Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #11855 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C19 · Schur multiplier (H2) = C24 |
| direct product | C19×#11886 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C2×#102 |
| commutator | C2×C8 | C22×C4×C19 |
| Frattini, cosocle | C22×C8 | C23×C19 |
| prime radical | C2×C19×#466 | C2 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ C23×C4×C19 ◁ C23×C8×C19 ◁ G | |
470 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)(22,26,27,24)(23,25)(28,29)(30,39)(31,34)(32,43)(33,38)(35,40)(36,42)(37,41);(20,22)(21,24)(23,27)(25,26)(29,34)(30,40)(31,42)(32,41)(35,43)(36,37)(38,39);(22,27)(24,26)(28,30,41,42,33,31,32,40)(29,35,43,34,38,36,37,39)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 4874);