Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C5 · Schur multiplier (H2) = C23×C3 |
| direct product | C3×C5×C22⋊SL(2,𝔽3) |
| unambiguous semidirect product | (C22×C3)⋊(C5×SL(2,𝔽3)) |
| unambiguous semidirect product | (C22×C3×C5)⋊SL(2,𝔽3) |
| Fitting | C22×C3×C5×Q8 ⋊ C3 |
| derived, Sylow | C22×Q8 ⋊ C32×C5 |
| Hall | C22×C5×Q8 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C5 | C22⋊A4 |
| commutator, cosocle, hypocenter | C22×Q8 | C32×C5 |
| Frattini | C2 | C3×C5×C22⋊A4 |
| Fitting | C22×C3×C5×Q8 | C3 |
| socle | C23×C3×C5 | A4 |
| LCS | G ▷ C22×Q8 | |
| UCS | C1 ◁ C2×C3×C5 | |
200 conjugacy classes of subgroups.
| transitive degree | μt(G) = 360 |
180 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 5758);