Finite Group DatabasebetaFinite Group Databasebeta| order | 1080 |
| isoclinism | isoclinic class of A4×C3⋊D15 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C2×C3 |
| direct product | A4×C3⋊D15 |
| unambiguous semidirect product | C3⋊(A4×D15) |
| unambiguous semidirect product | C5⋊(A4×C3⋊D3) |
| Fitting, socle, derived | C22×C32×C5 ⋊ C2×C3 |
| Sylow | C5 ⋊ A4×C3⋊D3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C22×C32×C5 | C2×C3 |
| LCS | G ▷ C22×C32×C5 | |
| UCS | C1 | |
176 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(1080, 552);