Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C5 ⋊ C2×#336 |
528 conjugacy classes of subgroups; only the 206 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 206 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,e^2=g,b^a=bd,h^a=h^2,h^c=h^4,h^e=h^4112 conjugacy classes — view the full character table.
| maximal subgroup of | #13013217, #13013232, #13013241, … |
| maximal normal subgroup of | #13013217, #13013232, #13013241, … |
| maximal quotient of | D5⋊#1273, #13015272, #13015278, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 6253);