Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C5×#342 ⋊ C2 |
| Sylow | C5 ⋊ #1799 |
380 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 87 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=d,b^a=bd,c^a=ce,e^a=eg,h^b=h^4,f^c=fg,h^c=h^476 conjugacy classes — view the full character table.
| maximal subgroup of | #12010058, #12010060, #12010063, … |
| maximal normal subgroup of | #12010058, #12010060, #12010063, … |
| maximal quotient of | #11991956, #11991960, #11991964, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 1834);