Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C9 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | #5968⋊C9 |
754 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 754 conjugacy classes of subgroups — too many to draw. Only its 109 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 288 |
Polycyclic presentation:
2^3,3^2,2^2,3,2|b^2=i,d^3=e,f^2=i,g^2=i,c^a=ci,h^a=h^2,c^b=ci,f^d=fg,g^d=f,g^f=gi171 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 30701);