Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10440 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C19 · Schur multiplier (H2) = C23 |
| direct product | C19×#10447 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | #394 |
| commutator, Frattini, cosocle | C2×C42 | C23×C19 |
| prime radical | C23×C19 | #123 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C2×C42×C19 ◁ G | |
408 conjugacy classes of subgroups.
| minimal degree | μ(G) = 59 |
| transitive degree | μt(G) = 2432 |
A minimal faithful permutation representation — 3 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)(23,25)(26,27)(28,29,33,37)(30,38,41,53)(31,42,45,35)(32,46,48,36)(34,47,50,40)(39,55,43,54)(44,52,59,57)(49,56,51,58);(21,24)(25,26)(28,30,33,41)(29,34,37,50)(31,43,45,39)(32,47,48,40)(35,51,42,49)(36,53,46,38)(44,56,59,58)(52,54,57,55);(21,25)(23,27)(24,26)(28,31,32,44,33,45,48,59)(29,35,36,52,37,42,46,57)(30,39,40,56,41,43,47,58)(34,49,38,54,50,51,53,55)703 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 3435);