Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#65137 |
| Fitting | C2×C5×C4⋊C8 ⋊ C2 |
| Sylow | C5 ⋊ C2×#460 |
584 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 173 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 320 |
118 conjugacy classes — view the full character table.
| maximal subgroup of | #11994067, #11994069, #11994074, … |
| maximal normal subgroup of | #11994067, #11994069, #11994074, … |
| maximal quotient of | C2×#10599339, C2×#10599379, C2×#10599380, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 12844);