Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C22×C4 |
| direct product | C19×#32780 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C19 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C24×C19 | C2×D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ C2×C19×#117 ◁ G | |
652 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)(20,21)(22,24)(23,25)(26,27)(28,29,32,31)(30,34,35,33)(36,37)(38,41)(39,43)(40,42)(44,48)(45,49)(46,50)(47,51);(20,22)(21,24)(23,26)(25,27)(28,30,32,35)(29,33,31,34)(38,44)(39,46)(41,48)(43,50)(45,47)(49,51);(21,25)(24,27)(29,31)(33,34)(36,38,40,45)(37,41,42,49)(39,47,46,44)(43,51,50,48);(22,26)(24,27)(28,31,32,29)(30,34,35,33)(37,42)(41,49)(43,50)(48,51)646 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 25768);