Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C5×#495 ⋊ C2 |
| Sylow | C5 ⋊ #3168 |
380 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 121 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|b^2=g,c^2=f,d^2=e,f^2=g,b^a=be,c^a=cf,f^a=fg,h^b=h^4,h^d=h^488 conjugacy classes — view the full character table.
| maximal subgroup of | #12010602, #12010607, #12010612, … |
| maximal normal subgroup of | #12010602, #12010607, #12010612, … |
| maximal quotient of | #12099844, #12103506, #12103517, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 15622);