Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #11692 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C23 |
| direct product | C19×#11698 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#99 |
| commutator | C22×C4 | C22×C4×C19 |
| Frattini, cosocle | C2×C4⋊C4 | C23×C19 |
| prime radical | C2×C19×#121 | C4 |
| LCS | G ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C24×C19 ◁ C22×C4⋊C4×C19 ◁ G | |
514 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 3 generators on 43 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)(28,29,31,35,32,34,39,42)(30,36,38,43,37,33,40,41);(21,24)(22,27)(25,26)(28,30)(29,33)(31,38)(32,37)(34,36)(35,43)(39,40)(41,42);(30,37)(33,36)(38,40)(41,43)760 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 4686);