Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#18994 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C19 |
| prime radical | C19×#3153 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
936 conjugacy classes of subgroups.
| minimal degree | μ(G) = 59 |
| transitive degree | μt(G) = 1216 |
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)(25,27)(28,29)(30,40)(31,44)(32,39)(33,38)(34,37)(35,42)(36,45)(41,49)(43,52)(46,53)(47,50)(48,51)(54,56)(55,58)(57,59);(22,26)(24,27)(28,30)(29,35)(31,41)(32,47)(33,42)(34,43)(36,49)(37,50)(38,52)(39,40)(44,58)(45,56)(46,57)(48,55)(51,59)(53,54);(20,21)(22,27)(23,25)(24,26)(28,31,34,46)(29,36,37,51)(30,41,43,57)(32,45,33,48)(35,49,50,59)(38,44,39,53)(40,54,52,58)(42,55,47,56);(29,37)(35,50)(36,51)(38,39)(40,52)(44,53)(49,59)(54,58)646 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 11982);