Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×D5×#100 |
| Fitting | C2×C5×#100 ⋊ C2 |
| Sylow | C5 ⋊ C22×#100 |
992 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 992 conjugacy classes of subgroups — too many to draw. Only its 221 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 80 |
88 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#1390, #12014245, #12016776, … |
| maximal normal subgroup of | D5×#1390, #12014245, #12016776, … |
| maximal quotient of | C2×D5×#323, D5×#1460, C2×#10598894, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 12508);