Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C5×#494 ⋊ C2 |
| Sylow | C5 ⋊ #3276 |
472 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 125 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=g,c^2=g,e^2=g,b^a=be,c^a=cf,e^a=eg,c^b=cg,d^b=de,e^b=eg,h^b=h^4,h^c=h^4,e^d=eg,h^d=h^473 conjugacy classes — view the full character table.
| maximal subgroup of | #12088674, #12088676, #12088719, … |
| maximal normal subgroup of | #12088674, #12088676, #12088719, … |
| maximal quotient of | #12090612, #12090718, #12090826, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 15618);