Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C5 ⋊ #1275 |
152 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 66 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=d,b^2=e,c^2=f,d^2=g,e^2=f,b^a=bc,e^a=ef,h^a=h^2,d^b=df,h^d=h^476 conjugacy classes — view the full character table.
| maximal subgroup of | #13013409, #13013410, #13013411, … |
| maximal normal subgroup of | #13013409, #13013410, #13013411, … |
| maximal quotient of | #13013206, #13013216, #13013218, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 855);