Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Sylow | C5 ⋊ #21756 |
1254 conjugacy classes of subgroups; only the 216 normal subgroups are shown.
This group has 1254 conjugacy classes of subgroups — too many to draw. Only its 216 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,c^2=h,g^2=h,b^a=be,c^a=cf,d^a=de,f^a=fh,i^a=i^2,c^b=ce,d^b=dh,g^c=gh,i^d=i^4,i^g=i^474 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1107260);