Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C5 ⋊ #2117 |
220 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 78 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=e,d^2=g,e^2=f,f^2=g,b^a=bd,c^a=cg,h^a=h^2,d^b=dg,e^b=eg,h^b=h^4,h^e=h^464 conjugacy classes — view the full character table.
| maximal subgroup of | #13025722, #13025723, #13025780, … |
| maximal normal subgroup of | #13025722, #13025723, #13025780, … |
| maximal quotient of | #13023093, #13023096, #13023163, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 6827);