Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C5 ⋊ #1763 |
324 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 129 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 640 |
Polycyclic presentation:
2^7,5|a^2=e,b^2=f,c^2=eg,d^2=g,f^2=g,b^a=bd,d^a=dg,f^a=fg,h^a=h^4,c^b=cg124 conjugacy classes — view the full character table.
| maximal subgroup of | #11991186, #11991188, #11991200, … |
| maximal normal subgroup of | #11991186, #11991188, #11991200, … |
| maximal quotient of | #11989908, #11989918, #11989943, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 2688);