Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C22×C4 |
| direct product | C19×#13149 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C19 | C2×D8 |
| commutator | C2×C8 | C22×C4×C19 |
| Frattini, cosocle | C22×C8 | C23×C19 |
| prime radical | C22×D8×C19 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ C2×C42×C19 ◁ C2×C4×C8×C19 ◁ G | |
386 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 2432 |
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)(22,23)(24,25,27,26)(29,35)(30,37)(31,36)(32,41)(33,39)(38,43)(40,42);(24,26,27,25)(28,29,36,40,33,37,41,43,34,38,32,30,39,42,31,35);(21,23)(28,30,31,38,39,43,32,37,34,40,41,29,33,35,36,42)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 6137);