Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23 |
| direct product | C3×#67⋊Dic5 |
| unambiguous semidirect product | #67⋊(C3×Dic5) |
| Hall | C32×C5 ⋊ C4×D4 |
| Sylow | C32 ⋊ D4×Dic5 |
| Sylow | C5 ⋊ C3×#67⋊C4 |
410 conjugacy classes of subgroups.
| transitive degree | μt(G) = 240 |
198 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 3020);