Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#18996 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C19 |
| prime radical | C19×#3529 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
948 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)(28,29,34,39)(30,40,44,50)(31,45,47,53)(32,38,33,37)(35,42,51,43)(36,48,52,46)(41,49,57,59)(54,56,58,55);(22,26)(24,27)(28,30)(29,35)(31,41)(32,42)(33,43)(34,44)(36,49)(37,50)(38,40)(39,51)(45,58)(46,55)(47,57)(48,56)(52,59)(53,54);(20,21)(22,27)(23,25)(24,26)(28,31)(29,36)(30,41)(32,46)(33,48)(34,47)(35,49)(37,45)(38,53)(39,52)(40,54)(42,55)(43,56)(44,57)(50,58)(51,59);(28,32,34,33)(29,37,39,38)(30,42,44,43)(31,46,47,48)(35,50,51,40)(36,45,52,53)(41,55,57,56)(49,58,59,54)646 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 11984);