Finite Group DatabasebetaFinite Group Databasebeta| order | 17536 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C22⋊#17984138 |
| Sylow | C137 ⋊ C22⋊C32 |
82 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8768 |
Polycyclic presentation:
2^7,137|a^2=d,d^2=e,e^2=f,f^2=g,b^a=bc,h^a=h^100,h^d=h^1361168 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17536, 19623);