Finite Group DatabasebetaFinite Group Databasebeta| order | 17536 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | M64×C137 ⋊ C2 |
| Sylow | C137 ⋊ #1401 |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8768 |
Polycyclic presentation:
2^7,137|a^2=d,c^2=g,d^2=e,e^2=f,f^2=g,b^a=bc,h^a=h^136,c^b=cg,d^b=dg,h^b=h^1362776 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17536, 2653);