Finite Group DatabasebetaFinite Group Databasebeta| order | 16768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | (C2×D131)⋊C32 |
| Fitting | C2×C32×C131 ⋊ C2 |
| Sylow | C131 ⋊ C22⋊C32 |
82 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8384 |
Polycyclic presentation:
2^7,131|a^2=d,d^2=e,e^2=f,f^2=g,b^a=bc,h^b=h^1304240 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16768, 2647);