Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #6195⋊C9 |
| Sylow | C3×C9⋊C9 ⋊ D4 |
248 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
Polycyclic presentation:
2^2,3,2,3^4|b^2=d,c^3=e,f^3=h,b^a=bd,g^a=g^2,f^b=f^2h^2,h^b=h^2,f^c=fh^2153 conjugacy classes — view the full character table.
| maximal subgroup of | #72229019, D3×#611⋊C9 |
| maximal normal subgroup of | #72229019, D3×#611⋊C9 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 1169);