Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C5 ⋊ #1680 |
150 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 150 conjugacy classes of subgroups — too many to draw. Only its 51 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=f,b^2=dg,c^2=g,d^2=f,e^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,h^a=h^4,h^b=h^4,e^c=eg,h^c=h^467 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#1680, C2×#10599262, #12081707, … |
| maximal normal subgroup of | D5×#1680, C2×#10599262, #12081707, … |
| maximal quotient of | #11992368, #11995457, #11995475, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 1344);