Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C25×C4 |
| direct product | C19×#21232 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C19 | C22×D4 |
| commutator | C2×C4 | C23×C4×C19 |
| Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C24×C19 | C2×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ C2×C19×#117 ◁ G | |
1470 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)(21,23)(24,25,26,27)(28,29)(30,40)(31,45)(32,37)(33,38)(34,39)(35,43)(36,47)(41,49)(42,51)(44,50)(46,53)(48,52)(54,55)(56,58)(57,59);(20,21,22,23)(25,27)(28,30,32,43,34,44,33,42)(29,35,38,40,39,51,37,50)(31,41,46,56,48,57,47,55)(36,49,52,54,53,59,45,58);(28,31,32,46,34,48,33,47)(29,36,38,52,39,53,37,45)(30,41,43,56,44,57,42,55)(35,49,40,54,51,59,50,58);(28,32,34,33)(29,37,39,38)(30,42,44,43)(31,46,48,47)(35,40,51,50)(36,45,53,52)(41,55,57,56)(49,54,59,58)1216 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 14220);