Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of D5×A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C32 · Schur multiplier (H2) = C24×C3 |
| direct product | C22×C3×D5×A4 |
| unambiguous semidirect product | C5⋊(C23×C3×A4) |
| unambiguous semidirect product | (C2×C5)⋊(C22×C3×A4) |
| Fitting, socle | C24×C3×C5 ⋊ C2×C3 |
| derived | C22×C5 ⋊ C23×C32 |
| Hall | C24×D5 ⋊ C32 |
| Sylow | C5 ⋊ C23×C3×A4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C3 | D5×A4 |
| commutator, cosocle, hypocenter | C22×C5 | C23×C32 |
| Frattini | C1 | G |
| Fitting, socle | C24×C3×C5 | C2×C3 |
| LCS | G ▷ C22×C5 | |
| UCS | C1 ◁ C22×C3 | |
840 conjugacy classes of subgroups; only the 168 normal subgroups are shown.
This group has 840 conjugacy classes of subgroups — too many to draw. Only its 168 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 180 |
192 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 5933);