Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23886 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#26196 |
| 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 | |
742 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 1216 |
A minimal faithful permutation representation — 4 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)(22,25)(23,27)(24,26)(28,29)(30,39)(31,41)(32,35)(33,38)(34,37)(36,43)(40,42);(20,22,24,23)(21,25,26,27)(28,30)(29,32)(31,37)(33,41)(34,40)(35,43)(36,42)(38,39);(20,23,24,22)(21,25,26,27)(28,31)(29,35)(30,38)(32,34)(33,42)(36,40)(37,41)(39,43);(28,32)(29,30)(31,34)(33,42)(35,38)(36,41)(37,40)(39,43)817 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 19184);