Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C22⋊#3926 |
| Sylow | C5 ⋊ C22⋊C32 |
82 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^7,5|a^2=d,d^2=e,e^2=f,f^2=g,b^a=bc,h^a=h^4208 conjugacy classes — view the full character table.
| maximal subgroup of | #11986638, #11986639, #11986640, … |
| maximal normal subgroup of | #11986638, #11986639, #11986640, … |
| maximal quotient of | #11986639, #11986699, D4⋊#3926, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 376);