Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | M16×C22⋊D5 |
| Fitting | C22×C5×M16 ⋊ 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 | #12114647, #100×C22⋊D5, #12114655, … |
| maximal normal subgroup of | #12114647, #100×C22⋊D5, #12114655, … |
| maximal quotient of | M16×#686, #12070728, M16×#687, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 17571);