Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of PGL(2,𝔽9) |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C22 |
| direct product | C2×PGL(2,𝔽9) |
| socle | C2×A6 ⋊ C2 |
| derived | A6 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, Fitting, hypercenter | C2 | PGL(2,𝔽9) |
| commutator, cosocle, hypocenter | A6 | C22 |
| Frattini | C1 | G |
| socle | C2×A6 | C2 |
| LCS | G ▷ A6 | |
| UCS | C1 ◁ C2 | |
78 conjugacy classes of subgroups.
| transitive degree | μt(G) = 20 |
22 conjugacy classes — view the full character table.
| maximal subgroup of | C4×PGL(2,𝔽9) |
| maximal normal subgroup of | C4×PGL(2,𝔽9) |
| maximal quotient of | C4×PGL(2,𝔽9) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 5843);