Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C24×C3 |
No aliases for this group.
| Fitting | C24×C33 ⋊ C3 |
| Sylow | C24 ⋊ AΣL(1,𝔽27) |
700 conjugacy classes of subgroups.
| transitive degree | μt(G) = 36 |
Polycyclic presentation:
3^4,2^4|b^a=bc,c^a=cd,e^a=ef,f^a=e,g^a=gh,h^a=g152 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 1900);