Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #24289 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#26271 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | D42 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C2×C19×#135 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C22×C4×C19 ◁ G | |
752 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)(22,26)(23,24)(25,27)(28,29)(30,41)(31,47)(32,50)(33,39)(34,40)(35,44)(36,43)(37,52)(38,51)(42,57)(45,55)(46,58)(48,54)(49,59)(53,56);(21,24)(25,26)(28,30,33,44,34,46,51,45)(29,35,38,41,40,55,39,58)(31,32,43,52,49,53,48,42)(36,56,47,37,54,50,59,57);(28,31,33,43,34,49,51,48)(29,36,38,47,40,54,39,59)(30,42,44,32,46,52,45,53)(35,37,41,50,55,57,58,56);(20,22,23,27)(21,25,24,26)(28,32,51,42,34,53,33,52)(29,37,39,56,40,57,38,50)(30,43,45,31,46,48,44,49)(35,54,58,47,55,36,41,59)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 19259);