Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C16 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C5×C22⋊C16 ⋊ C4 |
| Sylow | C5 ⋊ C16×C22⋊C4 |
510 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^8,5|a^2=e,b^2=f,c^2=e,e^2=g,g^2=h,b^a=bd,i^a=i^3,i^b=i^3,i^c=i^2,i^e=i^4,i^f=i^4200 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1095999);