Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C25 |
| direct product | D5×#340 |
| Fitting | C5×#340 ⋊ C2 |
| Sylow | C5 ⋊ C2×#340 |
512 conjugacy classes of subgroups; only the 193 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 193 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 | D5×#1347, D5×#1348, #12009530, … |
| maximal normal subgroup of | D5×#1347, D5×#1348, #12009530, … |
| maximal quotient of | D5×#1277, #11988764, #11988774, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 1740);