Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C23×C3 |
| unambiguous semidirect product | #3830⋊A4 |
| Fitting | C22×C32×D4 ⋊ C2×C3 |
1122 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 1122 conjugacy classes of subgroups — too many to draw. Only its 81 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:
2^3,3,2^3,3^2|b^2=e,c^a=ce,h^a=h^2,i^a=i^2,c^b=ce,f^d=fg,g^d=f,h^d=hi80 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 30677);