Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| isoclinism | isoclinic class of AGL(1,𝔽9) |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C82 · Schur multiplier (H2) = C8 |
| direct product | C3×C8×AGL(1,𝔽9) |
| Fitting | C33×C8 ⋊ C8 |
| derived | C32 ⋊ C3×C82 |
| Sylow | C33 ⋊ C82 |
178 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 178 conjugacy classes of subgroups — too many to draw. Only its 82 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 192 |
216 conjugacy classes — view the full character table.
| maximal subgroup of | C3×C8×AΓL(1,𝔽9), C3×C16×AGL(1,𝔽9), C3×AGL(1,𝔽9)⋊C16 |
| maximal normal subgroup of | C3×C8×AΓL(1,𝔽9), C3×C16×AGL(1,𝔽9), C3×AGL(1,𝔽9)⋊C16 |
| maximal quotient of | C3×C16×AGL(1,𝔽9) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 32240);