Finite Group DatabasebetaFinite Group Databasebeta| order | 1512 |
| isoclinism | isoclinic class of D3×AGL(1,𝔽7) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C9 · Schur multiplier (H2) = C2 |
| direct product | D3×Dic7⋊C9 |
| unambiguous semidirect product | (D3×Dic7)⋊C9 |
| unambiguous semidirect product | (D3×C7⋊C9)⋊C4 |
| derived | C3×C7 ⋊ C2×C4×C9 |
| Hall | C3×C7⋊C9 ⋊ C2×C4 |
| Sylow | C7 ⋊ C4×D3×C9 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2×C3 | D3×AGL(1,𝔽7) |
| commutator, hypocenter | C3×C7 | C2×C4×C9 |
| Fitting, socle, cosocle | C2×C32×C7 | C22×C3 |
| prime radical | C2×C3×D3×C7 | C2×C3 |
| LCS | G ▷ C3×C7 | |
| UCS | C1 ◁ C2×C3 | |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 504 |
126 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1512, 119);