Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×D5×#107 |
| Fitting | C2×C5×#107 ⋊ C2 |
| Sylow | C5 ⋊ C22×#107 |
600 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 600 conjugacy classes of subgroups — too many to draw. Only its 269 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×#1380, #12014181, D5×#1387, … |
| maximal normal subgroup of | D5×#1380, #12014181, D5×#1387, … |
| maximal quotient of | C2×D5×#335, D5×#1567, C2×#10599362, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 12956);