Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Sylow | C5 ⋊ #21444 |
1436 conjugacy classes of subgroups; only the 232 normal subgroups are shown.
This group has 1436 conjugacy classes of subgroups — too many to draw. Only its 232 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 640 |
Polycyclic presentation:
2^8,5|a^2=g,d^2=g,g^2=h,b^a=be,c^a=cf,d^a=dh,i^a=i^3,c^b=ch,i^b=i^4,i^c=i^4,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, 1106411);