Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of D32 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C5 · Schur multiplier (H2) = C26 |
| direct product | C22×C5×D3×Dic3 |
| derived, Sylow | C32 ⋊ C23×C4×C5 |
| Hall | C32×C5 ⋊ C23×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23×C5 | D32 |
| commutator, hypocenter | C32 | C23×C4×C5 |
| Frattini | C2 | C22×C5×D32 |
| Fitting, socle | C23×C32×C5 | C22 |
| prime radical | C23×C3×C5×D3 | C2 |
| cosocle | C2×C32 | C24×C5 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C23×C5 | |
998 conjugacy classes of subgroups; only the 456 normal subgroups are shown.
This group has 998 conjugacy classes of subgroups — too many to draw. Only its 456 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 480 |
360 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 5651);