Finite Group DatabasebetaFinite Group Databasebeta| order | 20096 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | #532×C157 ⋊ C2 |
| Sylow | C157 ⋊ #3529 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C23×D157 |
| commutator, socle, cosocle | C22×C157 | C25 |
| Frattini | C22 | C24×D157 |
| Fitting | #532×C157 | C2 |
| hypercenter | #532 | D157 |
| hypocenter | C157 | #3529 |
| LCS | G ▷ C22×C157 ▷ C157 | |
| UCS | C1 ◁ C2×C4 ◁ #532 | |
1058 conjugacy classes of subgroups.
| minimal degree | μ(G) = 181 |
| transitive degree | μt(G) = 5024 |
A minimal faithful permutation representation — 5 generators on 181 points:
(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)(166,169,170,177)(167,173,172,179)(168,176,175,181)(171,178,174,180);(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)(159,163)(162,165)(167,172)(168,175)(173,179)(176,181);(159,163)(160,164)(168,175)(171,174)(176,181)(178,180);(158,160)(159,162)(161,164)(163,165)(166,168)(167,171)(169,176)(170,175)(172,174)(173,178)(177,181)(179,180);(158,159)(160,162)(161,163)(164,165)(166,167)(168,174)(169,173)(170,172)(171,175)(176,180)(177,179)(178,181)Polycyclic presentation:
2^7,157|e^2=f,b^a=bf,c^a=cg,d^a=dfg,c^b=cfg,d^b=df,h^d=h^1562222 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20096, 18646);