Finite Group DatabasebetaFinite Group Databasebeta| order | 1008 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C9 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊(Dic7⋊C9) |
| unambiguous semidirect product | (C4⋊Dic7)⋊C9 |
| Hall | C4⋊Dic7 ⋊ C9 |
| Hall | C7⋊C9 ⋊ C4⋊C4 |
| Sylow | C7 ⋊ C9×C4⋊C4 |
78 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1008 |
Polycyclic presentation:
2^2,3,2^2,3,7|a^2=e,b^2=d,c^3=f,b^a=bd,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, 16);