Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C2×D8×Dic5 |
| Sylow | C5 ⋊ C2×C4×D8 |
616 conjugacy classes of subgroups; only the 245 normal subgroups are shown.
This group has 616 conjugacy classes of subgroups — too many to draw. Only its 245 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 320 |
112 conjugacy classes — view the full character table.
| maximal subgroup of | Dic5×#357, #12014516, Dic5×#361, … |
| maximal normal subgroup of | Dic5×#357, #12014516, Dic5×#361, … |
| maximal quotient of | C2×D8×#168, C2×#10601672, C2×#10601674, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 17634);