Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C5×#1852 ⋊ C2 |
| Sylow | C5 ⋊ #10394 |
772 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^8,5|c^2=d,e^2=g,b^a=bd,c^a=ce,e^a=eg,f^a=fh,i^a=i^4,c^b=cf,e^b=eh,i^b=i^4,e^c=eg116 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 72838);