Finite Group DatabasebetaFinite Group Databasebeta| order | 32128 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C2×#126×C251 ⋊ C2 |
| Sylow | C251 ⋊ #3564 |
936 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8032 |
Polycyclic presentation:
2^7,251|a^2=g,c^2=f,d^2=fg,b^a=bf,c^a=cg,d^a=dg,e^a=ef,h^a=h^250,c^b=cg,d^b=df3538 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32128, 19134);