Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C5 ⋊ #29132 |
710 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1280 |
Polycyclic presentation:
2^8,5|a^2=fg,b^2=g,c^2=h,d^2=eh,f^2=h,b^a=be,c^a=cf,d^a=deh,i^a=i^4,c^b=cg,f^c=fh158 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 269321);