Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C5×#479 ⋊ C2 |
| Sylow | C5 ⋊ #3371 |
344 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^7,5|b^2=e,c^2=g,d^2=eg,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^4,c^b=cg,d^b=de,f^c=fg,h^c=h^4,h^d=h^467 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#3371, C2×#10612949, #12979117, … |
| maximal normal subgroup of | D5×#3371, C2×#10612949, #12979117, … |
| maximal quotient of | #12115989, #12116183, #12118297, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 15031);