Finite Group DatabasebetaFinite Group Databasebeta| order | 1008 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C9 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | #1157⋊C9 |
| Hall | #1157 ⋊ C9 |
| Hall | C7⋊C9 ⋊ #41 |
| Sylow | C7 ⋊ C9×#41 |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 504 |
Polycyclic presentation:
2^3,3,2,3,7|b^2=e,d^3=f,c^a=ce,g^a=g^6,g^d=g^2114 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1008, 133);