Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
| direct product | C8×#713 |
| Fitting | C5×C8×Q8 ⋊ C2 |
| Sylow | C5 ⋊ C8×#41 |
456 conjugacy classes of subgroups; only the 225 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 225 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 320 |
160 conjugacy classes — view the full character table.
| maximal subgroup of | #12009131, #12009141, #12009171, … |
| maximal normal subgroup of | #12009131, #12009141, #12009171, … |
| maximal quotient of | C8×#4038, C8×#4039, C8×Q8×Dic5, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 13715);