Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C2×#65764 |
| unambiguous semidirect product | D5⋊#381 |
| Fitting | C23×C4×C5 ⋊ C4 |
| Sylow | C5 ⋊ C2×#381 |
1144 conjugacy classes of subgroups; only the 258 normal subgroups are shown.
This group has 1144 conjugacy classes of subgroups — too many to draw. Only its 258 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
88 conjugacy classes — view the full character table.
| maximal subgroup of | #13015545, #13015548, C2×#10598692, … |
| maximal normal subgroup of | #13015545, #13015548, C2×#10598692, … |
| maximal quotient of | C2×#10604909, C2×#10604197, C4×#65764, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 19561);