Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33758 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C23×C4 |
| direct product | C19×#33785 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C19 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ C2×C4×C8×C19 ◁ G | |
594 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)(22,26)(23,25)(24,27)(28,29)(30,40)(31,39)(32,35)(33,46)(34,37)(36,43)(38,48)(41,57)(42,56)(44,51)(45,53)(47,55)(49,54)(50,58)(52,59);(20,22,23,27)(21,24,25,26)(29,35)(36,50)(37,39)(38,51)(40,56)(46,53)(52,55)(54,57);(22,27)(24,26)(28,30)(29,36)(31,41)(32,42)(33,47)(34,49)(35,50)(37,52)(38,54)(39,55)(40,46)(43,48)(44,58)(45,59)(51,57)(53,56);(21,25)(24,26)(28,31,32,34)(29,37,35,39)(30,41,42,49)(33,44,45,48)(36,52,50,55)(38,53,51,46)(40,54,56,57)(43,47,58,59)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26773);