Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C9 · Schur multiplier (H2) = C3 |
| unambiguous semidirect product | (#41⋊C9)⋊C9 |
| Sylow | #41 ⋊ C9⋊C9 |
135 conjugacy classes of subgroups.
| transitive degree | μt(G) = 648 |
Polycyclic presentation:
2,3^4,2^3|a^2=h,b^3=e,c^3=d,f^2=h,g^2=h,c^b=ce,f^b=fg,g^b=f,g^f=gh186 conjugacy classes — view the full character table.
| maximal subgroup of | #72276069 |
| maximal normal subgroup of | #72276069 |
| maximal quotient of | #72276047 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 983);