Finite Group DatabasebetaFinite Group Databasebeta| order | 1512 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C32 |
| unambiguous semidirect product | Dic14⋊H(3,𝔽3) |
| unambiguous semidirect product | (C3×ΓL(1,𝔽8)⋊Q8)⋊C3 |
| Hall | C7⋊H(3,𝔽3) ⋊ Q8 |
| Hall | Dic14 ⋊ H(3,𝔽3) |
| Sylow | C7 ⋊ Q8×H(3,𝔽3) |
132 conjugacy classes of subgroups.
| transitive degree | μt(G) = 504 |
Polycyclic presentation:
2^2,3^2,2,3,7|a^2=e,b^2=e,b^a=be,g^a=g^6,d^c=df,g^c=g^291 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1512, 162);