Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #6880⋊Q8 |
| Sylow | #6880 ⋊ Q8 |
90 conjugacy classes of subgroups.
| transitive degree | μt(G) = 216 |
Polycyclic presentation:
2^2,3,2,3^4|a^2=d,b^2=d,c^3=gh^2,e^3=h^2,f^3=h^2,b^a=bd,e^a=e^2h,f^a=f^2g,g^a=gh,h^a=h^2,e^c=ef,f^e=fg,g^e=gh97 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 396);