Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of AGL(1,𝔽9) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5×C8 · Schur multiplier (H2) = C23 |
| direct product | C22×C5×AGL(1,𝔽9) |
| Fitting, socle | C22×C32×C5 ⋊ C8 |
| derived, Sylow | C32 ⋊ C22×C5×C8 |
| Hall | C32×C5 ⋊ C22×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C5 | AGL(1,𝔽9) |
| commutator, hypocenter | C32 | C22×C5×C8 |
| Frattini | C1 | G |
| Fitting, socle | C22×C32×C5 | C8 |
| prime radical | C22×C5×C3⋊D3 | C4 |
| cosocle | #157 | C23×C5 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C22×C5 | |
184 conjugacy classes of subgroups.
| transitive degree | μt(G) = 180 |
180 conjugacy classes — view the full character table.
| maximal subgroup of | C22×C5×AΓL(1,𝔽9), C22×C3×C5×AGL(1,𝔽9) |
| maximal normal subgroup of | C22×C5×AΓL(1,𝔽9), C22×C3×C5×AGL(1,𝔽9) |
| maximal quotient of | C22×C3×C5×AGL(1,𝔽9) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 5910);