Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C5×#504 ⋊ C2 |
| Sylow | C5 ⋊ #2221 |
148 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 148 conjugacy classes of subgroups — too many to draw. Only its 49 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^7,5|b^2=df,d^2=fg,e^2=g,f^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,f^a=fg,h^a=h^4,e^c=eg106 conjugacy classes — view the full character table.
| maximal subgroup of | #12019984, #12019986, #12019991, … |
| maximal normal subgroup of | #12019984, #12019986, #12019991, … |
| maximal quotient of | #12013506, #12013523, #12013557, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 4329);