Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of C42⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5×C9 · Schur multiplier (H2) = C4 |
| direct product | C2×C5×C42⋊C9 |
| unambiguous semidirect product | (C2×C42)⋊(C5×C9) |
| unambiguous semidirect product | (C2×C42×C5)⋊C9 |
| derived | C42 ⋊ C2×C5×C9 |
| Hall | C2×C42×C5 ⋊ C9 |
| Sylow | C2×C42 ⋊ C5×C9 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C3×C5 | C42⋊C3 |
| commutator, hypocenter | C42 | C2×C5×C9 |
| Frattini | C22×C3 | C2×C5×A4 |
| Fitting | C2×C3×C42×C5 | C3 |
| socle, prime radical | C23×C3×C5 | A4 |
| cosocle | C3×C42 | C2×C3×C5 |
| LCS | G ▷ C42 | |
| UCS | C1 ◁ C2×C3×C5 | |
100 conjugacy classes of subgroups.
| transitive degree | μt(G) = 180 |
240 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 654);