Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | D5×#2177 |
| Fitting | C5×#2177 ⋊ C2 |
| Sylow | C5 ⋊ C2×#2177 |
798 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
128 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#2177, D5×#12067, #72242075, … |
| maximal normal subgroup of | AGL(1,𝔽5)×#2177, D5×#12067, #72242075, … |
| maximal quotient of | D5×#13658, C5⋊D5×#2177 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 322867);