Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33517 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#33677 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C22×D8 |
| commutator, Frattini, cosocle | C2×C8 | C24×C19 |
| prime radical | C19×#466 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ C2×C4×C8×C19 ◁ G | |
548 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)(30,38)(31,34)(32,44)(33,47)(35,40)(36,46)(37,43)(39,54)(41,58)(42,55)(45,53)(48,52)(49,56)(50,57)(51,59);(21,24)(25,27)(29,34)(35,49)(36,50)(37,47)(38,54)(44,55)(51,53)(52,58);(28,30,31,39)(29,35,34,49)(32,45,42,59)(33,48,43,41)(36,52,50,58)(37,53,47,51)(38,55,54,44)(40,57,56,46);(20,22,23,26)(21,25,24,27)(30,39)(35,49)(38,54)(40,56)(41,48)(45,59)(51,53)(52,58)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 26665);