124,263)(125,262)(126,261)(127,260)(128,259)(129,258)(130,257)(131,256)(132,255)(133,254)(134,253)(135,252)(136,251)(137,250)(138,249)(139,248)(140,247)(141,246)(142,245)(143,244)(144,243)(145,242)(146,241)(147,240)(148,239)(149,238)(150,237)(151,236)(152,235)(153,234)(154,233)(155,232)(156,231)(157,230)(158,229)(159,228)(160,227)(161,226)(162,225)(163,224)(164,223)(165,222)(166,221)(167,220)(168,219)(169,218)(170,217)(171,216)(172,215)(173,214)(174,213)(175,212)(176,211)(177,210)(178,209)(179,208)(180,207)(181,206)(182,205)(183,204)(184,203)(185,202)(186,201)(187,200)(188,199)(189,198)(190,197)(191,196)(192,195)(193,194)Polycyclic presentation:
2,109,167|b^a=b^108,c^a=c^1669103 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36406, 3);