Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C32 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C9×#585 ⋊ C3 |
| Sylow | #585 ⋊ 3−1+2 |
657 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 657 conjugacy classes of subgroups — too many to draw. Only its 163 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:
2^3,3^3,2^3|b^2=i,e^3=f,g^2=i,h^2=i,c^a=ci,e^d=ef,g^d=gh,h^d=g,h^g=hi182 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 30901);