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×#33686 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C19 |
| prime radical | C19×#3176 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C19×#117 ◁ C19×#405 ◁ G | |
544 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)(29,34)(30,38)(32,43)(33,42)(35,49)(36,52)(39,57)(40,58)(41,56)(44,45)(46,50)(47,54)(51,53)(55,59);(21,24)(25,27)(28,29)(30,35)(31,34)(32,36)(33,37)(38,50)(39,46)(40,51)(41,47)(42,48)(43,54)(44,53)(45,55)(49,57)(52,56)(58,59);(28,30,31,39)(29,35,34,46)(32,44,41,58)(33,45,42,40)(36,53,47,59)(37,55,48,51)(38,56,57,43)(49,54,50,52);(20,22,23,26)(21,25,24,27)(29,34)(35,46)(36,47)(37,48)(49,50)(51,55)(52,54)(53,59)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26674);