Finite Group DatabasebetaFinite Group Databasebeta| order | 1512 |
| isoclinism | isoclinic class of A4×C3⋊D3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C7 · Schur multiplier (H2) = C2×C3 |
| direct product | C7×A4×C3⋊D3 |
| unambiguous semidirect product | C3⋊(D3×C7×A4) |
| Fitting, socle | C22×C32×C7 ⋊ C2×C3 |
| derived | C22×C32 ⋊ C2×C3×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | A4×C3⋊D3 |
| commutator, cosocle, hypocenter | C22×C32 | C2×C3×C7 |
| Frattini | C1 | G |
| Fitting, socle | C22×C32×C7 | C2×C3 |
| LCS | G ▷ C22×C32 | |
| UCS | C1 ◁ C7 | |
176 conjugacy classes of subgroups.
| transitive degree | μt(G) = 252 |
168 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1512, 859);