Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C5 ⋊ #2040 |
290 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 71 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|c^2=dg,e^2=g,f^2=g,b^a=bd,c^a=ce,e^a=eg,c^b=cf,f^b=fg,e^c=eg,f^c=fg,h^c=h^470 conjugacy classes — view the full character table.
| maximal subgroup of | #12011628, #12011630, #12011642, … |
| maximal normal subgroup of | #12011628, #12011630, #12011642, … |
| maximal quotient of | #12002626, #12002631, #12002650, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 4752);