Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | C2×#66063 |
| Fitting | C2×C5×C4⋊Q8 ⋊ C2 |
| Sylow | C5 ⋊ C2×#544 |
1080 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
100 conjugacy classes — view the full character table.
| maximal subgroup of | #11991832, #12103836, #12103844, … |
| maximal normal subgroup of | #11991832, #12103836, #12103844, … |
| maximal quotient of | C2×#10607926, C2×#10606090, C2×#10607699, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 20193);