Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33764 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#33828 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C19 |
| prime radical | C19×#2215 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C19×#117 ◁ C19×#405 ◁ G | |
488 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)(21,24)(22,26)(28,29)(30,39)(31,36)(32,35)(33,46)(34,40)(37,45)(38,44)(41,47)(42,49)(43,51)(48,57)(50,55)(52,59)(53,58)(54,56);(20,21)(22,25)(23,24)(26,27)(28,30,31,40)(29,34,36,39)(32,41,43,55)(33,42,44,56)(35,50,51,47)(37,48,52,53)(38,49,46,54)(45,58,59,57);(21,24)(25,27)(29,35)(30,40)(32,45)(33,44)(34,47)(36,51)(37,38)(39,50)(41,57)(43,59)(46,52)(48,54)(49,53)(55,58);(20,22,23,26)(21,25,24,27)(29,36)(30,40)(35,51)(37,52)(38,46)(41,55)(42,56)(57,58)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26816);