Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#65198 |
| Fitting | C2×C5×M32 ⋊ C2 |
| Sylow | C5 ⋊ C2×#510 |
360 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 133 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 320 |
112 conjugacy classes — view the full character table.
| maximal subgroup of | #12016433, #12016435, #12016454, … |
| maximal normal subgroup of | #12016433, #12016435, #12016454, … |
| maximal quotient of | C2×#10602238, C2×#10602232, C2×#10602221, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 15823);