Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C5×#430 ⋊ C2 |
| Sylow | C5 ⋊ #2069 |
216 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 65 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^7,5|a^2=d,b^2=de,d^2=g,b^a=bde,c^a=ce,e^a=eg,f^a=fg,c^b=cf,f^b=fg,d^c=dg,h^c=h^467 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#2069, C2×#10601523, #12128024, … |
| maximal normal subgroup of | D5×#2069, C2×#10601523, #12128024, … |
| maximal quotient of | #12003924, #12003926, #12003928, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 3605);