Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| isoclinism | isoclinic class of D3×AGL(1,ℤ/9) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C8 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | (C3⋊AGL(1,ℤ/9))⋊C8 |
| unambiguous semidirect product | ((C3⋊D9)⋊C8)⋊C3 |
| derived | C3×C9 ⋊ C2×C3×C8 |
| Sylow | C3×3−1+2 ⋊ C2×C8 |
190 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 51 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 72 |
Polycyclic presentation:
2^2,3,2^2,3^3|a^2=d,b^2=d,d^2=e,g^3=h,g^a=g^2h^2,h^a=h^2,f^b=f^2,g^c=gh^2120 conjugacy classes — view the full character table.
| maximal subgroup of | #72219866, #72219893, #72219901, … |
| maximal normal subgroup of | #72219893, #72219901, #72219928 |
| maximal quotient of | #72219866 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 1301);