Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | D5×#510 |
| Fitting | C5×#510 ⋊ C2 |
| Sylow | C5 ⋊ C2×#510 |
360 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 115 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
64 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#2180, #12252763, D5×#2191, … |
| maximal normal subgroup of | D5×#2180, #12252763, D5×#2191, … |
| maximal quotient of | D5×#2141, D5×#2139, D5×#2159, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 15851);