Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
| direct product | C2×#65002 |
| Fitting | C2×C5×#97 ⋊ C2 |
| Sylow | C5 ⋊ C2×#490 |
488 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 149 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 | #11994233, #12000586, #12000588, … |
| maximal normal subgroup of | #11994233, #12000586, #12000588, … |
| maximal quotient of | C2×#10600608, C2×#10600611, C2×#10600616, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 12309);