Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33522 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#33633 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C19 |
| prime radical | C2×C19×#135 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C19×#117 ◁ C19×#405 ◁ G | |
534 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)(22,26,27,24)(28,29)(30,35)(31,37)(32,45)(33,49)(34,39)(36,41)(38,47)(40,50)(42,53)(43,52)(44,56)(46,51)(48,59)(54,58)(55,57);(20,22,23,27)(21,24,25,26)(28,30)(29,35)(31,43)(32,41)(33,40)(34,42)(36,45)(37,52)(38,51)(39,53)(44,58)(46,47)(48,57)(49,50)(54,56)(55,59);(28,30)(29,36)(31,40)(32,46)(33,43)(34,42)(35,45)(37,51)(38,52)(39,55)(41,47)(44,57)(48,58)(49,54)(50,56)(53,59);(28,31,34,33)(29,37,39,49)(30,40,42,43)(32,44,48,47)(35,50,53,52)(36,51,55,54)(38,45,56,59)(41,46,57,58)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26621);