Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C5×#494 ⋊ C4 |
| Sylow | C5 ⋊ #21691 |
1062 conjugacy classes of subgroups; only the 244 normal subgroups are shown.
This group has 1062 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=g,b^2=e,c^2=f,d^2=gh,e^2=h,b^a=be,c^a=cf,e^a=eh,i^a=i^3,d^b=dh,i^d=i^2,i^g=i^486 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1107100);