Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #11757788⋊C2 |
| Fitting | C22×C9⋊C9 ⋊ C2×C3 |
182 conjugacy classes of subgroups; only the 35 normal subgroups are shown.
This group has 182 conjugacy classes of subgroups — too many to draw. Only its 35 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:
2,3^3,2^2,3^2|c^3=d,g^3=h,g^a=g^2h^2,h^a=h^2,c^b=cd,e^b=ef,f^b=e,g^b=gh,g^c=gh^272 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 2536);