Finite Group DatabasebetaFinite Group Databasebeta| order | 1440 |
| isoclinism | isoclinic class of D5×C22⋊A4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C24 |
| direct product | D5×C22⋊(C22⋊C9) |
| unambiguous semidirect product | C5⋊(C2×C22⋊(C22⋊C9)) |
| derived | C24×C5 ⋊ C2×C9 |
| Hall | C24×D5 ⋊ C9 |
| Sylow | C5 ⋊ C2×C22⋊(C22⋊C9) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | D5×C22⋊A4 |
| commutator, hypocenter | C24×C5 | C2×C9 |
| Fitting, socle, cosocle | C24×C3×C5 | C2×C3 |
| prime radical | C24×C3×D5 | C3 |
| LCS | G ▷ C24×C5 | |
| UCS | C1 ◁ C3 | |
564 conjugacy classes of subgroups.
| transitive degree | μt(G) = 180 |
96 conjugacy classes — view the full character table.
| maximal subgroup of | D5×(C22⋊A4)⋊C9, D5×#88881, D5×#88907, … |
| maximal normal subgroup of | D5×(C22⋊A4)⋊C9, D5×#88881, D5×#88907, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1440, 4579);