Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C27×C4 |
No aliases for this group.
| Fitting | C5×#2875 ⋊ C2 |
| Sylow | C5 ⋊ #60627 |
1998 conjugacy classes of subgroups.
| transitive degree | μt(G) = 640 |
Polycyclic presentation:
2^8,5|a^2=h,b^2=gh,c^2=f,f^2=h,g^2=h,b^a=bf,c^a=cg,f^a=fh,g^a=gh,i^a=i^4,c^b=ch,e^d=eh194 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1038961);