Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Sylow | C5 ⋊ C2×#343 |
432 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 138 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^7,5|a^2=e,b^2=f,e^2=g,b^a=bd,d^a=dg,h^a=h^2,e^b=eg,h^c=h^4,h^e=h^464 conjugacy classes — view the full character table.
| maximal subgroup of | #13013838, AGL(1,𝔽5)×#343, #13021833, … |
| maximal normal subgroup of | #13013838, AGL(1,𝔽5)×#343, #13021833, … |
| maximal quotient of | #13015523, #13015532, #13015535, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 6416);