Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | SD16×C22⋊D5 |
| Fitting | C22×C5×SD16 ⋊ C2 |
| Sylow | C5 ⋊ D4×SD16 |
546 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
91 conjugacy classes — view the full character table.
| maximal subgroup of | D4×D5×SD16, C2×SD16×C22⋊D5, #12974589, … |
| maximal normal subgroup of | D4×D5×SD16, C2×SD16×C22⋊D5, #12974589, … |
| maximal quotient of | #12088763, #12088768, #12088778, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 17678);