Finite Group DatabasebetaFinite Group Databasebeta| order | 1512 |
| isoclinism | isoclinic class of A4×AGL(1,𝔽7) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C9 · Schur multiplier (H2) = C2×C3 |
| direct product | A4×D7⋊C9 |
| unambiguous semidirect product | (A4×D7)⋊C9 |
| derived | C22×C7 ⋊ C2×C3×C9 |
| Hall | C22×D7 ⋊ C3×C9 |
| Sylow | C7 ⋊ C2×C9×A4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | A4×AGL(1,𝔽7) |
| commutator, hypocenter | C22×C7 | C2×C3×C9 |
| Fitting, socle, cosocle | C22×C3×C7 | C2×C32 |
| prime radical | C3×A4×D7 | C3 |
| LCS | G ▷ C22×C7 | |
| UCS | C1 ◁ C3 | |
104 conjugacy classes of subgroups.
| transitive degree | μt(G) = 252 |
84 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1512, 455);