Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C5×#353 ⋊ C2 |
| Sylow | C5 ⋊ #2198 |
246 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 246 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.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^7,5|b^2=g,c^2=g,b^a=bd,c^a=ce,f^a=fg,h^a=h^4,e^b=efg,h^b=h^4,d^c=df,h^c=h^4,e^d=eg46 conjugacy classes — view the full character table.
| maximal subgroup of | #12020022, #12020023, #12020027, … |
| maximal normal subgroup of | #12020022, #12020023, #12020027, … |
| maximal quotient of | #12011341, #12011370, #12011512, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 2023);