Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C2×C5×M16 ⋊ C4 |
| Sylow | C5 ⋊ C2×H(3,ℤ/4) |
404 conjugacy classes of subgroups; only the 128 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 128 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^7,5|a^2=e,b^2=f,d^2=g,b^a=bd,f^a=fg,h^a=h^2,e^b=eg,h^b=h^3,h^c=h^4,h^e=h^4,h^f=h^464 conjugacy classes — view the full character table.
| maximal subgroup of | #13013850, #13013858, AGL(1,𝔽5)×H(3,ℤ/4), … |
| maximal normal subgroup of | #13013850, #13013858, AGL(1,𝔽5)×H(3,ℤ/4), … |
| maximal quotient of | #13015290, #13015294, #13015297, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 6844);