Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8×C19 · Schur multiplier (H2) = C24×C4 |
| direct product | C19×#10797 |
| subgroup | G/H | |
|---|---|---|
| center | C23×C4×C19 | C23 |
| commutator | C22 | C2×C4×C8×C19 |
| Frattini, cosocle | C23×C4 | C23×C19 |
| socle, prime radical | C24×C19 | C22×C4 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C4×C19 ◁ G | |
918 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 4864 |
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)(24,25,26,27)(29,30)(32,33,35,38,37,39,36,34);(28,29,31,30)(32,34,36,39,37,38,35,33);(21,23)(28,30,31,29)2128 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 3785);