Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C19 · Schur multiplier (H2) = C23×C4 |
| direct product | C19×#9080 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C19 | C2×C22⋊C4 |
| commutator | C23 | C22×C8×C19 |
| Frattini, cosocle | C23×C4 | C23×C19 |
| prime radical | C25×C19 | C2×C4 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ C22×C42×C19 ◁ G | |
736 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 3 generators on 39 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,23)(24,25,27,30,28,26,29,31)(32,33,37,38,36,39,35,34);(24,26,27,31,28,25,29,30)(32,34,37,39,36,38,35,33);(21,23)(32,35,36,37)(33,38,39,34)1216 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 2068);