Finite Group DatabasebetaFinite Group Databasebeta| order | 1280 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | D5×#1368 |
| Fitting | C5×#1368 ⋊ C2 |
| Sylow | C5 ⋊ C2×#1368 |
254 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 254 conjugacy classes of subgroups — too many to draw. Only its 111 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 640 |
128 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#1368, D5×#12067, #72242072, … |
| maximal normal subgroup of | AGL(1,𝔽5)×#1368, D5×#12067, #72242072, … |
| maximal quotient of | D5×#7457, C5⋊D5×#1368 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1280, 81118);