Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C9 · Schur multiplier (H2) = C32 |
| unambiguous semidirect product | (C9⋊SL(2,𝔽3))⋊C9 |
| Fitting | Q8×C9⋊C9 ⋊ C3 |
| Sylow | Q8 ⋊ C9×3−1+2 |
239 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 239 conjugacy classes of subgroups — too many to draw. Only its 85 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 648 |
Polycyclic presentation:
3^5,2^3|b^3=e,c^3=d,f^2=h,g^2=h,b^a=be,f^a=fg,g^a=f,c^b=ce,g^f=gh231 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 1587);