Finite Group DatabasebetaFinite Group Databasebeta| order | 32128 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #435×C251 ⋊ C2 |
| Sylow | C251 ⋊ #3307 |
394 conjugacy classes of subgroups.
| transitive degree | μt(G) = 16064 |
Polycyclic presentation:
2^7,251|a^2=e,d^2=g,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^250,c^b=cg,d^b=de,f^c=fg,h^c=h^2503529 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32128, 16488);