Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
| direct product | Q8×#689 |
| Sylow | C5 ⋊ Q8×Q16 |
336 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 149 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 640 |
85 conjugacy classes — view the full character table.
| maximal subgroup of | #12089450, #12089453, #12089458, … |
| maximal normal subgroup of | #12089450, #12089453, #12089458, … |
| maximal quotient of | Q8×#3942, Q8×#3967, C4⋊C4×#689, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 17515);