Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | D5⋊#332 |
| Sylow | C5 ⋊ C2×#332 |
256 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 84 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=e,b^2=f,d^2=g,e^2=fg,b^a=bd,d^a=df,h^a=h^2,d^b=dg,e^b=efg,h^c=h^4,h^e=h^452 conjugacy classes — view the full character table.
| maximal subgroup of | AGL(1,𝔽5)×#332, #13017101, #13017110, … |
| maximal normal subgroup of | AGL(1,𝔽5)×#332, #13017101, #13017110, … |
| maximal quotient of | D5⋊#1271, #13014655, #13014656, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 6738);