Finite Group DatabasebetaFinite Group Databasebeta| order | 1008 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #1141⋊C9 |
| Hall | #1141 ⋊ C9 |
| Hall | C7⋊C9 ⋊ D8 |
| Sylow | C7 ⋊ C9×D8 |
66 conjugacy classes of subgroups.
| transitive degree | μt(G) = 504 |
Polycyclic presentation:
2^2,3,2,3,2,7|c^3=e,d^2=f,b^a=bd,d^a=df,g^a=g^6,d^b=df,g^c=g^278 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1008, 18);