Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33830 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#33889 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C19 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C4×D4×C19 ◁ C8×D4×C19 ◁ G | |
574 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)(20,21,23,25)(22,26,27,24)(28,29)(30,34)(31,35)(32,45)(33,36)(37,42)(38,43)(39,47)(40,50)(41,57)(44,51)(46,53)(48,56)(49,54)(52,58)(55,59);(20,22)(21,24)(23,27)(25,26)(28,30)(29,34)(31,40)(32,41)(33,39)(35,50)(36,47)(37,48)(38,49)(42,56)(43,54)(44,53)(45,57)(46,51)(52,59)(55,58);(29,35)(30,39)(31,42)(32,43)(34,46)(36,51)(37,38)(40,55)(44,58)(45,52)(47,50)(48,57)(49,59)(53,56);(22,27)(24,26)(29,36)(34,47)(35,51)(37,52)(38,45)(46,50)(48,59)(49,57)817 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26877);