Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C5×#3381 ⋊ C2 |
| Sylow | C5 ⋊ Q8×#135 |
1786 conjugacy classes of subgroups.
| transitive degree | μt(G) = 640 |
Polycyclic presentation:
2^8,5|a^2=f,b^2=f,d^2=f,e^2=h,g^2=h,b^a=bf,c^a=cg,g^a=gh,d^b=df,g^c=gh,i^d=i^4,i^e=i^4140 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1050030);