Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33522 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#33653 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C19 |
| prime radical | C19×#3061 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×#41×C19 ◁ C2×C19×#131 ◁ G | |
568 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)(20,21)(22,25)(23,24)(26,27)(28,29,34,39)(30,35,42,53)(31,37,33,49)(32,45,48,59)(36,54,56,41)(38,44,57,47)(40,50,43,52)(46,51,58,55);(21,24)(25,27)(28,30)(29,35)(31,43)(32,41)(33,40)(34,42)(36,45)(37,52)(38,51)(39,53)(44,58)(46,47)(48,54)(49,50)(55,57)(56,59);(20,22,23,26)(21,25,24,27)(28,30)(29,36)(31,40)(32,46)(33,43)(34,42)(35,45)(37,51)(38,52)(39,56)(41,47)(44,54)(48,58)(49,55)(50,57)(53,59);(28,31,34,33)(29,37,39,49)(30,40,42,43)(32,44,48,47)(35,50,53,52)(36,51,56,55)(38,45,57,59)(41,46,54,58)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26641);