Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊(C3⋊(#41⋊C9)) |
| unambiguous semidirect product | #5577⋊C9 |
336 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 65 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 576 |
Polycyclic presentation:
2^2,3,2,3,2^2,3,2|a^2=i,b^2=d,c^3=e,f^2=i,g^2=i,b^a=bd,h^a=h^2,f^c=fg,g^c=f,g^f=gi189 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 13267);