Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C26 |
| direct product | C2×D5×#97 |
| Fitting | C2×C5×#97 ⋊ C2 |
| Sylow | C5 ⋊ C22×#97 |
680 conjugacy classes of subgroups; only the 365 normal subgroups are shown.
This group has 680 conjugacy classes of subgroups — too many to draw. Only its 365 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 320 |
160 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#1275, #11988720, D5×#1281, … |
| maximal normal subgroup of | D5×#1275, #11988720, D5×#1281, … |
| maximal quotient of | C2×D5×#322, D5×#1451, C2×#10598862, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 12296);