Finite Group DatabasebetaFinite Group Databasebeta| order | 32128 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C64×C251 ⋊ C2 |
| Sylow | C251 ⋊ SD128 |
38 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16064 |
Polycyclic presentation:
2^7,251|a^2=g,c^2=de,d^2=ef,e^2=fg,f^2=g,b^a=bc,c^a=cd,d^a=de,e^a=ef,f^a=fg,h^a=h^250,c^b=cd,d^b=de,e^b=ef,f^b=fg,h^b=h^2508035 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32128, 2726);