Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C23×C4 |
| direct product | C19×#16279 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C24×C19 | C24 |
| commutator, Frattini, cosocle | C24 | C24×C19 |
| LCS | G ▷ C24 ▷ C1 | |
| UCS | C1 ◁ C24×C19 ◁ G | |
1250 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 4864 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(21,23)(28,29,32,30)(31,34,35,33)(36,37)(38,41)(39,43)(40,42);(25,27)(29,30)(33,34)(36,38,40,43)(37,41,42,39);(24,25)(26,27)(28,30,32,29)(31,33,35,34)(36,38)(37,39)(40,43)(41,42);(20,21)(22,23)(28,31,32,35)(29,33,30,34)(36,39)(37,38)(40,41)(42,43)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 9267);