Finite Group DatabasebetaFinite Group Databasebeta| order | 20096 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | #562×C157 ⋊ C2 |
| Sylow | C157 ⋊ #3531 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D157 |
| commutator, socle, cosocle | C22×C157 | C25 |
| Fitting | #562×C157 | C2 |
| hypercenter | #562 | D157 |
| hypocenter | C157 | #3531 |
| LCS | G ▷ C22×C157 ▷ C157 | |
| UCS | C1 ◁ C22 ◁ #562 | |
930 conjugacy classes of subgroups.
| minimal degree | μ(G) = 189 |
| transitive degree | μt(G) = 10048 |
A minimal faithful permutation representation — 5 generators on 189 points:
(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)(174,177,178,185)(175,181,180,187)(176,184,183,189)(179,186,182,188);(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,80,82,84,86,88,90,92,94,96,98,100,102,104,106,108,110,112,114,116,118,120,122,124,126,128,130,132,134,136,138,140,142,144,146,148,150,152,154,156,157,155,153,151,149,147,145,143,141,139,137,135,133,131,129,127,125,123,121,119,117,115,113,111,109,107,105,103,101,99,97,95,93,91,89,87,85,83,81,79,77,75,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(159,165)(163,172)(164,168)(171,173)(175,180)(176,183)(181,187)(184,189);(158,161,162,170)(159,164,165,168)(160,166,167,169)(163,171,172,173)(176,183)(179,182)(184,189)(186,188);(158,160,162,167)(159,163,165,172)(161,169,170,166)(164,173,168,171)(174,176)(175,179)(177,184)(178,183)(180,182)(181,186)(185,189)(187,188);(158,159)(160,163)(161,168)(162,165)(164,170)(166,173)(167,172)(169,171)(174,175)(176,182)(177,181)(178,180)(179,183)(184,188)(185,187)(186,189)Polycyclic presentation:
2^7,157|b^2=g,c^2=g,e^2=f,b^a=bf,c^a=cg,d^a=dfg,c^b=cfg,d^b=df,h^e=h^1561520 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20096, 18654);