Finite Group DatabasebetaFinite Group Databasebeta| order | 32128 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C251 ⋊ #2165 |
128 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4016 |
Polycyclic presentation:
2^7,251|a^2=e,c^2=d,e^2=f,f^2=g,b^a=bd,c^a=cf,d^a=dg,h^a=h^250,e^b=eg,e^c=eg5032 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32128, 6322);