Finite Group DatabasebetaFinite Group Databasebeta| order | 17536 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | Q16×C137 ⋊ C8 |
| Sylow | C137 ⋊ #1336 |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2192 |
Polycyclic presentation:
2^7,137|a^2=d,c^2=e,d^2=f,e^2=g,f^2=g,b^a=bc,c^a=ce,e^a=eg,h^a=h^127,c^b=ceg,d^b=dg,e^b=eg,h^b=h^136,h^d=h^100,h^f=h^136151 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17536, 21563);