Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C5×#324 ⋊ C2 |
| Sylow | C5 ⋊ #1318 |
170 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 170 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) = 160 |
Polycyclic presentation:
2^7,5|a^2=d,c^2=g,d^2=f,b^a=bc,c^a=ce,e^a=eg,c^b=cg,d^b=deg,h^b=h^4,d^c=dg70 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#1318, C2×#10597945, #12008404, … |
| maximal normal subgroup of | D5×#1318, C2×#10597945, #12008404, … |
| maximal quotient of | #11985922, #11985930, #11986045, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 27);