Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
| direct product | M16×Dic10 |
| Sylow | C5 ⋊ Q8×M16 |
388 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
130 conjugacy classes — view the full character table.
| maximal subgroup of | #11993634, #11993638, #11993648, … |
| maximal normal subgroup of | #11993634, #11993638, #11993648, … |
| maximal quotient of | M16×C4⋊Dic5, M16×#683, #12097949, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 12322);