Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C5×#365 ⋊ C2 |
| Sylow | C5 ⋊ #2239 |
124 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 41 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=g,c^2=df,e^2=fg,f^2=g,b^a=bd,c^a=ce,e^a=ef,f^a=fg,h^a=h^4,e^b=eg,h^b=h^4,d^c=dg,e^c=efg,f^c=fg52 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#2239, C2×#10600107, #12254193, … |
| maximal normal subgroup of | D5×#2239, C2×#10600107, #12254193, … |
| maximal quotient of | #12015626, #12015865, #12016339, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 2189);