Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C5 ⋊ #12067 |
246 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 246 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 640 |
Polycyclic presentation:
2^8,5|a^2=e,c^2=efh,d^2=f,e^2=g,f^2=h,b^a=bd,c^a=cf,d^a=df,f^a=fh,i^a=i^2,d^b=dfh,e^b=eh,f^b=fh,d^c=dh,i^c=i^3,i^e=i^468 conjugacy classes — view the full character table.
| maximal subgroup of | #72242075, #72253161 |
| maximal normal subgroup of | #72242075 |
| maximal quotient of | #72242266, #72242269, #72253161 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1095545);