Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C9 · Schur multiplier (H2) = C1 |
| direct product | AGL(1,𝔽5)×Q8⋊C9 |
| unambiguous semidirect product | (Q8×AGL(1,𝔽5))⋊C9 |
| derived | C5×Q8 ⋊ C4×C9 |
| Hall | Q8×AGL(1,𝔽5) ⋊ C9 |
| Sylow | C5 ⋊ C4×Q8⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2×C3 | A4×AGL(1,𝔽5) |
| commutator, hypocenter | C5×Q8 | C4×C9 |
| Fitting | C3×C5×Q8 | C3×C4 |
| socle | C2×C3×C5 | C4×A4 |
| prime radical | C2×C3×D5 | C2×A4 |
| cosocle | C3×Q8×D5 | C2×C3 |
| LCS | G ▷ C5×Q8 | |
| UCS | C1 ◁ C2×C3 | |
98 conjugacy classes of subgroups.
| transitive degree | μt(G) = 360 |
105 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 1461);