Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| isoclinism | isoclinic class of Dic10 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4 |
| direct product | C8×#683 |
| Sylow | C5 ⋊ C8×C4⋊C4 |
296 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 157 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 640 |
208 conjugacy classes — view the full character table.
| maximal subgroup of | #12014641, C16×#683, #12014646, … |
| maximal normal subgroup of | #12014641, C16×#683, #12014646, … |
| maximal quotient of | C8×#3946, #11990430, #11990446, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 2657);