Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#11143 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | #394 |
| commutator | C22×C4 | C22×C4×C19 |
| Frattini, cosocle | C23×C4 | C23×C19 |
| prime radical | C24×C19 | #41 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C23×C4×C19 ◁ G | |
838 conjugacy classes of subgroups.
| minimal degree | μ(G) = 55 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 3 generators on 55 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,23)(24,25,29,33,30,35,28,34)(26,36,40,48,39,47,38,31)(27,41,44,32,45,49,43,50)(37,52,54,51,42,46,53,55);(24,26,28,38,30,39,29,40)(25,31,33,36,35,48,34,47)(27,42,43,54,45,37,44,53)(32,46,49,55,50,52,41,51);(21,23)(24,27,30,45)(25,32,35,50)(26,37,39,42)(28,44,29,43)(31,46,48,52)(33,41,34,49)(36,51,47,55)(38,54,40,53)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 4131);