Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C8 |
| direct product | D5×#1715 |
| Fitting | C5×#1715 ⋊ C2 |
| Sylow | C5 ⋊ C2×#1715 |
1030 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
104 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#19745, #72221443, AGL(1,𝔽5)×#1715, … |
| maximal normal subgroup of | D5×#19745, #72221443, AGL(1,𝔽5)×#1715, … |
| maximal quotient of | C5⋊D5×#1715 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 157285);