Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C23 |
| direct product | C19×#32795 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C19 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C24×C19 | C2×D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ C2×C19×#117 ◁ G | |
584 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)(22,24)(23,25)(26,27)(28,29,33,36)(30,37,31,34)(32,35,40,43)(38,42,39,41)(44,45,48,52)(46,53,55,50)(47,56,49,51)(54,59,57,58);(20,22)(21,24)(23,26)(25,27)(28,30,33,31)(29,34,36,37)(32,39,40,38)(35,42,43,41)(46,54)(47,49)(50,58)(51,56)(53,59)(55,57);(21,25)(24,27)(28,31,33,30)(29,34,36,37)(32,38,40,39)(35,42,43,41)(44,46)(45,50)(47,54)(48,55)(49,57)(51,59)(52,53)(56,58);(22,26)(24,27)(28,32,33,40)(29,35,36,43)(30,38,31,39)(34,41,37,42)(44,47,48,49)(45,51,52,56)(46,54,55,57)(50,59,53,58)646 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 25783);