Finite Group DatabasebetaFinite Group Databasebeta| order | 1512 |
| isoclinism | isoclinic class of C3⋊D3×C22⋊ΓL(1,𝔽8) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C2×C3 |
| direct product | C3⋊D3×C22⋊ΓL(1,𝔽8) |
| unambiguous semidirect product | C3⋊(D3×C22⋊ΓL(1,𝔽8)) |
| Fitting, socle, derived | C22×C32×C7 ⋊ C2×C3 |
| Sylow | C7 ⋊ A4×C3⋊D3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C22×C32×C7 | C2×C3 |
| LCS | G ▷ C22×C32×C7 | |
| UCS | C1 | |
176 conjugacy classes of subgroups.
| transitive degree | μt(G) = 252 |
72 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1512, 861);