Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| isoclinism | isoclinic class of #64945 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
| direct product | C2×#64962 |
| Fitting | C2×C5×#95 ⋊ C2 |
| Sylow | C5 ⋊ C2×#393 |
1036 conjugacy classes of subgroups; only the 253 normal subgroups are shown.
This group has 1036 conjugacy classes of subgroups — too many to draw. Only its 253 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 320 |
124 conjugacy classes — view the full character table.
| maximal subgroup of | #11994288, #11994303, #11999509, … |
| maximal normal subgroup of | #11994288, #11994303, #11999509, … |
| maximal quotient of | C2×#10600221, C2×#10600220, C2×#10600206, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 7184);