Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33758 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#33822 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C19 |
| prime radical | C19×#2218 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ C2×C4×C8×C19 ◁ G | |
496 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)(41,52)(42,49)(43,50)(47,55)(48,59)(51,58)(53,57)(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)(35,47,50,52)(37,48,51,53)(38,49,46,54)(45,57,58,59);(21,24)(25,27)(29,35)(32,45)(33,44)(34,47)(36,50)(37,38)(39,52)(41,57)(42,56)(43,58)(46,51)(48,49)(53,54)(55,59);(20,22,23,26)(21,25,24,27)(29,36)(34,39)(35,50)(37,51)(38,46)(47,52)(48,53)(49,54)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26810);