Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C5 ⋊ #1479 |
248 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 97 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=f,d^2=f,e^2=g,b^a=bd,d^a=df,h^a=h^4,c^b=cf,d^b=df,h^b=h^4124 conjugacy classes — view the full character table.
| maximal subgroup of | #11990720, #11990721, #11990723, … |
| maximal normal subgroup of | #11990720, #11990721, #11990723, … |
| maximal quotient of | #11987290, #11987299, #11987328, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 3642);