Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C4×C5×C16 ⋊ C2 |
| Sylow | C5 ⋊ D4⋊C16 |
110 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 110 conjugacy classes of subgroups — too many to draw. Only its 47 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^7,5|a^2=d,c^2=e,d^2=f,f^2=g,b^a=bc,c^a=ce,h^a=h^4,c^b=ce,h^b=h^4184 conjugacy classes — view the full character table.
| maximal subgroup of | D5×D4⋊C16, C2×#10597994, #12009001, … |
| maximal normal subgroup of | D5×D4⋊C16, C2×#10597994, #12009001, … |
| maximal quotient of | #11985950, #11985953, #11985956, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 76);