Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C5×M32 ⋊ C4 |
| Sylow | C5 ⋊ #1377 |
140 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 140 conjugacy classes of subgroups — too many to draw. Only its 54 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^7,5|a^2=d,b^2=e,d^2=f,f^2=g,b^a=bc,c^a=cg,d^b=dg,h^b=h^2,h^e=h^464 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#10598671, #13025455, #13025649, … |
| maximal normal subgroup of | C2×#10598671, #13025455, #13025649, … |
| maximal quotient of | #13013469, #13013480, #13013490, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 753);