Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33517 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#33583 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C19 |
| prime radical | C2×C19×#135 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ C2×C4×C8×C19 ◁ G | |
702 conjugacy classes of subgroups.
| minimal degree | μ(G) = 55 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 4 generators on 55 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(21,23)(24,25,30,35)(26,36,39,53)(27,34,29,32)(28,41,44,49)(31,46,48,38)(33,40,51,43)(37,54,45,50)(42,52,55,47);(20,21,22,23);(24,26)(25,31)(27,37)(28,42)(29,45)(30,39)(32,47)(33,50)(34,52)(35,48)(36,41)(38,43)(40,46)(44,55)(49,53)(51,54);(24,27,30,29)(25,32,35,34)(26,37,39,45)(28,40,44,43)(31,47,48,52)(33,49,51,41)(36,50,53,54)(38,42,46,55)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26571);