Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C5 · Schur multiplier (H2) = C2×C3 |
| Fitting, Hall | C22×C5×Q8 ⋊ C32 |
| derived, Sylow | C22×Q8 ⋊ C32×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C5 | A42 |
| commutator, cosocle, hypocenter | C22×Q8 | C32×C5 |
| Frattini | C2 | C5×A42 |
| Fitting | C22×C5×Q8 | C32 |
| socle | C23×C5 | C3×A4 |
| LCS | G ▷ C22×Q8 | |
| UCS | C1 ◁ C2×C5 | |
118 conjugacy classes of subgroups; only the 28 normal subgroups are shown.
This group has 118 conjugacy classes of subgroups — too many to draw. Only its 28 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 120 |
140 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 4923);