Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C22×C4 |
| direct product | C19×#32833 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C19 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C22×D4×C19 | C23 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ C19×#376 ◁ G | |
612 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)(20,21,23,25)(22,24,26,27)(28,29)(30,35)(31,33)(32,34)(36,37)(38,45)(39,48)(40,44)(41,43)(42,47)(46,51)(49,50);(20,22)(21,24)(23,26)(25,27)(28,30,32,31)(29,33,34,35)(38,46)(39,41)(42,50)(43,48)(45,51)(47,49);(21,25)(24,27)(29,34)(30,31)(36,38)(37,42)(39,46)(40,47)(41,49)(43,51)(44,45)(48,50);(22,26)(24,27)(28,31,32,30)(29,33,34,35)(36,39,40,41)(37,43,44,48)(38,46,47,49)(42,51,45,50)646 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 25821);