Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| isoclinism | isoclinic class of AGL(1,𝔽9) |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C16 · Schur multiplier (H2) = C4 |
| direct product | C3×#10593254 |
| derived | C32 ⋊ C3×C4×C16 |
| Sylow | C33 ⋊ C4×C16 |
146 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 146 conjugacy classes of subgroups — too many to draw. Only its 66 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×PSU(3,𝔽2)⋊C16, C3×GO+(4,𝔽2)⋊C16, C3×C16×AGL(1,𝔽9) |
| maximal normal subgroup of | C3×PSU(3,𝔽2)⋊C16, C3×GO+(4,𝔽2)⋊C16, C3×C16×AGL(1,𝔽9) |
| maximal quotient of | C3×#11772656 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 32244);