Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C2×D5×D16 |
| Fitting | C2×C5×D16 ⋊ C2 |
| Sylow | C5 ⋊ C22×D16 |
440 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 125 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 | D5×#1415, #12019741, D5×#1419, … |
| maximal normal subgroup of | D5×#1415, #12019741, D5×#1419, … |
| maximal quotient of | C2×D5×#357, C2×D5×#366, C4×D5×D16, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 15829);