Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#19054 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C19 |
| prime radical | C19×#3150 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
926 conjugacy classes of subgroups.
| minimal degree | μ(G) = 59 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 4 generators on 59 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(21,24)(22,26)(25,27)(28,29)(30,40)(31,45)(32,37)(33,38)(34,39)(35,43)(36,47)(41,49)(42,50)(44,53)(46,51)(48,52)(54,56)(55,58)(57,59);(22,26)(24,27)(28,30)(29,35)(31,41)(32,42)(33,43)(34,44)(36,49)(37,40)(38,53)(39,50)(45,58)(46,55)(47,56)(48,57)(51,59)(52,54);(20,21)(22,27)(23,25)(24,26)(28,31,34,48)(29,36,39,51)(30,41,44,57)(32,47,33,46)(35,49,50,59)(37,52,38,45)(40,54,53,58)(42,56,43,55);(28,32,34,33)(29,37,39,38)(30,42,44,43)(31,46,48,47)(35,40,50,53)(36,45,51,52)(41,55,57,56)(49,58,59,54)646 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 12042);