Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #19186 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#19188 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#121 |
| commutator, Frattini, cosocle | C42 | C24×C19 |
| prime radical | C19×#532 | C22 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
714 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)(22,24)(23,26)(25,27)(28,29,33,37)(30,38,42,52)(31,35,43,49)(32,45,39,36)(34,46,48,41)(40,51,54,59)(44,56,53,50)(47,57,58,55);(28,30,39,46,33,42,32,41)(29,34,45,52,37,48,36,38)(31,40,53,57,43,54,44,55)(35,47,56,59,49,58,50,51);(21,24)(22,27)(25,26)(28,31)(29,35)(30,40)(32,44)(33,43)(34,47)(36,50)(37,49)(38,51)(39,53)(41,55)(42,54)(45,56)(46,57)(48,58)(52,59);(31,43)(35,49)(40,54)(44,53)(47,58)(50,56)(51,59)(55,57)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 12176);