Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C5 ⋊ #2205 |
224 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 224 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,d^2=g,e^2=g,b^a=bd,c^a=ce,d^a=dg,e^a=eg,f^a=fg,c^b=cg,d^b=dg,e^b=efg,h^b=h^4,d^c=df,e^c=eg,e^d=eg52 conjugacy classes — view the full character table.
| maximal subgroup of | #12020069, #12020070, #12020074, … |
| maximal normal subgroup of | #12020069, #12020070, #12020074, … |
| maximal quotient of | #12011390, #12011391, #12011555, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 3870);