Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32×C5 · Schur multiplier (H2) = C2×C3 |
| direct product | C3×C5×2−1+4⋊C3 |
| unambiguous semidirect product | (C5×2−1+4)⋊C32 |
| unambiguous semidirect product | (C3×C5×2−1+4)⋊C3 |
| Fitting | C3×C5×2−1+4 ⋊ C3 |
| Hall | C5×2−1+4 ⋊ C32 |
| Sylow | 2−1+4 ⋊ C32×C5 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C3×C5 | C22×A4 |
| commutator, cosocle, hypocenter | Q8 | C22×C32×C5 |
| Frattini | C2 | C22×C3×C5×A4 |
| Fitting | C3×C5×2−1+4 | C3 |
| hypercenter | C3×C5×D4 | A4 |
| LCS | G ▷ Q8 | |
| UCS | C1 ◁ C2×C3×C5 ◁ C3×C5×D4 | |
236 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 236 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) = 240 |
285 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 5757);