Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C5×#106 ⋊ C2 |
| Sylow | C5 ⋊ #2079 |
198 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 198 conjugacy classes of subgroups — too many to draw. Only its 63 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,c^2=d,e^2=g,f^2=g,b^a=bd,c^a=ceg,c^b=cf,f^b=fg,h^b=h^4,e^c=eg,f^c=fg82 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#2079, C2×#10601386, #12128203, … |
| maximal normal subgroup of | D5×#2079, C2×#10601386, #12128203, … |
| maximal quotient of | #12004021, #12004028, #12004035, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 3468);