Finite Group DatabasebetaFinite Group Databasebeta| order | 1512 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C8 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #4430⋊C8 |
| Hall | #4430 ⋊ C8 |
| Hall | C7⋊C8 ⋊ 3−1+2 |
| Sylow | C7 ⋊ C8×3−1+2 |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 504 |
Polycyclic presentation:
2,3^2,2,3,2,7|a^2=d,b^3=e,d^2=f,g^a=g^6,c^b=ce,g^b=g^2124 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1512, 46);