Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| isoclinism | isoclinic class of D160 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | C2×#64669 |
| Fitting | C2×C5×C32 ⋊ C2 |
| Sylow | C5 ⋊ C2×SD64 |
112 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
166 conjugacy classes — view the full character table.
| maximal subgroup of | #12019878, C4×#64669, #12019890, … |
| maximal normal subgroup of | #12019878, C4×#64669, #12019890, … |
| maximal quotient of | C2×#10598087, C2×#10598088, C2×#10598083, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 2243);