Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C5×#518 ⋊ C4 |
| Sylow | C5 ⋊ #8534 |
1408 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 1408 conjugacy classes of subgroups — too many to draw. Only its 104 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^a=bd,c^a=ce,d^a=dg,i^a=i^2,e^b=eh,f^b=fg,i^b=i^4,d^c=dh,i^f=i^474 conjugacy classes — view the full character table.
| maximal subgroup of | #72243241 |
| maximal normal subgroup of | #72243241 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1088302);