Finite Group DatabasebetaFinite Group Databasebeta| order | 17536 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C137 ⋊ #1313 |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 17536 |
Polycyclic presentation:
2^7,137|a^2=c,b^2=d,c^2=e,d^2=f,e^2=g,b^a=be,d^a=dg,h^a=h^37,c^b=cg,h^b=h^100,h^c=h^136,h^d=h^1361132 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17536, 19429);