Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C3 |
| unambiguous semidirect product | C4⋊(C3⋊(C3⋊(#41⋊C3))) |
610 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 610 conjugacy classes of subgroups — too many to draw. Only its 93 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:
2^2,3,2^3,3^2,2|a^2=i,b^2=d,e^2=i,f^2=i,b^a=bd,g^a=g^2,h^a=h^2,e^c=ef,f^c=e,f^e=fi147 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 39208);