Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C2×C42 |
| direct product | C19×#32769 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C19 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C19×#1999 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ C2×C19×#117 ◁ G | |
820 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)(20,21,23,24)(22,25,26,27)(28,29)(30,32)(31,33)(34,35)(36,37)(38,44)(39,41)(40,43)(42,46)(45,50)(47,49)(48,51);(21,24)(22,26)(28,30)(29,32)(31,34)(33,35)(37,41)(38,45)(40,47)(42,50)(44,51)(46,48);(22,26)(25,27)(29,33)(32,35)(36,38)(37,42)(39,46)(40,48)(41,44)(43,50)(45,47)(49,51);(20,22,23,26)(21,25,24,27)(30,34)(32,35)(37,41)(38,46)(43,49)(45,48)646 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 25757);