Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of D5×C42⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C4 |
| direct product | D5×C42⋊C9 |
| unambiguous semidirect product | C5⋊(C2×C42⋊C9) |
| unambiguous semidirect product | (C42×D5)⋊C9 |
| derived | C42×C5 ⋊ C2×C9 |
| Hall | C42×D5 ⋊ C9 |
| Sylow | C5 ⋊ C2×C42⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D5×C42⋊C3 |
| commutator, hypocenter | C42×C5 | C2×C9 |
| Frattini | C22×C3 | D5×A4 |
| Fitting, cosocle | C3×C42×C5 | C2×C3 |
| socle | C22×C3×C5 | C2×A4 |
| prime radical | C22×C3×D5 | A4 |
| LCS | G ▷ C42×C5 | |
| UCS | C1 ◁ C3 | |
100 conjugacy classes of subgroups.
| transitive degree | μt(G) = 180 |
96 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 262);