Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×D5×SD32 |
| Fitting | C2×C5×SD32 ⋊ C2 |
| Sylow | C5 ⋊ C22×SD32 |
400 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 400 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 | C4×D5×SD32, D5×#2175, #12252664, … |
| maximal normal subgroup of | C4×D5×SD32, D5×#2175, #12252664, … |
| maximal quotient of | C2×D5×#357, C2×D5×#358, C2×D5×#367, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 15833);