Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×Q16×AGL(1,𝔽5) |
| unambiguous semidirect product | D5⋊(C4×Q16) |
| Fitting | C2×C5×Q16 ⋊ C4 |
| Sylow | C5 ⋊ C2×C4×Q16 |
488 conjugacy classes of subgroups; only the 178 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 178 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
70 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#358, #13025879, AGL(1,𝔽5)×#362, … |
| maximal normal subgroup of | AGL(1,𝔽5)×#358, #13025879, AGL(1,𝔽5)×#362, … |
| maximal quotient of | C2×Q16×#170, C2×#10603968, Q16×D5⋊C8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 19514);