Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of D5×C22⋊A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C24×C3 |
| direct product | C3×D5×C22⋊A4 |
| unambiguous semidirect product | C5⋊(C2×C3×C22⋊A4) |
| Fitting, socle | C24×C3×C5 ⋊ C2×C3 |
| derived | C24×C5 ⋊ C2×C32 |
| Hall | C24×D5 ⋊ C32 |
| Sylow | C5 ⋊ C2×C3×C22⋊A4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | D5×C22⋊A4 |
| commutator, cosocle, hypocenter | C24×C5 | C2×C32 |
| Frattini | C1 | G |
| Fitting, socle | C24×C3×C5 | C2×C3 |
| LCS | G ▷ C24×C5 | |
| UCS | C1 ◁ C3 | |
648 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, 5936);