Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C22⋊C4×C22⋊D5 |
| Fitting | C22×C5×C22⋊C4 ⋊ C2 |
| Sylow | C5 ⋊ D4×C22⋊C4 |
1252 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
130 conjugacy classes — view the full character table.
| maximal subgroup of | #12114620, #99×C22⋊D5, #12115428, … |
| maximal normal subgroup of | #12114620, #99×C22⋊D5, #12115428, … |
| maximal quotient of | C22⋊C4×#685, C22⋊C4×C22⋊Dic5, C22⋊C4×#683, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 15935);