Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C5 ⋊ #23732 |
1098 conjugacy classes of subgroups.
| transitive degree | μt(G) = 640 |
Polycyclic presentation:
2^8,5|a^2=e,b^2=ef,c^2=h,e^2=h,f^2=h,b^a=be,c^a=cf,d^a=dh,c^b=cg,e^b=eh,f^b=fh,i^b=i^4,e^c=eh,f^c=fh140 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 199383);