Finite Group DatabasebetaFinite Group Databasebeta| order | 32128 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊(C251⋊C32) |
| Sylow | C251 ⋊ C4⋊C32 |
62 conjugacy classes of subgroups.
| transitive degree | μt(G) = 32128 |
Polycyclic presentation:
2^7,251|a^2=d,b^2=c,d^2=e,e^2=f,f^2=g,b^a=bc,h^a=h^2508080 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(32128, 2706);