Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | C2×C4×C5×C22⋊C4 ⋊ C2 |
| Sylow | C5 ⋊ #34754 |
2182 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^8,5|a^2=h,b^2=g,e^2=f,b^a=bf,c^a=cg,c^b=ch,d^b=dh,i^b=i^4236 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 338599);