Finite Group DatabasebetaFinite Group Databasebeta| order | 4864 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23387 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C27 |
| direct product | C19×#23424 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C19 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C19 |
| prime radical | C22×C19×AGL(1,ℤ/8) | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C19 ◁ C2×C19×#117 ◁ G | |
2098 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)(22,23)(29,33)(30,36)(31,39)(35,40)(38,41)(42,43);(21,23)(24,25)(26,27)(28,29)(30,37)(31,40)(32,35)(33,39)(34,38)(36,43)(41,42);(25,27)(28,30,32,38)(29,34,35,37)(31,41,39,36)(33,42,40,43);(29,35)(33,40)(34,37)(42,43)988 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4864, 16412);