Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C27 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C81⋊SL(2,𝔽3) |
| Fitting | Q8×C81 ⋊ C3 |
| Sylow | Q8 ⋊ C81⋊C3 |
53 conjugacy classes of subgroups.
| transitive degree | μt(G) = 648 |
Polycyclic presentation:
3^5,2^3|b^3=c,c^3=d,d^3=e,f^2=h,g^2=h,b^a=be,f^a=fg,g^a=f,g^f=gh279 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 221);