Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C5×#2317 ⋊ C2 |
| Sylow | C5 ⋊ #23738 |
1098 conjugacy classes of subgroups.
| transitive degree | μt(G) = 640 |
Polycyclic presentation:
2^8,5|a^2=eh,b^2=ef,d^2=h,e^2=h,f^2=h,b^a=be,c^a=cf,i^a=i^4,c^b=cg,d^b=dh,e^b=eh,f^b=fh,i^b=i^4,e^c=eh,f^c=fh,i^c=i^4140 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 199447);