Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #1343 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C2×C4 |
| direct product | C19×#11715 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C19 | #99 |
| commutator | C22×C4 | C22×C4×C19 |
| Frattini, cosocle | C2×C22⋊C4 | C23×C19 |
| socle | C22×C19 | C2×#99 |
| prime radical | C24×C19 | C2×D4 |
| LCS | G ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C19 ◁ C22×C4×C19 ◁ C2×C19×#117 ◁ G | |
468 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)(21,24,25,26)(28,29)(30,34)(31,38,39,33)(32,35)(36,42,43,40)(37,41);(20,21)(22,26)(23,25)(24,27)(29,33,35,38)(31,39)(34,40,41,42)(36,43);(28,30,32,37)(29,34,35,41)(31,36,39,43)(33,40,38,42)874 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 4703);