Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
| direct product | C4×#3999 |
| Fitting | C2×C42×C5 ⋊ C4 |
| Sylow | C5 ⋊ C4×#99 |
412 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 96 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
76 conjugacy classes — view the full character table.
| maximal subgroup of | #13013684, #13013685, #13013937, … |
| maximal normal subgroup of | #13013684, #13013685, #13013937, … |
| maximal quotient of | C4×#64915, C4×#64913, #13016742, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 6248);