Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #10619679⋊C3 |
| Fitting | C22×#6909 ⋊ C2 |
| Sylow | #6909 ⋊ D4 |
416 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 57 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 108 |
Polycyclic presentation:
2^2,3,2,3^4|b^a=bd,e^a=e^2,f^a=f^2,g^a=gh^2,h^a=h^2,f^c=fh^2,f^e=fg,g^e=gh97 conjugacy classes — view the full character table.
| maximal subgroup of | #72228545, D4×#4183⋊C3, #72259864, … |
| maximal normal subgroup of | D4×#4183⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 2106);