Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#19051 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C19 |
| prime radical | C19×#3545 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
950 conjugacy classes of subgroups.
| minimal degree | μ(G) = 59 |
| transitive degree | μt(G) = 1216 |
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)(28,29,34,39)(30,40,43,52)(31,44,45,53)(32,38,33,37)(35,47,50,42)(36,48,51,46)(41,49,55,59)(54,56,58,57);(22,26)(24,27)(28,30)(29,35)(31,41)(32,47)(33,42)(34,43)(36,49)(37,52)(38,40)(39,50)(44,58)(45,55)(46,57)(48,56)(51,59)(53,54);(20,21)(22,27)(23,25)(24,26)(28,31)(29,36)(30,41)(32,46)(33,48)(34,45)(35,49)(37,44)(38,53)(39,51)(40,54)(42,56)(43,55)(47,57)(50,59)(52,58);(31,45)(36,51)(41,55)(44,53)(46,48)(49,59)(54,58)(56,57)646 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 12039);