Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C5×M16 ⋊ C4 |
| Sylow | C5 ⋊ C2×#344 |
388 conjugacy classes of subgroups.
| transitive degree | μt(G) = 80 |
Polycyclic presentation:
2^7,5|a^2=e,b^2=f,f^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 | AGL(1,𝔽5)×#344, #13021627, #13021745, … |
| maximal normal subgroup of | AGL(1,𝔽5)×#344, #13021627, #13021745, … |
| maximal quotient of | #13015564, #13015568, #13015572, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 6845);