Finite Group DatabasebetaFinite Group Databasebeta| order | 17536 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C137 ⋊ #1780 |
612 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8768 |
Polycyclic presentation:
2^7,137|a^2=f,f^2=g,b^a=bd,c^a=ce,h^a=h^100,c^b=cg,h^b=h^136,h^c=h^136,h^f=h^136724 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17536, 20335);