Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C5×#508 ⋊ C2 |
| Sylow | C5 ⋊ #3415 |
370 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 370 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|e^2=fg,f^2=g,b^a=be,e^a=ef,f^a=fg,h^a=h^4,e^b=ef,f^b=fg,h^b=h^4,d^c=dg,h^c=h^476 conjugacy classes — view the full character table.
| maximal subgroup of | #12019981, #12019985, #12019995, … |
| maximal normal subgroup of | #12019981, #12019985, #12019995, … |
| maximal quotient of | #12252208, #12252341, #12252637, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 15844);