Finite Group DatabasebetaFinite Group Databasebeta| order | 1512 |
| isoclinism | isoclinic class of #67356⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C4 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #67356⋊C4 |
| derived | C7×C9 ⋊ C2×C3×C4 |
| Hall | #4427 ⋊ C2×C4 |
| Sylow | C7 ⋊ C2×3−1+2⋊C4 |
106 conjugacy classes of subgroups.
| transitive degree | μt(G) = 252 |
Polycyclic presentation:
2^2,3,2,3,7,3|b^2=d,e^3=g,f^a=f^6,e^b=e^2g^2,g^b=g^2,e^c=eg,f^c=f^252 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1512, 111);