Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C5 ⋊ C2×#1313 |
302 conjugacy classes of subgroups; only the 140 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 140 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=d,b^2=e,d^2=f,e^2=g,f^2=h,b^a=bf,e^a=eh,i^a=i^2,d^b=dh,i^c=i^4,i^d=i^4128 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#1313, #72242079, #72242119, … |
| maximal normal subgroup of | AGL(1,𝔽5)×#1313, #72242079, #72242119 |
| maximal quotient of | #72242096, #72242151, #72242194, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1093257);