Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33605 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#33749 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C19 |
| prime radical | C23×C19 | C2×D8 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ C2×C4×C8×C19 ◁ G | |
504 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)(28,29,33,37)(30,38,39,52)(31,43,45,58)(32,46,44,36)(34,47,48,41)(35,50,51,40)(42,57,55,54)(49,56,53,59);(21,24)(25,27)(30,39)(34,48)(38,52)(41,47)(42,55)(49,53)(54,57)(56,59);(28,30,40,56,32,42,45,47,33,39,50,59,44,55,31,41)(29,34,43,54,36,49,51,52,37,48,58,57,46,53,35,38);(20,22,23,26)(21,25,24,27)(30,39)(34,48)(38,52)(41,47)(42,55)(49,53)(54,57)(56,59)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26737);