Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C5 ⋊ #7390 |
128 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 128 conjugacy classes of subgroups — too many to draw. Only its 40 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^8,5|a^2=d,c^2=eh,d^2=f,e^2=g,f^2=h,g^2=h,b^a=bc,c^a=ce,e^a=eg,g^a=gh,i^a=i^3,c^b=ceg,d^b=dg,e^b=egh,f^b=fh,g^b=gh,d^c=dh,i^d=i^456 conjugacy classes — view the full character table.
| maximal subgroup of | #72242212, #72242259, #72242266 |
| maximal normal subgroup of | #72242212, #72242259, #72242266 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1084472);