Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of #700 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C8 · Schur multiplier (H2) = C3 |
| direct product | C32×#3990 |
| Hall | C32×C5 ⋊ M32 |
| Sylow | C5 ⋊ C32×M32 |
156 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 720 |
A minimal faithful permutation representation — 2 generators on 27 points:
(1,2,3)(7,8,9,11,10)(12,14,16,23,17,15,22,24)(13,18,19,25,20,21,26,27);(4,5,6)(8,9,10,11)(12,13,15,18,16,19,24,25,17,20,14,21,22,26,23,27)252 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 2559);