Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C2×C5×#117 ⋊ C4 |
| Sylow | C5 ⋊ C2×#1733 |
2270 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^8,5|a^2=f,b^2=g,e^2=h,b^a=be,e^a=eh,g^a=gh,c^b=ch,i^b=i^2,i^d=i^4,i^g=i^4128 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1103424);