Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13323 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#13324 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C19 | #1999 |
| commutator, Frattini, cosocle | C22×C8 | C23×C19 |
| prime radical | C19×#3067 | C2 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C19 ◁ C22×C4×C19 ◁ C2×C19×#131 ◁ G | |
514 conjugacy classes of subgroups.
| minimal degree | μ(G) = 83 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 3 generators on 83 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,27,33)(22,34,39,67)(23,40,44,64)(24,45,50,62)(25,32,26,31)(28,52,56,36)(29,51,59,43)(30,48,63,49)(35,68,71,83)(37,66,38,60)(41,75,70,65)(42,61,47,58)(46,55,73,54)(53,79,82,76)(57,72,81,69)(74,80,78,77);(20,22)(21,28)(23,41)(24,46)(25,37)(26,38)(27,39)(29,57)(30,60)(31,54)(32,55)(33,56)(34,45)(35,43)(36,49)(40,53)(42,72)(44,70)(47,69)(48,52)(50,73)(51,71)(58,65)(59,81)(61,75)(62,67)(63,66)(64,82)(68,74)(76,77)(78,83)(79,80);(20,23)(21,29)(22,35)(24,47)(25,51)(26,43)(27,44)(28,53)(30,61)(31,64)(32,40)(33,59)(34,65)(36,72)(37,41)(38,70)(39,71)(42,50)(45,78)(46,79)(48,77)(49,80)(52,69)(54,57)(55,81)(56,82)(58,63)(60,83)(62,74)(66,68)(67,75)(73,76)646 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 6312);