Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C8×C32⋊C9 ⋊ C2 |
| Sylow | C32⋊C9 ⋊ D8 |
217 conjugacy classes of subgroups.
| transitive degree | μt(G) = 144 |
Polycyclic presentation:
2^4,3^4|b^2=cd,c^2=d,f^3=h,b^a=bc,c^a=cd,e^a=e^2,f^a=f^2h^2,h^a=h^2,f^e=fg141 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 455);