Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of (C24⋊C5)⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C22 |
| direct product | C9×(C24⋊C5)⋊C2 |
| Fitting | C24×C9 ⋊ D5 |
| derived | C24⋊C5 ⋊ C2×C9 |
129 conjugacy classes of subgroups.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 90 |
A minimal faithful permutation representation — 2 generators on 19 points:
(1,2,3,4,5,6,7,8,9)(11,13,15,16)(14,19,18,17);(10,11,14,17,13)(12,15,18,19,16)90 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 4570);