Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C22×C4 |
| direct product | C19×#32845 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C19 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C22×D4×C19 | C23 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ C19×#376 ◁ G | |
590 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)(20,21,23,25)(22,24,26,27)(28,29)(30,34)(31,35)(32,33)(36,42)(37,40)(38,41)(39,43)(44,45,47,49)(46,52,54,50)(48,51,55,57)(53,58,56,59);(20,22)(21,24)(23,26)(25,27)(29,33)(31,38)(34,40)(36,39)(45,49)(46,53)(48,55)(50,58)(52,59)(54,56);(21,25)(24,27)(28,30,32,37)(29,34,33,40)(31,39,38,36)(35,43,41,42)(44,46,47,54)(45,50,49,52)(48,56,55,53)(51,58,57,59);(22,26)(24,27)(28,31,32,38)(29,35,33,41)(30,36,37,39)(34,42,40,43)(45,49)(46,54)(51,57)(53,56)646 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 25833);