Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | #67⋊AGL(1,𝔽9) |
| Fitting | C22×C33 ⋊ C2×C8 |
| Sylow | C33 ⋊ C8×D4 |
338 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 96 |
Polycyclic presentation:
2^6,3^3|a^2=d,d^2=f,c^a=ce,h^a=h^2i^2,i^a=h^2,c^b=ce,g^b=g^2,h^d=h^2i,i^d=hi,h^f=h^2,i^f=i^269 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 46441);