Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2×C32 |
| unambiguous semidirect product | C4⋊(C3⋊((C3⋊D3)⋊C9)) |
| Fitting | C3×C4×C32⋊C9 ⋊ C2 |
| Sylow | C3×C32⋊C9 ⋊ D4 |
489 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 489 conjugacy classes of subgroups — too many to draw. Only its 87 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 216 |
Polycyclic presentation:
2^2,3,2,3^4|b^2=d,c^3=e,b^a=bd,f^a=f^2,g^a=g^2,h^a=h^2,g^c=gh225 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 1890);