Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C5 ⋊ #1361 |
118 conjugacy classes of subgroups; only the 34 normal subgroups are shown.
This group has 118 conjugacy classes of subgroups — too many to draw. Only its 34 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=d,c^2=fg,d^2=efg,e^2=g,f^2=g,b^a=bc,c^a=ce,e^a=eg,f^a=fg,h^a=h^2,c^b=cf,d^b=defg,e^b=eg,f^b=fg,h^d=h^443 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#10598802, D5⋊#1361, #13024855, … |
| maximal normal subgroup of | C2×#10598802, D5⋊#1361, #13024855, … |
| maximal quotient of | #13013379, #13013380, #13013383, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 884);