Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C2×C4×C5×C8 ⋊ C2 |
| Sylow | C5 ⋊ #1753 |
348 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 137 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,e^2=g,b^a=bd,c^a=cg,h^a=h^4184 conjugacy classes — view the full character table.
| maximal subgroup of | #12017082, #12017084, D5×#1753, … |
| maximal normal subgroup of | #12017082, #12017084, D5×#1753, … |
| maximal quotient of | #11989779, #11989785, #11989790, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 2656);