Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C5×Q32 ⋊ C4 |
| Sylow | C5 ⋊ #2180 |
142 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 142 conjugacy classes of subgroups — too many to draw. Only its 44 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^7,5|a^2=e,c^2=ef,d^2=f,f^2=g,b^a=bd,c^a=cf,d^a=df,f^a=fg,h^a=h^2,d^b=dfg,e^b=eg,f^b=fg,h^b=h^4,d^c=dg,h^c=h^3,h^e=h^434 conjugacy classes — view the full character table.
| maximal subgroup of | D5⋊#2180, C2×#10604138, #13043613, … |
| maximal normal subgroup of | D5⋊#2180, C2×#10604138, #13043613, … |
| maximal quotient of | #13025263, #13025267, #13025269, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 6220);