Finite Group DatabasebetaFinite Group Databasebeta| order | 1008 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | Dic28⋊C9 |
| Hall | Dic28 ⋊ C9 |
| Hall | C7⋊C9 ⋊ Q16 |
| Sylow | C7 ⋊ C9×Q16 |
54 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1008 |
Polycyclic presentation:
2^2,3,2,3,2,7|a^2=f,b^2=df,c^3=e,d^2=f,b^a=bd,d^a=df,g^a=g^6,g^c=g^287 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1008, 11);