Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of #3788 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C8 · Schur multiplier (H2) = C2×C3 |
| direct product | C5×C4⋊#622 |
| unambiguous semidirect product | C4⋊(C5×#622) |
| Hall | C32×C5 ⋊ C4⋊C8 |
| Sylow | C32 ⋊ C5×C4⋊C8 |
136 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 480 |
A minimal faithful permutation representation — 2 generators on 23 points:
(1,2,3,4,5)(6,8,11)(7,10,9)(12,13,14,15);(6,7)(8,10,11,9)(13,15)(16,17,18,20,19,21,22,23)180 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 2647);