Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C9 · Schur multiplier (H2) = C24×C32 |
No aliases for this group.
| Fitting | C24×C3×C9 ⋊ C3 |
| Sylow | C24 ⋊ C32⋊C9 |
361 conjugacy classes of subgroups.
| transitive degree | μt(G) = 324 |
Polycyclic presentation:
3^4,2^4|b^3=c,b^a=bd,e^a=ef,f^a=e,g^a=gh,h^a=g168 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 1892);