Finite Group DatabasebetaFinite Group Databasebeta| order | 32128 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | #322×C251 ⋊ C2 |
| Sylow | C251 ⋊ #1336 |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4016 |
Polycyclic presentation:
2^7,251|a^2=d,c^2=e,d^2=f,e^2=g,f^2=g,b^a=bc,c^a=ce,e^a=eg,h^a=h^250,c^b=ceg,d^b=dg,e^b=eg,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, 2487);