Finite Group DatabasebetaFinite Group Databasebeta| order | 640 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C5×#335 ⋊ C2 |
| Sylow | C5 ⋊ #1361 |
118 conjugacy classes of subgroups.
| transitive degree | μt(G) = 320 |
Polycyclic presentation:
2^7,5|a^2=d,c^2=fg,d^2=efg,e^2=g,f^2=g,b^a=bc,c^a=ce,e^a=eg,f^a=fg,c^b=cf,d^b=defg,e^b=eg,f^b=fg,h^b=h^485 conjugacy classes — view the full character table.
| maximal subgroup of | D5×#1361, C2×#10597964, #12010543, … |
| maximal normal subgroup of | D5×#1361, C2×#10597964, #12010543, … |
| maximal quotient of | #11986024, #11986030, #11986034, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(640, 46);