Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
| direct product | C2×#65506 |
| Fitting | C23×C5×D4 ⋊ C2 |
| Sylow | C5 ⋊ C2×#447 |
1048 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 1048 conjugacy classes of subgroups — too many to draw. Only its 197 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
118 conjugacy classes — view the full character table.
| maximal subgroup of | #11994434, #11994440, #11995745, … |
| maximal normal subgroup of | #11994434, #11994440, #11995745, … |
| maximal quotient of | C2×#10602638, C2×#10602636, C2×#10602671, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 17850);