Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C33 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Fitting | Q8×C9⋊C9 ⋊ C3 |
| Sylow | Q8 ⋊ #6900 |
227 conjugacy classes of subgroups.
| transitive degree | μt(G) = 648 |
Polycyclic presentation:
3^5,2^3|a^3=e,b^3=e,c^3=d,f^2=h,g^2=h,b^a=be^2,f^a=fg,g^a=f,c^b=cd,g^f=gh135 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 1583);