Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C4×#4095 |
| Fitting | C4×C5×#41 ⋊ C2 |
| Sylow | C5 ⋊ C4×AGL(1,ℤ/8) |
548 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
124 conjugacy classes — view the full character table.
| maximal subgroup of | #11993922, #11993924, #11993936, … |
| maximal normal subgroup of | #11993922, #11993924, #11993936, … |
| maximal quotient of | C8×#4095, #12068881, #12068907, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 16337);