Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C8 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C5×C8×C4⋊C4 ⋊ C2 |
| Sylow | C5 ⋊ #20533 |
1122 conjugacy classes of subgroups.
| transitive degree | μt(G) = 640 |
Polycyclic presentation:
2^8,5|a^2=f,b^2=g,c^2=e,f^2=h,b^a=be,d^a=de,c^b=ce,i^d=i^4296 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 168296);