Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
| direct product | D5×#2008 |
| Fitting | C5×#2008 ⋊ C2 |
| Sylow | C5 ⋊ C2×#2008 |
2118 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
92 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#23882, D5×#23872, AGL(1,𝔽5)×#2008, … |
| maximal normal subgroup of | D5×#23882, D5×#23872, AGL(1,𝔽5)×#2008, … |
| maximal quotient of | #72223375 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 196557);