Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of S6 |
| 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 | S6 |
| commutator, hypocenter | A6 | C4 |
| socle, prime radical, cosocle | C2×A6 | C2 |
| LCS | G ▷ A6 | |
| UCS | C1 ◁ C2 | |
95 conjugacy classes of subgroups.
| transitive degree | μt(G) = 24 |
Permutation generators:
(1,5,6)(2,4)(7,9,10,8);(1,6,4,3,5,2)(7,8,10,9)22 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 4590);