Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C19 · Schur multiplier (H2) = C23 |
| direct product | C19×#11472 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C19 | #99 |
| commutator | C23 | C22×C8×C19 |
| Frattini, cosocle | C2×C22⋊C4 | C23×C19 |
| socle | C22×C19 | C2×#99 |
| prime radical | C22×D4×C19 | C2×C4 |
| LCS | G ▷ C23 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C19 ◁ C22×C4×C19 ◁ C2×C4×D4×C19 ◁ G | |
488 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 3 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,23,26,24,27,22,25)(28,29)(30,36)(31,39,40,34)(32,35)(33,37,41,43)(38,42);(28,30,32,38)(29,33,35,41)(31,37,40,43)(34,36,39,42);(20,22,24,23)(21,25,27,26)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 4460);