Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#33667 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C19 | C2×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C19 |
| socle | C22×C19 | C22×D8 |
| prime radical | C2×C19×#135 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C19 ◁ C2×C42×C19 ◁ C2×C4×C8×C19 ◁ G | |
552 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)(22,25)(23,24)(26,27)(28,29,31,36)(30,39,40,34)(32,35,43,50)(33,46,44,38)(37,52,51,45)(41,53,56,47)(42,49,57,55)(48,58,54,59);(21,24)(25,27)(28,30,31,40)(29,34,36,39)(32,41,43,56)(33,42,44,57)(35,47,50,53)(37,48,51,54)(38,49,46,55)(45,58,52,59);(29,35)(32,45)(33,44)(34,47)(36,50)(37,38)(39,53)(41,58)(42,57)(43,52)(46,51)(48,49)(54,55)(56,59);(20,22,23,26)(21,25,24,27)1102 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26655);