Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C5 ⋊ #2231 |
120 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 120 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|a^2=d,b^2=df,e^2=f,f^2=g,b^a=bdfg,c^a=ce,e^a=ef,f^a=fg,h^a=h^4,d^c=dg,e^c=efg,f^c=fg79 conjugacy classes — view the full character table.
| maximal subgroup of | #12013691, #12013693, #12013696, … |
| maximal normal subgroup of | #12013691, #12013693, #12013696, … |
| maximal quotient of | #12015406, #12015997, #12016999, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 3795);