Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C4 |
No aliases for this group.
| Sylow | C5 ⋊ #9892 |
432 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1280 |
Polycyclic presentation:
2^8,5|a^2=f,b^2=def,c^2=eg,d^2=gh,f^2=g,b^a=bd,c^a=ce,d^a=dg,d^b=dh,f^b=fh,i^b=i^4,i^c=i^4134 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 69667);