Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C23×C4 |
| direct product | Dic5×C22⋊C8 |
| Sylow | C5 ⋊ C4×C22⋊C8 |
436 conjugacy classes of subgroups; only the 177 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 177 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 | #11989801, Dic5×#323, #11989805, … |
| maximal normal subgroup of | #11989801, Dic5×#323, #11989805, … |
| maximal quotient of | C22⋊C8×#168, #11989771, #11989780, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 2780);