Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | D4×#676 |
| Fitting | C5×C8×D4 ⋊ C2 |
| Sylow | C5 ⋊ D4×M16 |
544 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
130 conjugacy classes — view the full character table.
| maximal subgroup of | #12070181, #12070187, #12070192, … |
| maximal normal subgroup of | #12070181, #12070187, #12070192, … |
| maximal quotient of | D8×#676, #12070725, SD16×#676, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 13237);