Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C22 |
| direct product | Q8×#672 |
| Sylow | C5 ⋊ Q8×C16 |
134 conjugacy classes of subgroups.
| transitive degree | μt(G) = 640 |
160 conjugacy classes — view the full character table.
| maximal subgroup of | #12011063, SD16×#672, #12011077, … |
| maximal normal subgroup of | #12011063, SD16×#672, #12011077, … |
| maximal quotient of | C4⋊C4×#672, #12016917, #12017301, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 3823);