Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C5 ⋊ #1941 |
248 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 248 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) = 640 |
Polycyclic presentation:
2^7,5|a^2=f,b^2=f,c^2=e,e^2=g,b^a=bd,c^a=ce,e^a=eg,h^a=h^4172 conjugacy classes — view the full character table.
| maximal subgroup of | #12015997, #12016000, #12016999, … |
| maximal normal subgroup of | #12015997, #12016000, #12016999, … |
| maximal quotient of | #11997837, #11997857, #11997931, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 2644);