Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| isoclinism | isoclinic class of Dic10 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C24 |
| direct product | C2×#64727 |
| Fitting | C22×C5×C16 ⋊ C2 |
| Sylow | C5 ⋊ C2×C22⋊C16 |
272 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 320 |
208 conjugacy classes — view the full character table.
| maximal subgroup of | #11986638, #12014326, C4×#64727, … |
| maximal normal subgroup of | #11986638, #12014326, C4×#64727, … |
| maximal quotient of | C2×#10598013, C2×#10598015, #12008496, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 4283);