Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of #6758 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×C3×C4⋊ΓL(1,𝔽16) |
| unambiguous semidirect product | D5⋊(C3×C4⋊Dic3) |
| Fitting | C2×C32×C4×C5 ⋊ C4 |
| Hall | C32×C5 ⋊ C2×C4⋊C4 |
| Sylow | C32 ⋊ C2×C4⋊AGL(1,𝔽5) |
| Sylow | C5 ⋊ C2×C3×C4⋊Dic3 |
422 conjugacy classes of subgroups.
| transitive degree | μt(G) = 240 |
180 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 5457);