Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C22×#3938 |
| Fitting | C22×C5×C22⋊C4 ⋊ C2 |
| Sylow | C5 ⋊ C22×#99 |
1112 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 1112 conjugacy classes of subgroups — too many to draw. Only its 269 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
124 conjugacy classes — view the full character table.
| maximal subgroup of | #12004641, #12004644, #12004686, … |
| maximal normal subgroup of | #12004641, #12004644, #12004686, … |
| maximal quotient of | C22×#64688, C22×#64689, C2×#10600712, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 15931);