Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23×C3 |
| unambiguous semidirect product | #10596577⋊C3 |
| Fitting | C22×C32×D4 ⋊ D3 |
718 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 718 conjugacy classes of subgroups — too many to draw. Only its 70 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:
2^3,3,2,3^2,2^2|b^2=e,c^a=ce,f^a=f^2,g^a=g^2,h^a=hi,c^b=ce,f^d=fg^2,h^f=i,i^f=hi95 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 30466);