Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C26×C4 |
No aliases for this group.
| Fitting | C2×C4×C5×C4⋊C4 ⋊ C2 |
| Sylow | C5 ⋊ #13820 |
2666 conjugacy classes of subgroups.
| transitive degree | μt(G) = 640 |
Polycyclic presentation:
2^8,5|a^2=g,b^2=h,c^2=fg,d^2=fg,b^a=be,c^a=cf,i^a=i^4,d^b=de,i^d=i^4260 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 91136);