Finite Group DatabasebetaFinite Group Databasebeta| order | 17536 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C137 ⋊ #1370 |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17536 |
Polycyclic presentation:
2^7,137|a^2=d,b^2=ce,c^2=e,d^2=f,f^2=g,b^a=bc,c^a=ce,h^a=h^127,h^d=h^100,h^f=h^136328 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17536, 21574);