Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| isoclinism | isoclinic class of #700 |
| automorphism | ? |
| homology | Abelianization (H1) = C43 · Schur multiplier (H2) = C23×C42 |
| direct product | C4×(C2×AGL(1,𝔽5))⋊C4 |
| Fitting | C2×C42×C5 ⋊ C4 |
| Sylow | C5 ⋊ C4×#95 |
752 conjugacy classes of subgroups; only the 254 normal subgroups are shown.
This group has 752 conjugacy classes of subgroups — too many to draw. Only its 254 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
112 conjugacy classes — view the full character table.
| maximal subgroup of | #13013211, #13013238, #13013240, … |
| maximal normal subgroup of | #13013211, #13013238, #13013240, … |
| maximal quotient of | (C2×AGL(1,𝔽5))⋊#95, #13014607, C4×(C2×AGL(1,𝔽5))⋊C8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 6278);