Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C210 |
| direct product | C22×D5×C4⋊C4 |
| Fitting | C22×C5×C4⋊C4 ⋊ C2 |
| Sylow | C5 ⋊ C23×C4⋊C4 |
2488 conjugacy classes of subgroups; only the 1157 normal subgroups are shown.
This group has 2488 conjugacy classes of subgroups — too many to draw. Only its 1157 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 | #11990628, #12004566, #12004576, … |
| maximal normal subgroup of | #11990628, #12004566, #12004576, … |
| maximal quotient of | C22×D5×#95, C2×C4×D5×C4⋊C4, C22×#64938, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 19691);