Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C25 |
| direct product | C2×#64874 |
| Fitting | C2×C5×C4⋊C4 ⋊ C4 |
| Sylow | C5 ⋊ C2×#340 |
512 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
76 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#340, C4×#64874, #13021593, … |
| maximal normal subgroup of | AGL(1,𝔽5)×#340, C4×#64874, #13021593, … |
| maximal quotient of | C2×#10598587, #13015383, #13015393, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 6366);