Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C2×C42 |
| direct product | C19×#16211 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C19 | C24 |
| commutator, Frattini, cosocle | C24 | C24×C19 |
| prime radical | C25×C19 | C23 |
| LCS | G ▷ C24 ▷ C1 | |
| UCS | C1 ◁ C24×C19 ◁ G | |
1230 conjugacy classes of subgroups.
| minimal degree | μ(G) = 51 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 4 generators on 51 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(21,24)(22,26)(30,34)(33,35)(36,37)(38,41)(39,40)(42,43)(45,46)(47,51);(29,32)(33,35)(37,40)(38,42)(44,45,48,46)(47,50,51,49);(20,21)(22,25)(23,24)(26,27)(28,29,31,32)(30,33,34,35)(36,37)(38,41)(39,40)(42,43)(44,46,48,45)(47,50,51,49);(20,22,23,26)(21,25,24,27)(28,30)(29,33)(31,34)(32,35)(36,38,39,42)(37,41,40,43)(44,47)(45,49)(46,50)(48,51)1102 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 9199);