Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33522 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#33590 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C19 |
| prime radical | C2×C19×#508 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C19×#117 ◁ C19×#405 ◁ G | |
694 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)(26,31,38,49)(27,33,29,45)(28,41,44,55)(32,50,52,37)(34,40,53,43)(36,46,39,48)(42,47,54,51);(20,21,22,23)(24,26)(25,31)(27,39)(28,37)(29,36)(30,38)(32,41)(33,48)(34,47)(35,49)(40,54)(42,43)(44,50)(45,46)(51,53)(52,55);(24,26)(25,32)(27,36)(28,42)(29,39)(30,38)(31,41)(33,47)(34,48)(35,52)(37,43)(40,50)(44,54)(45,51)(46,53)(49,55);(24,27,30,29)(25,33,35,45)(26,36,38,39)(28,40,44,43)(31,46,49,48)(32,47,52,51)(34,41,53,55)(37,42,50,54)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26578);