Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C33 |
No aliases for this group.
| Fitting | C32×C8×C9 ⋊ C2 |
| Sylow | C32×C9 ⋊ D8 |
550 conjugacy classes of subgroups.
| transitive degree | μt(G) = 648 |
Polycyclic presentation:
2^4,3^4|b^2=cd,c^2=d,g^3=h,b^a=bc,c^a=cd,e^a=e^2,f^a=f^2,g^a=g^2h^2,h^a=h^2327 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 1719);