Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| automorphism | ? |
| homology | Abelianization (H1) = C33 · Schur multiplier (H2) = C32×C4 |
No aliases for this group.
| Fitting | C3×C42×C9 ⋊ C3 |
| Sylow | C42 ⋊ #737 |
139 conjugacy classes of subgroups.
| transitive degree | μt(G) = 108 |
Polycyclic presentation:
3^4,2^4|b^3=d,e^2=g,f^2=gh,c^a=cd,e^a=ef,f^a=egh,g^a=h,h^a=gh168 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 1499);