Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | #88642⋊C3 |
| Sylow | C3×3−1+2 ⋊ #41 |
312 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 73 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:
2^3,3,2,3^3|b^2=e,c^2=e,g^3=h,b^a=be,f^a=f^2,c^b=ce,g^b=g^2h^2,h^b=h^2,g^d=gh^293 conjugacy classes — view the full character table.
| maximal subgroup of | #72219897, #72219953, #72219954, … |
| maximal normal subgroup of | #72219953, #72219954, #72219964 |
| maximal quotient of | #72219897 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 2285);