Finite Group DatabasebetaFinite Group Databasebeta| order | 1080 |
| isoclinism | isoclinic class of A4×D15 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C2 |
| direct product | D15×C22⋊C9 |
| unambiguous semidirect product | C3⋊(D5×C22⋊C9) |
| unambiguous semidirect product | C5⋊(D3×C22⋊C9) |
| unambiguous semidirect product | (C22×D15)⋊C9 |
| derived | C22×C3×C5 ⋊ C2×C9 |
| Sylow | C5 ⋊ D3×C22⋊C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | A4×D15 |
| commutator, hypocenter | C22×C3×C5 | C2×C9 |
| Fitting, socle, cosocle | C22×C32×C5 | C2×C3 |
| prime radical | C22×C3×D15 | C3 |
| LCS | G ▷ C22×C3×C5 | |
| UCS | C1 ◁ C3 | |
90 conjugacy classes of subgroups.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 180 |
108 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1080, 313);