Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of D45 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
| direct product | C2×C9⋊#672 |
| unambiguous semidirect product | (C2×C9)⋊#672 |
| derived, Hall | C5×C9 ⋊ C2×C16 |
| Sylow | C9 ⋊ C2×#672 |
| Sylow | C5 ⋊ C2×C9⋊C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C8 | D45 |
| commutator, hypocenter | C5×C9 | C2×C16 |
| Frattini | C3×C8 | C2×D15 |
| Fitting | C2×C5×C8×C9 | C2 |
| socle, prime radical | C22×C3×C5 | C3⋊C8 |
| cosocle | C5×C8×C9 | C22 |
| LCS | G ▷ C5×C9 | |
| UCS | C1 ◁ C2×C8 | |
84 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1440 |
384 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 171);