Finite Group DatabasebetaFinite Group Databasebeta| order | 1008 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #41⋊(C7⋊C9) |
| Hall | C7×#41 ⋊ C9 |
| Sylow | #41 ⋊ C7⋊C9 |
| Sylow | C7 ⋊ #41⋊C9 |
50 conjugacy classes of subgroups.
| transitive degree | μt(G) = 504 |
Polycyclic presentation:
2,3^2,2^2,7,2|a^2=g,b^3=c,d^2=g,e^2=g,d^b=de,e^b=d,f^b=f^2,e^d=eg102 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1008, 182);