Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C5×Q8⋊C8 ⋊ C2 |
| Sylow | C5 ⋊ C8×SD16 |
180 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 73 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=e,b^2=f,c^2=e,d^2=f,e^2=g,b^a=bd,d^a=df,d^b=df,h^c=h^4112 conjugacy classes — view the full character table.
| maximal subgroup of | C8×D5×SD16, C2×#10599005, #12068674, … |
| maximal normal subgroup of | C8×D5×SD16, C2×#10599005, #12068674, … |
| maximal quotient of | #11990063, #11990074, #11990523, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 1087);