Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of D3×D5×A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C24 |
| Fitting, socle | C23×C3×C5 ⋊ C22×C3 |
| derived | C22×C3×C5 ⋊ C23×C3 |
| Sylow | C5 ⋊ C22×D3×A4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D3×D5×A4 |
| commutator, cosocle, hypocenter | C22×C3×C5 | C23×C3 |
| Frattini | C1 | G |
| Fitting, socle | C23×C3×C5 | C22×C3 |
| LCS | G ▷ C22×C3×C5 | |
| UCS | C1 ◁ C2 | |
732 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 732 conjugacy classes of subgroups — too many to draw. Only its 84 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 90 |
96 conjugacy classes — view the full character table.
| maximal subgroup of | D3×D5×#997, C2×D3×A4×AGL(1,𝔽5), C2×D3×D5×S4, … |
| maximal normal subgroup of | C2×D3×A4×AGL(1,𝔽5), C2×D3×D5×S4, C2×D3×A4⋊AGL(1,𝔽5) |
| maximal quotient of | C2×D5×A4×S4 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 5903);