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×#33732 |
| 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 | |
482 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)(20,21,23,25)(22,26,27,24)(28,29,31,34)(30,38,40,52)(32,45,43,58)(33,46,44,37)(35,49,47,41)(36,51,48,39)(42,57,56,54)(50,55,53,59);(20,22,23,27)(21,24,25,26)(29,34)(35,47)(36,48)(37,46)(38,52)(45,58)(50,53)(54,57);(28,30,39,55,33,42,43,49,31,40,51,59,44,56,32,41)(29,35,45,54,37,50,48,52,34,47,58,57,46,53,36,38);(30,40)(35,47)(38,52)(41,49)(42,56)(50,53)(54,57)(55,59)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26720);