Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #88416⋊C3 |
| Sylow | C3×3−1+2 ⋊ SD16 |
184 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 184 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|a^2=e,b^2=d,d^2=e,g^3=h,b^a=bd,d^a=de,g^a=g^2h^2,h^a=h^2,f^b=f^2,g^c=gh^284 conjugacy classes — view the full character table.
| maximal subgroup of | #72219870, #72219901, #72219914, … |
| maximal normal subgroup of | #72219901, #72219914, #72219923 |
| maximal quotient of | #72219870 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 1305);