Finite Group DatabasebetaFinite Group Databasebeta| order | 17536 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| unambiguous semidirect product | D137⋊#568 |
| Sylow | C137 ⋊ C2×#568 |
1460 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2192 |
Polycyclic presentation:
2^7,137|a^2=f,f^2=g,d^a=dg,h^a=h^100,c^b=cg,h^e=h^136,h^f=h^136748 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17536, 21502);