Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C5 · Schur multiplier (H2) = C23×C3 |
| direct product | C3×C5×#997 |
| Fitting | C3×C5×H(5,𝔽2) ⋊ C3 |
| derived, Sylow | H(5,𝔽2) ⋊ C32×C5 |
| Hall | C5×H(5,𝔽2) ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, socle, hypercenter | C2×C3×C5 | C22⋊A4 |
| commutator, cosocle, hypocenter | H(5,𝔽2) | C32×C5 |
| Frattini | C2 | C3×C5×C22⋊A4 |
| Fitting | C3×C5×H(5,𝔽2) | C3 |
| LCS | G ▷ H(5,𝔽2) | |
| UCS | C1 ◁ C2×C3×C5 | |
228 conjugacy classes of subgroups.
| transitive degree | μt(G) = 120 |
165 conjugacy classes — view the full character table.
| derived subgroup of | #72230913, D5×C3⋊#5935, #72230966, … |
| maximal subgroup of | C3×D5×#997, C5×D3×#997, D15×#997, … |
| maximal normal subgroup of | C3×D5×#997, C5×D3×#997, D15×#997, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 5759);