Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | D3×D5×Dic6 |
| unambiguous semidirect product | (C3×D3×D5)⋊Q8 |
| Hall | C32×C5 ⋊ C22×Q8 |
| Sylow | C32 ⋊ C2×Q8×D5 |
| Sylow | C5 ⋊ C2×D3×Dic6 |
662 conjugacy classes of subgroups.
| transitive degree | μt(G) = 240 |
108 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 5215);