Finite Group DatabasebetaFinite Group Databasebeta| order | 17536 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C137 ⋊ #1400 |
74 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4384 |
Polycyclic presentation:
2^7,137|a^2=d,d^2=e,e^2=f,f^2=g,b^a=bc,c^a=cg,h^a=h^127,d^b=dg,h^b=h^136,h^d=h^100,h^e=h^136316 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17536, 21605);