Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | C2×#66031 |
| Fitting | C2×C5×#125 ⋊ C2 |
| Sylow | C5 ⋊ C2×#541 |
1004 conjugacy classes of subgroups; only the 485 normal subgroups are shown.
This group has 1004 conjugacy classes of subgroups — too many to draw. Only its 485 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 320 |
100 conjugacy classes — view the full character table.
| maximal subgroup of | #11991839, #12104457, #12104583, … |
| maximal normal subgroup of | #11991839, #12104457, #12104583, … |
| maximal quotient of | C2×#10605955, C2×#10607701, C2×#10607928, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 20076);