Finite Group DatabasebetaFinite Group Databasebeta| order | 1944 |
| isoclinism | isoclinic class of #4207⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C8 · Schur multiplier (H2) = C32 |
| unambiguous semidirect product | #10619724⋊C3 |
| derived | C3×C9 ⋊ C32×C8 |
| Sylow | 3−1+4 ⋊ C8 |
455 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 455 conjugacy classes of subgroups — too many to draw. Only its 117 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:
2,3^2,2^2,3^3|a^2=d,d^2=e,g^3=h,f^a=f^2,g^a=g^2h^2,h^a=h^2,g^b=gh^2,f^c=fh^2220 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1944, 2271);