Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C5 · Schur multiplier (H2) = C22 |
| direct product | C5×#63964 |
| Hall | C32×C5 ⋊ C22⋊Q8 |
| Sylow | C32 ⋊ C5×C22⋊Q8 |
330 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 240 |
A minimal faithful permutation representation — 3 generators on 23 points:
(1,2,3,4,5)(6,7,8)(9,10,11)(13,15)(17,21)(20,23);(7,8)(13,15)(16,18,19,22)(17,20,21,23);(10,11)(12,13,14,15)(16,17)(18,20)(19,21)(22,23)240 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 3568);