Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| isoclinism | isoclinic class of #700 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4 |
| direct product | C2×#170⋊C8 |
| Sylow | C5 ⋊ C2×#322 |
248 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 138 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 640 |
112 conjugacy classes — view the full character table.
| maximal subgroup of | #13013649, #13013652, C4×#170⋊C8, … |
| maximal normal subgroup of | #13013649, #13013652, C4×#170⋊C8, … |
| maximal quotient of | C4×#170⋊C8, C2×#10598765, #13016662, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 6766);