Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C5 ⋊ #1271 |
158 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 158 conjugacy classes of subgroups — too many to draw. Only its 65 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=d,b^2=e,c^2=f,d^2=g,b^a=bc,c^a=ce,h^a=h^4,c^b=cf,d^b=def94 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#1271, C2×#10598129, #11987238, … |
| maximal normal subgroup of | D5×#1271, C2×#10598129, #11987238, … |
| maximal quotient of | #11985851, #11986082, #11986085, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 211);