Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C5×#492 ⋊ C4 |
| Sylow | C5 ⋊ #23198 |
946 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 946 conjugacy classes of subgroups — too many to draw. Only its 192 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=g,b^2=eg,c^2=f,d^2=e,e^2=h,f^2=h,g^2=h,b^a=be,c^a=cf,f^a=fh,i^a=i^3,d^b=de,e^b=eh,g^b=gh,i^b=i^2,i^g=i^480 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#3291, #72221480, #72221552, … |
| maximal normal subgroup of | AGL(1,𝔽5)×#3291, #72221480, #72221552, … |
| maximal quotient of | #72223146, #72223531 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1112305);