Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C5×#467 ⋊ C2 |
| Sylow | C5 ⋊ #3344 |
344 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^7,5|a^2=e,c^2=eg,f^2=g,b^a=beg,c^a=cf,f^a=fg,h^a=h^4,c^b=cg,d^b=deg,h^b=h^4,f^c=fg,h^c=h^473 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#3344, C2×#10612486, #12977962, … |
| maximal normal subgroup of | D5×#3344, C2×#10612486, #12977962, … |
| maximal quotient of | #12115594, #12115684, #12116980, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 14568);