Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C19 · Schur multiplier (H2) = C24×C4 |
| direct product | C19×#14040 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C19 | C24 |
| commutator | C23 | C23×C4×C19 |
| Frattini, cosocle | C24 | C24×C19 |
| prime radical | C25×C19 | C23 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C24×C19 ◁ G | |
1862 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 2432 |
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)(24,25,27,26)(28,29,31,32)(30,34,35,33)(36,37,40,43)(38,42,39,41);(24,26,27,25)(29,32)(33,34)(36,38,40,39)(37,41,43,42);(20,21)(22,23)(28,29)(30,33)(31,32)(34,35)(36,39,40,38)(37,42,43,41);(28,30)(29,33)(31,35)(32,34)(36,37)(38,41)(39,42)(40,43)1444 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 7028);