Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C23 |
| direct product | C19×#29470 |
| 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 | |
700 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)(22,26)(23,24)(25,27)(28,29)(30,34)(31,33)(32,35)(36,37,41,46,42,47,40,45)(38,43,48,44,39,49,50,51);(21,24)(25,26)(28,30)(29,32)(31,35)(33,34)(36,38)(37,43)(39,42)(40,50)(41,48)(44,46)(45,51)(47,49);(30,35)(32,34)(36,39,42,38)(37,44,47,51)(40,50,41,48)(43,45,49,46);(20,22,23,27)(21,25,24,26)(29,33)(32,34)(36,40,42,41)(37,45,47,46)(38,48,39,50)(43,44,49,51)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 22458);