Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22×C3 |
| unambiguous semidirect product | C4⋊(A4⋊#157) |
| Fitting | C22×C32×C4 ⋊ Dic3 |
374 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 36 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:
2^4,3^3,2^2|a^2=c,b^2=d,b^a=bd,e^a=e^2,f^a=fg,g^a=fg^2,h^a=hi,f^c=f^2,g^c=g^2,h^e=i,i^e=hi60 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 46714);