Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C43 · Schur multiplier (H2) = C22×C8 |
No aliases for this group.
| Fitting | C5×#322 ⋊ C4 |
| Sylow | C5 ⋊ #7846 |
582 conjugacy classes of subgroups; only the 244 normal subgroups are shown.
This group has 582 conjugacy classes of subgroups — too many to draw. Only its 244 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,b^2=e,c^2=f,d^2=g,e^2=h,c^a=cg,i^a=i^3,c^b=ch,i^c=i^2,i^d=i^4,i^f=i^4152 conjugacy classes — view the full character table.
| maximal subgroup of | #72221176, #72221430, #72221443, … |
| maximal normal subgroup of | #72221430, #72221443, AGL(1,𝔽5)×#1455, … |
| maximal quotient of | #72221176 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1085536);