Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C2×D4×Dic10 |
| Sylow | C5 ⋊ C2×D4×Q8 |
1568 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
130 conjugacy classes — view the full character table.
| maximal subgroup of | #11990981, #11990984, #11991027, … |
| maximal normal subgroup of | #11990981, #11990984, #11991027, … |
| maximal quotient of | C2×C22⋊C4×Dic10, C2×D4×#683, C2×D4×C4⋊Dic5, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 19738);