Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×#65303 |
| Fitting | C2×C4×C5×D4 ⋊ C2 |
| Sylow | C5 ⋊ C2×#442 |
608 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 608 conjugacy classes of subgroups — too many to draw. Only its 205 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 | #11994722, #11994723, #11994725, … |
| maximal normal subgroup of | #11994722, #11994723, #11994725, … |
| maximal quotient of | C2×#10601633, C2×#10601656, C2×#10601637, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 16104);