Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4 |
| direct product | AGL(1,𝔽5)×#127 |
| Fitting | C5×#127 ⋊ C4 |
| Sylow | C5 ⋊ C4×#127 |
924 conjugacy classes of subgroups; only the 210 normal subgroups are shown.
This group has 924 conjugacy classes of subgroups — too many to draw. Only its 210 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 80 |
70 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#331, #13017095, #13017104, … |
| maximal normal subgroup of | AGL(1,𝔽5)×#331, #13017095, #13017104, … |
| maximal quotient of | AGL(1,𝔽5)×#390, AGL(1,𝔽5)×#384, AGL(1,𝔽5)×#392, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 19449);