Finite Group DatabasebetaFinite Group Databasebeta| order | 37442 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D18721 |
| unambiguous semidirect product | C97⋊D193 |
| unambiguous semidirect product | C193⋊D97 |
| Fitting, socle, derived, Hall | C97×C193 ⋊ C2 |
| Sylow | C193 ⋊ D97 |
| Sylow | C97 ⋊ D193 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C97×C193 | C2 |
| LCS | G ▷ C97×C193 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 290 |
| transitive degree | μt(G) = 18721 |
A minimal faithful permutation representation — 2 generators on 290 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)(98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250,251,252,253,254,255,256,257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,272,273,274,275,276,277,278,279,280,281,282,283,284,285,286,287,288,289,290);(2,97)(3,96)(4,95)(5,94)(6,93)(7,92)(8,91)(9,90)(10,89)(11,88)(12,87)(13,86)(14,85)(15,84)(16,83)(17,82)(18,81)(19,80)(20,79)(21,78)(22,77)(23,76)(24,75)(25,74)(26,73)(27,72)(28,71)(29,70)(30,69)(31,68)(32,67)(33,66)(34,65)(35,64)(36,63)(37,62)(38,61)(39,60)(40,59)(41,58)(42,57)(43,56)(44,55)(45,54)(46,53)(47,52)(48,51)(49,50)(99,290)(100,289)(101,288)(102,287)(103,286)(104,285)(105,284)(106,283)(107,282)(108,281)(109,280)(110,279)(111,278)(112,277)(113,276)(114,275)(115,274)(116,273)(117,272)(118,271)(119,270)(120,269)(121,268)(122,267)(123,266)(124,265)(125,264)(126,263)(127,262)(128,261)(129,260)(130,259)(131,258)(132,257)(133,256)(134,255)(135,254)(136,253)(137,252)(138,251)(139,250)(140,249)(141,248)(142,247)(143,246)(144,245)(145,244)(146,243)(147,242)(148,241)(149,240)(150,239)(151,238)(152,237)(153,236)(154,235)(155,234)(156,233)(157,232)(158,231)(159,230)(160,229)(161,228)(162,227)(163,226)(164,225)(165,224)(166,223)(167,222)(168,221)(169,220)(170,219)(171,218)(172,217)(173,216)(174,215)(175,214)(176,213)(177,212)(178,211)(179,210)(180,209)(181,208)(182,207)(183,206)(184,205)(185,204)(186,203)(187,202)(188,201)(189,200)(190,199)(191,198)(192,197)(193,196)(194,195)Polycyclic presentation:
2,97,193|b^a=b^96,c^a=c^1929362 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37442, 3);