Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C23 |
| direct product | C19×#29102 |
| 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 ◁ C4×C4⋊C4×C19 ◁ G | |
668 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)(22,26,27,25)(28,29,31,33)(30,34,35,32)(36,37)(38,41)(39,43)(40,44)(42,45)(46,51)(47,49)(48,50);(21,24)(25,26)(28,30,31,35)(29,32,33,34)(36,38,45,46,40,48,39,47)(37,41,42,51,44,50,43,49);(29,33)(32,34)(36,38,40,48)(37,41,44,50)(39,46,45,47)(42,49,43,51);(20,22,23,27)(21,25,24,26)(29,33)(32,34)(36,39,40,45)(37,42,44,43)(38,46,48,47)(41,49,50,51)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 22090);