Finite Group DatabasebetaFinite Group Databasebeta| order | 32128 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C251 ⋊ #2253 |
116 conjugacy classes of subgroups.
| transitive degree | μt(G) = 32128 |
Polycyclic presentation:
2^7,251|a^2=d,b^2=dg,c^2=ef,e^2=fg,f^2=g,b^a=bd,c^a=ce,e^a=ef,f^a=fg,h^c=h^2502788 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32128, 6786);