Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C5×#364 ⋊ C4 |
| Sylow | C5 ⋊ #13186 |
310 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 92 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^8,5|a^2=f,b^2=fg,c^2=e,d^2=g,e^2=h,g^2=h,b^a=bd,c^a=ce,d^a=dg,e^a=eh,g^a=gh,i^a=i^3,d^b=dg,f^b=fh,g^b=gh,i^b=i^2,i^f=i^474 conjugacy classes — view the full character table.
| maximal subgroup of | #72221504, #72221523, #72221537, … |
| maximal normal subgroup of | #72221504, #72221523, #72221537, … |
| maximal quotient of | #72223166 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1097500);