Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C22 |
No aliases for this group.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D3×S5 |
| commutator, socle, cosocle | C2×C3×A5 | C22 |
| Fitting | C2×C3 | C2×S5 |
| hypocenter | C3×A5 | D4 |
| LCS | G ▷ C2×C3×A5 ▷ C3×A5 | |
| UCS | C1 ◁ C2 | |
223 conjugacy classes of subgroups; only the 14 normal subgroups are shown.
This group has 223 conjugacy classes of subgroups — too many to draw. Only its 14 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 60 |
Permutation generators:
(1,4,2)(3,5)(6,7,9,8)(11,12);(1,5,2,3)(6,7)(8,9)(10,12,11)33 conjugacy classes — view the full character table.
| maximal subgroup of | D3×C22⋊S5 |
| maximal normal subgroup of | D3×C22⋊S5 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 4605);