Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×#65784 |
| Fitting | C22×C5×Q8 ⋊ C4 |
| Sylow | C5 ⋊ C2×#421 |
772 conjugacy classes of subgroups; only the 202 normal subgroups are shown.
This group has 772 conjugacy classes of subgroups — too many to draw. Only its 202 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
64 conjugacy classes — view the full character table.
| maximal subgroup of | #13021837, #13021845, #13021860, … |
| maximal normal subgroup of | #13021837, #13021845, #13021860, … |
| maximal quotient of | C2×#10604270, C2×#10604967, C2×#10604437, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 19594);