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×#33586 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C19 |
| prime radical | C2×C19×#509 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C19×#117 ◁ C19×#405 ◁ G | |
716 conjugacy classes of subgroups.
| minimal degree | μ(G) = 55 |
| transitive degree | μt(G) = 1216 |
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)(24,25,29,34)(26,30,35,43)(27,31,40,47)(28,41,39,33)(32,48,46,38)(36,42,49,53)(37,52,50,45)(44,55,54,51);(20,21,22,23)(24,26)(25,30)(27,36)(28,37)(29,35)(31,42)(32,44)(33,45)(34,43)(38,51)(39,50)(40,49)(41,52)(46,54)(47,53)(48,55);(25,31)(27,38)(28,39)(30,42)(32,33)(34,47)(36,51)(37,50)(40,48)(41,46)(43,53)(44,45)(49,55)(52,54);(26,35)(30,43)(36,49)(37,50)(42,53)(44,54)(45,52)(51,55)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26574);