Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C22×C5×C22⋊C8 ⋊ C2 |
| Sylow | C5 ⋊ #21758 |
1914 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^8,5|a^2=g,f^2=h,b^a=be,c^a=cf,d^a=de,f^a=fh,i^a=i^4,c^b=ce,f^c=fh,i^c=i^4224 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 178574);