Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| isoclinism | isoclinic class of Dic10 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C23×C4 |
| direct product | C8×#685 |
| Fitting | C2×C4×C5×C8 ⋊ C2 |
| Sylow | C5 ⋊ C8×C22⋊C4 |
384 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 384 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) = 320 |
208 conjugacy classes — view the full character table.
| maximal subgroup of | #12014378, C16×#685, #12014383, … |
| maximal normal subgroup of | #12014378, C16×#685, #12014383, … |
| maximal quotient of | C8×#3952, #11989774, #11989790, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 2655);