Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
No aliases for this group.
| Fitting | C2×C5×B(4,𝔽2) ⋊ C2 |
| Sylow | C5 ⋊ #60399 |
5128 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^8,5|b^a=bf,c^a=cg,g^b=gh,f^c=fh,e^d=eh,i^e=i^4122 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#60399, #72253568, #72253602 |
| maximal normal subgroup of | D5×#60399, #72253568, #72253602 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1036316);