Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C22 |
| direct product | C3×D5×ΓL(1,𝔽25) |
| Fitting | C32×C5×C8 ⋊ C22 |
| Hall | C32×C5 ⋊ C2×M16 |
| Sylow | C32 ⋊ D5×M16 |
| Sylow | C5 ⋊ C2×C3×ΓL(1,𝔽25) |
294 conjugacy classes of subgroups.
| transitive degree | μt(G) = 240 |
216 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 2709);