Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C8 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | #10619833⋊C3 |
| Sylow | 3−1+4 ⋊ C8 |
196 conjugacy classes of subgroups.
| transitive degree | μt(G) = 216 |
Polycyclic presentation:
2,3^2,2^2,3^3|a^2=d,c^3=h^2,d^2=e,f^a=fg,g^a=fg^2h^2,c^b=ch^2,f^d=f^2,g^d=g^2h,g^f=gh124 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 2983);