Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| isoclinism | isoclinic class of C3⋊#5450 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C3⋊#10589552 |
| unambiguous semidirect product | #5594⋊C9 |
| derived | C24×C3 ⋊ C22×C9 |
283 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 283 conjugacy classes of subgroups — too many to draw. Only its 39 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:
2^2,3^2,2^4,3|c^3=d,e^a=eg,f^a=fgh,i^a=i^2,e^b=egh,f^b=fh,e^c=ef,f^c=e,g^c=h,h^c=gh81 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 13284);