Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C5 ⋊ #1752 |
360 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 157 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^b=cg,h^b=h^4184 conjugacy classes — view the full character table.
| maximal subgroup of | #11986285, #11986286, #11986288, … |
| maximal normal subgroup of | #11986285, #11986286, #11986288, … |
| maximal quotient of | #11989769, #11989773, #11989795, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 4842);