Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of #157 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C16 · Schur multiplier (H2) = C2×C3 |
| direct product | C5×#63764 |
| derived, Sylow | C32 ⋊ C2×C5×C16 |
| Hall | C32×C5 ⋊ C2×C16 |
100 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 240 |
A minimal faithful permutation representation — 2 generators on 27 points:
(1,2,3,4,5)(6,8,11)(7,10,9)(12,14,16,23,17,15,22,24)(13,18,20,26,21,19,25,27);(6,7)(8,10,11,9)(12,13,15,19,16,20,24,27,17,21,14,18,22,25,23,26)240 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 2633);