Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of #700 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C8 · Schur multiplier (H2) = C2×C3 |
| direct product | C32×C4⋊#170 |
| unambiguous semidirect product | C4⋊(C32×#170) |
| Hall | C32×C5 ⋊ C4⋊C8 |
| Sylow | C5 ⋊ C32×C4⋊C8 |
228 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 1440 |
A minimal faithful permutation representation — 2 generators on 23 points:
(1,2,3)(7,8,9,11,10)(12,13,14,15);(4,5,6)(8,9,10,11)(13,15)(16,17,18,20,19,21,22,23)252 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 2572);