Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #18712 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#18719 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C19 |
| prime radical | C19×#532 | C22 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
928 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)(25,27)(28,29,34,39)(30,40,43,53)(31,36,45,51)(32,38,33,37)(35,47,49,42)(41,54,57,58)(44,52,46,50)(48,55,59,56);(22,26)(24,27)(28,30)(29,35)(31,41)(32,42)(33,47)(34,43)(36,48)(37,40)(38,53)(39,49)(44,55)(45,57)(46,56)(50,58)(51,59)(52,54);(20,21)(22,27)(23,25)(24,26)(28,31,34,45)(29,36,39,51)(30,41,43,57)(32,46,33,44)(35,48,49,59)(37,52,38,50)(40,54,53,58)(42,56,47,55);(28,32,34,33)(29,37,39,38)(30,42,43,47)(31,44,45,46)(35,40,49,53)(36,50,51,52)(41,55,57,56)(48,58,59,54)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 11707);