Finite Group DatabasebetaFinite Group Databasebeta| order | 1512 |
| isoclinism | isoclinic class of D7×AGL(1,ℤ/9) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2 |
| direct product | Dic7×AGL(1,ℤ/9) |
| unambiguous semidirect product | D9⋊(C3×Dic7) |
| unambiguous semidirect product | (C7×AGL(1,ℤ/9))⋊C4 |
| derived | C7×C9 ⋊ C2×C3×C4 |
| Hall | C7×3−1+2 ⋊ C2×C4 |
| Sylow | 3−1+2 ⋊ C2×Dic7 |
| Sylow | C7 ⋊ C4×AGL(1,ℤ/9) |
102 conjugacy classes of subgroups.
| transitive degree | μt(G) = 252 |
100 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1512, 245);