Finite Group DatabasebetaFinite Group Databasebeta| order | 17536 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C137 ⋊ Q8×C16 |
134 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17536 |
Polycyclic presentation:
2^7,137|a^2=e,b^2=d,c^2=de,e^2=f,f^2=g,b^a=bd,h^a=h^10,h^c=h^127,h^e=h^100,h^f=h^136250 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17536, 21734);