Finite Group DatabasebetaFinite Group Databasebeta| order | 1728 |
| isoclinism | isoclinic class of AGL(1,𝔽9) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C32 · Schur multiplier (H2) = C2 |
| direct product | C3×#10593248 |
| derived | C32 ⋊ C2×C3×C32 |
| Sylow | C33 ⋊ C2×C32 |
98 conjugacy classes of subgroups.
| transitive degree | μt(G) = 192 |
216 conjugacy classes — view the full character table.
| maximal subgroup of | C3×#11772656 |
| maximal normal subgroup of | C3×#11772656 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1728, 32238);