Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C27 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊(D9⋊C27) |
| unambiguous semidirect product | D36⋊C27 |
| Fitting | C4×C9⋊C27 ⋊ C2 |
| Sylow | C9⋊C27 ⋊ D4 |
117 conjugacy classes of subgroups.
| transitive degree | μt(G) = 216 |
Polycyclic presentation:
2^2,3,2,3^4|b^2=d,c^3=e,e^3=f,g^3=h,b^a=bd,g^a=g^2h^2,h^a=h^2,g^c=gh^2279 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 374);