Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of D32 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C5×C8 · Schur multiplier (H2) = C23 |
| direct product | C5×D32×C8 |
| Fitting | C32×C5×C8 ⋊ C22 |
| derived, Sylow | C32 ⋊ C22×C5×C8 |
| Hall | C32×C5 ⋊ C22×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5×C8 | D32 |
| commutator, hypocenter | C32 | C22×C5×C8 |
| Frattini | C4 | C2×C5×D32 |
| Fitting | C32×C5×C8 | C22 |
| socle | C2×C32×C5 | C22×C4 |
| prime radical | C2×C5×D32 | C4 |
| cosocle | C32×C4 | C23×C5 |
| LCS | G ▷ C32 | |
| UCS | C1 ◁ C5×C8 | |
326 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 128 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 240 |
360 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D32×AGL(1,𝔽41) |
| maximal quotient of | D32×AGL(1,𝔽41) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 3378);