Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C5×C22⋊C16 ⋊ C2 |
| Sylow | C5 ⋊ #1315 |
116 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 116 conjugacy classes of subgroups — too many to draw. Only its 37 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=d,c^2=g,d^2=f,f^2=g,b^a=bc,c^a=ce,c^b=cg,d^b=deg,h^b=h^4118 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#1315, C2×#10598014, #12008370, … |
| maximal normal subgroup of | D5×#1315, C2×#10598014, #12008370, … |
| maximal quotient of | #11985926, #11985928, #11985930, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 96);