Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×#65464 |
| Fitting | C22×C5×SD16 ⋊ C2 |
| Sylow | C5 ⋊ C2×#492 |
656 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 181 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 320 |
100 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#65464, #12107718, #12107765, … |
| maximal normal subgroup of | C4×#65464, #12107718, #12107765, … |
| maximal quotient of | C2×#10602047, C2×#10602125, C2×#10602048, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 17663);