Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of C9⋊AGL(1,𝔽5) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
| direct product | C2×C9⋊#674 |
| unambiguous semidirect product | (C2×C9)⋊#674 |
| derived, Hall | C5×C9 ⋊ C2×C16 |
| Sylow | C9 ⋊ C2×#674 |
| Sylow | C5 ⋊ C2×C9⋊C16 |
84 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1440 |
168 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 302);