Finite Group Databasebeta

← Group #368

Character table — Group #368

Order 64.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22
size1111222222222222228888
order124424888816161616161616168888
χ11111111111111111111111
χ2111111111111111111-1-1-1-1
χ31111111111-1-1-1-1-1-1-1-111-1-1
χ41111111111-1-1-1-1-1-1-1-1-1-111
χ511-1-1-11-1-1111111-1-1-1-1i−ii−i
χ611-1-1-11-1-1111111-1-1-1-1−ii−ii
χ711-1-1-11-1-111-1-1-1-11111i−i−ii
χ811-1-1-11-1-111-1-1-1-11111−iii−i
χ9222222-2-2-2-2000000000000
χ102222-2-2000022−2−222−2−20000
χ112222-2-20000−2−222−2−2220000
χ1222-2-22-2000022−2−2−2−2220000
χ1322-2-22-20000−2−22222−2−20000
χ1422-2-2-2222-2-2000000000000
χ152-22i−2i00i2−i22−2ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ70000
χ162-22i−2i00i2−i22−2−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ70000
χ172-22i−2i00−i2i2−22ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ50000
χ182-22i−2i00−i2i2−22−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ50000
χ192-2−2i2i00i2−i2−22ζ3+ζ5−ζ3−ζ5−ζ−ζ7ζ+ζ7−ζ+ζ7ζ−ζ7ζ3−ζ5−ζ3+ζ50000
χ202-2−2i2i00i2−i2−22−ζ3−ζ5ζ3+ζ5ζ+ζ7−ζ−ζ7ζ−ζ7−ζ+ζ7−ζ3+ζ5ζ3−ζ50000
χ212-2−2i2i00−i2i22−2ζ+ζ7−ζ−ζ7ζ3+ζ5−ζ3−ζ5−ζ3+ζ5ζ3−ζ5−ζ+ζ7ζ−ζ70000
χ222-2−2i2i00−i2i22−2−ζ−ζ7ζ+ζ7−ζ3−ζ5ζ3+ζ5ζ3−ζ5−ζ3+ζ5ζ−ζ7−ζ+ζ70000

Here ζ is a primitive root of unity of order 16 (ζ16 = 1); i = ζ4.