Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×#10604121 |
| unambiguous semidirect product | D5⋊#2177 |
| Fitting | C2×C5×D16 ⋊ C4 |
| Sylow | C5 ⋊ C2×#2177 |
798 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 798 conjugacy classes of subgroups — too many to draw. Only its 192 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
86 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#2177, #72242155, #72242165, … |
| maximal normal subgroup of | AGL(1,𝔽5)×#2177, #72242155, #72242165, … |
| maximal quotient of | #72242155, C2×#72242333 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 1113842);