Finite Group DatabasebetaFinite Group Databasebeta| order | 36058 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C1 |
| dihedral | D18029 |
| unambiguous semidirect product | C121⋊D149 |
| unambiguous semidirect product | C149⋊D121 |
| Fitting, derived, Hall | C121×C149 ⋊ C2 |
| Sylow | C149 ⋊ D121 |
| Sylow | C121 ⋊ D149 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, cosocle, hypocenter | C121×C149 | C2 |
| Frattini | C11 | D1639 |
| socle | C11×C149 | D11 |
| LCS | G ▷ C121×C149 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| minimal degree | μ(G) = 270 |
| transitive degree | μt(G) = 18029 |
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);(2,121)(3,120)(4,119)(5,118)(6,117)(7,116)(8,115)(9,114)(10,113)(11,112)(12,111)(13,110)(14,109)(15,108)(16,107)(17,106)(18,105)(19,104)(20,103)(21,102)(22,101)(23,100)(24,99)(25,98)(26,97)(27,96)(28,95)(29,94)(30,93)(31,92)(32,91)(33,90)(34,89)(35,88)(36,87)(37,86)(38,85)(39,84)(40,83)(41,82)(42,81)(43,80)(44,79)(45,78)(46,77)(47,76)(48,75)(49,74)(50,73)(51,72)(52,71)(53,70)(54,69)(55,68)(56,67)(57,66)(58,65)(59,64)(60,63)(61,62)(123,270)(124,269)(125,268)(126,267)(127,266)(128,265)(129,264)(130,263)(131,262)(132,261)(133,260)(134,259)(135,258)(136,257)(137,256)(138,255)(139,254)(140,253)(141,252)(142,251)(143,250)(144,249)(145,248)(146,247)(147,246)(148,245)(149,244)(150,243)(151,242)(152,241)(153,240)(154,239)(155,238)(156,237)(157,236)(158,235)(159,234)(160,233)(161,232)(162,231)(163,230)(164,229)(165,228)(166,227)(167,226)(168,225)(169,224)(170,223)(171,222)(172,221)(173,220)(174,219)(175,218)(176,217)(177,216)(178,215)(179,214)(180,213)(181,212)(182,211)(183,210)(184,209)(185,208)(186,207)(187,206)(188,205)(189,204)(190,203)(191,202)(192,201)(193,200)(194,199)(195,198)(196,197)Polycyclic presentation:
2,11,149,11|b^11=d^10,b^a=b^10d,c^a=c^148,d^a=d^109016 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36058, 4);