Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C5×SD32 ⋊ C2 |
| Sylow | C5 ⋊ #3416 |
360 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 113 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=g,e^2=fg,f^2=g,b^a=be,e^a=ef,f^a=fg,e^b=ef,f^b=fg,d^c=dg,h^c=h^476 conjugacy classes — view the full character table.
| maximal subgroup of | #12256043, #12256045, #12256060, … |
| maximal normal subgroup of | #12256043, #12256045, #12256060, … |
| maximal quotient of | #12252207, #12252214, #12252345, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 15837);