Finite Group DatabasebetaFinite Group Databasebeta| order | 1512 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Hall | C3×C7×C9 ⋊ Q8 |
| Sylow | C3×C9 ⋊ Dic14 |
| Sylow | C7 ⋊ #6226 |
120 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1512 |
Polycyclic presentation:
2^3,3^2,7,3|a^2=c,b^2=c,e^3=g,b^a=bc,d^a=d^2,e^a=e^2g^2,f^a=f^6,g^a=g^2381 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1512, 404);