Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C5 ⋊ #1886 |
324 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 89 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=f,b^2=df,c^2=g,d^2=g,f^2=g,b^a=bd,c^a=ce,e^a=eg,d^b=dg,e^b=eg,f^b=fg,h^b=h^4,d^c=dg,f^c=fg76 conjugacy classes — view the full character table.
| maximal subgroup of | #12015178, #12015182, #12015183, … |
| maximal normal subgroup of | #12015178, #12015182, #12015183, … |
| maximal quotient of | #11993948, #11993968, #11994220, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 2978);