Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C5×#102 ⋊ C2 |
| Sylow | C5 ⋊ #3295 |
462 conjugacy classes of subgroups.
| transitive degree | μt(G) = 160 |
Polycyclic presentation:
2^7,5|a^2=e,f^2=g,b^a=beg,c^a=cf,f^a=fg,d^b=deg,h^b=h^4,f^c=fg91 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#3295, C2×#10610489, #12975781, … |
| maximal normal subgroup of | D5×#3295, C2×#10610489, #12975781, … |
| maximal quotient of | #102×C22⋊D5, #12115536, #12116479, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 12571);