Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | D72⋊A4 |
| Fitting | C22×C8×C9 ⋊ C2×C3 |
287 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 287 conjugacy classes of subgroups — too many to draw. Only its 41 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:
2^2,3,2^4,3^2|b^2=de,d^2=e,h^3=i,b^a=bd,d^a=de,h^a=h^2i^2,i^a=i^2,f^c=fg,g^c=f,h^c=hi^292 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 13198);