Finite Group DatabasebetaFinite Group Databasebeta| order | 32128 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | #346×C251 ⋊ C2 |
| Sylow | C251 ⋊ #2177 |
172 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16064 |
Polycyclic presentation:
2^7,251|a^2=e,c^2=eg,d^2=fg,f^2=g,b^a=bd,c^a=cg,d^a=df,f^a=fg,h^a=h^250,d^b=df,f^b=fg,h^b=h^2505032 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32128, 6387);