Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4 |
| direct product | C2×#65688 |
| unambiguous semidirect product | D5⋊#384 |
| Fitting | C2×C42×C5 ⋊ C4 |
| Sylow | C5 ⋊ C2×#384 |
888 conjugacy classes of subgroups; only the 354 normal subgroups are shown.
This group has 888 conjugacy classes of subgroups — too many to draw. Only its 354 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 | C2×#10598586, #13016197, #13016207, … |
| maximal normal subgroup of | C2×#10598586, #13016197, #13016207, … |
| maximal quotient of | C2×#10604198, C4×#65688, C2×#10603804, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 19129);