Finite Group DatabasebetaFinite Group Databasebeta| order | 1296 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C16 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | #732 ⋊ C16 |
62 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 432 |
Polycyclic presentation:
2,3,2^3,3^3|a^2=c,b^3=h,c^2=d,d^2=e,f^a=f^2,g^a=g^2h,f^b=fg,g^f=gh176 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1296, 39);