Finite Group DatabasebetaFinite Group Databasebeta| order | 36562 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D18281 |
| unambiguous semidirect product | C101⋊D181 |
| unambiguous semidirect product | C181⋊D101 |
| Fitting, socle, derived, Hall | C101×C181 ⋊ C2 |
| Sylow | C181 ⋊ D101 |
| Sylow | C101 ⋊ D181 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C101×C181 | C2 |
| LCS | G ▷ C101×C181 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 282 |
| transitive degree | μt(G) = 18281 |
A minimal faithful permutation representation — 2 generators on 282 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)(102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282);(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)(103,282)(104,281)(105,280)(106,279)(107,278)(108,277)(109,276)(110,275)(111,274)(112,273)(113,272)(114,271)(115,270)(116,269)(117,268)(118,267)(119,266)(120,265)(121,264)(122,263)(123,262)(124,261)(125,260)(126,259)(127,258)(128,257)(129,256)(130,255)(131,254)(132,253)(133,252)(134,251)(135,250)(136,249)(137,248)(138,247)(139,246)(140,245)(141,244)(142,243)(143,242)(144,241)(145,240)(146,239)(147,238)(148,237)(149,236)(150,235)(151,234)(152,233)(153,232)(154,231)(155,230)(156,229)(157,228)(158,227)(159,226)(160,225)(161,224)(162,223)(163,222)(164,221)(165,220)(166,219)(167,218)(168,217)(169,216)(170,215)(171,214)(172,213)(173,212)(174,211)(175,210)(176,209)(177,208)(178,207)(179,206)(180,205)(181,204)(182,203)(183,202)(184,201)(185,200)(186,199)(187,198)(188,197)(189,196)(190,195)(191,194)(192,193)Polycyclic presentation:
2,101,181|b^a=b^100,c^a=c^1809142 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36562, 3);