Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C23×C4 |
| direct product | C19×#29505 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C19 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C19×#2011 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ C19×#376 ◁ G | |
822 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)(23,25)(24,27)(38,44)(39,45)(41,47)(43,48)(46,50)(49,51);(20,22,23,27)(21,24,25,26)(28,29)(30,33)(31,32)(34,35)(36,37)(38,41)(39,43)(40,42)(44,47)(45,48)(46,49)(50,51);(29,32)(33,35)(36,38,45,50,40,46,39,44)(37,41,48,51,42,49,43,47);(21,25)(24,26)(28,30,31,34)(29,33,32,35)(37,42)(41,49)(43,48)(47,51)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 22493);