Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C5×#336 ⋊ C2 |
| Sylow | C5 ⋊ #1869 |
432 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 117 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=f,b^2=df,f^2=g,b^a=bd,c^a=ce,h^a=h^4,h^c=h^4136 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#1869, C2×#10599461, #12100426, … |
| maximal normal subgroup of | D5×#1869, C2×#10599461, #12100426, … |
| maximal quotient of | #11993820, #11993825, #11993830, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 1543);