Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of PGL(2,𝔽9) |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| derived | A6 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, Fitting, hypercenter | C2 | PGL(2,𝔽9) |
| commutator, hypocenter | A6 | C4 |
| socle, prime radical, cosocle | C2×A6 | C2 |
| LCS | G ▷ A6 | |
| UCS | C1 ◁ C2 | |
55 conjugacy classes of subgroups.
| transitive degree | μt(G) = 20 |
Permutation generators:
(1,10,9,8,7,5,3,6,4,2)(11,14,12,13);(1,2,3)(4,5,7)(8,10,9)22 conjugacy classes — view the full character table.
| maximal subgroup of | #72224455, C4×PGL(2,𝔽9) |
| maximal normal subgroup of | #72224455, C4×PGL(2,𝔽9) |
| maximal quotient of | #72210859 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 4592);