Finite Group DatabasebetaFinite Group Databasebeta| order | 1008 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #1131⋊C9 |
| Hall | #1131 ⋊ C9 |
| Hall | C7⋊C9 ⋊ M16 |
| Sylow | C7 ⋊ C9×M16 |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 504 |
Polycyclic presentation:
2^2,3,2,3,2,7|b^2=d,c^3=e,d^2=f,b^a=bf,g^a=g^6,g^c=g^2114 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1008, 8);