Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of D3×S5 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | ΓL(2,𝔽4)⋊C4 |
| derived | C3×A5 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D3×S5 |
| commutator, hypocenter | C3×A5 | C2×C4 |
| Fitting | C2×C3 | C2×S5 |
| socle, cosocle | C2×C3×A5 | C22 |
| prime radical | C2×ΓL(2,𝔽4) | C2 |
| LCS | G ▷ C3×A5 | |
| UCS | C1 ◁ C2 | |
209 conjugacy classes of subgroups; only the 16 normal subgroups are shown.
This group has 209 conjugacy classes of subgroups — too many to draw. Only its 16 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:
(2,5,3)(6,8,9,7)(10,11);(1,5,4,2)(6,7,9,8)(10,12,11)42 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 4600);