Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33764 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C23×C4 |
| direct product | C19×#33791 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C19 |
| prime radical | C19×#2186 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C19×#117 ◁ C19×#405 ◁ G | |
574 conjugacy classes of subgroups.
| minimal degree | μ(G) = 59 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 4 generators on 59 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21)(22,26)(23,25)(24,27)(29,35)(30,39)(31,34)(33,46)(36,50)(38,55)(40,52)(41,58)(42,57)(44,45)(47,48)(49,54)(51,59)(53,56);(20,22,23,27)(21,24,25,26)(28,29)(30,40)(31,43)(32,35)(33,38)(34,37)(36,42)(39,50)(41,51)(44,55)(45,49)(46,54)(47,59)(48,53)(52,57)(56,58);(22,27)(24,26)(28,30)(29,36)(31,41)(32,42)(33,47)(34,48)(35,40)(37,51)(38,56)(39,46)(43,53)(44,57)(45,58)(49,59)(50,55)(52,54);(21,25)(24,26)(28,31,32,34)(29,37,35,43)(30,41,42,48)(33,44,45,46)(36,51,40,53)(38,54,49,55)(39,47,57,58)(50,56,52,59)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26779);