Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C5 ⋊ #1691 |
160 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 53 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^7,5|a^2=g,b^2=d,d^2=f,e^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,h^a=h^4,c^b=cf,h^b=h^4,e^c=eg61 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#1691, C2×#10601929, #12081839, … |
| maximal normal subgroup of | D5×#1691, C2×#10601929, #12081839, … |
| maximal quotient of | #11992382, #11995497, #11995507, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 4011);