Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C5×#1400 ⋊ C2 |
| Sylow | C5 ⋊ #7337 |
154 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 45 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^8,5|a^2=d,c^2=h,d^2=f,f^2=g,g^2=h,b^a=bc,c^a=ce,e^a=eh,c^b=ch,d^b=deh,i^b=i^4,d^c=dh140 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 56912);