Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
No aliases for this group.
| Fitting | C5×H(7,𝔽2) ⋊ C2 |
| Sylow | C5 ⋊ #60399 |
5128 conjugacy classes of subgroups; only the 807 normal subgroups are shown.
This group has 5128 conjugacy classes of subgroups — too many to draw. Only its 807 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|b^a=bf,c^a=cg,i^a=i^4,g^b=gh,f^c=fh,e^d=eh188 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#60399, #72253584 |
| maximal normal subgroup of | D5×#60399, #72253584 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1036319);