Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | #88422⋊C3 |
| Sylow | C3×3−1+2 ⋊ D8 |
198 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 43 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|b^2=de,d^2=e,f^3=h,b^a=bd,d^a=de,g^a=g^2,f^b=f^2h^2,h^b=h^2,f^c=fh^281 conjugacy classes — view the full character table.
| maximal subgroup of | #72219872, #72219914, #72219922, … |
| maximal normal subgroup of | #72219914, #72219922, #72219928 |
| maximal quotient of | #72219872 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 1311);