Finite Group Databasebeta

← Group #490385

Character table — Group #490385

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size11112222222222444444444444888888888888888161616161616161616161616161616163232
order12222244448888444444448888448888816161616161616162444444488881616161644
χ111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ3111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ51111111111111111-1-111-1-11111-1-11-1-1-1-111111111111-1-11-1-11111-1-1-1-1-1-1
χ61111111111111111-1-111-1-11111-1-11-1-1-1-111111111-1-1-111-111-1-1-1-1-1-1-1-111
χ71111111111111111-1-111-1-11111-1-11-1-1-1-1-1-1-1-1-1-1-1-1111-1-11-1-1-1-1-1-1111111
χ81111111111111111-1-111-1-11111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11111111111-1-1
χ91111-1-1111111111-111-1-1-1-1-1-111-11-111-1-11111-1-1-1-11-1-1111-1-111-1-111-1-11-1
χ101111-1-1111111111-111-1-1-1-1-1-111-11-111-1-11111-1-1-1-1-111-1-1-111-1-11111-1-1-11
χ111111-1-1111111111-111-1-1-1-1-1-111-11-111-1-1-1-1-1-111111-1-1111-1-1-1-111-1-111-11
χ121111-1-1111111111-111-1-1-1-1-1-111-11-111-1-1-1-1-1-11111-111-1-1-11111-1-1-1-1111-1
χ131111-1-1111111111-1-1-1-1-111-1-1111-1-1-1-1111111-1-1-1-11-1-1-1-111111-1-1-1-111-11
χ141111-1-1111111111-1-1-1-1-111-1-1111-1-1-1-1111111-1-1-1-1-11111-1-1-1-1-111-1-1111-1
χ151111-1-1111111111-1-1-1-1-111-1-1111-1-1-1-111-1-1-1-111111-1-1-1-1111-1-11111-1-11-1
χ161111-1-1111111111-1-1-1-1-111-1-1111-1-1-1-111-1-1-1-11111-11111-1-1-111-1-111-1-1-11
χ172222222222-2-2-2-222222222-2-2-2-222-2-2-2-2-200000000000000000000000000
χ182222222222-2-2-2-222-2-222-2-2-2-2-2-2-2-2-2222200000000000000000000000000
χ192222222-2-220000-2-222-22-2-200002-20000022−2−222−2−20000000000002−22−200
χ202222222-2-220000-2-222-22-2-200002-200000−2−222−2−222000000000000−22−2200
χ212222222-2-220000-2-2-2-2-22220000-220000022−2−222−2−2000000000000−22−2200
χ222222222-2-220000-2-2-2-2-22220000-2200000−2−222−2−2220000000000002−22−200
χ23222222-222-22222-2-2002-20022-2-200-200000000000022-200-2000000000000
χ24222222-222-22222-2-2002-20022-2-200-2000000000000-2-22002000000000000
χ25222222-222-2-2-2-2-2-2-2002-200-2-2220020000000000000002-202-20000000000
χ26222222-222-2-2-2-2-2-2-2002-200-2-222002000000000000000-220-220000000000
χ272222-2-22222-2-2-2-22-222-2-2-2-222-2-2-222-2-22200000000000000000000000000
χ282222-2-22222-2-2-2-22-2-2-2-2-22222-2-22-2222-2-200000000000000000000000000
χ292222-2-22-2-220000-22222-2220000-2-20000022−2−2−2−2220000000000002−2−2200
χ302222-2-22-2-220000-22222-2220000-2-200000−2−22222−2−2000000000000−222−200
χ312222-2-22-2-220000-22-2-22-2-2-20000220000022−2−2−2−222000000000000−222−200
χ322222-2-22-2-220000-22-2-22-2-2-200002200000−2−22222−2−20000000000002−2−2200
χ332222-2-2-222-22222-2200-2200-2-2-2-20020000000000002-2200-2000000000000
χ342222-2-2-222-22222-2200-2200-2-2-2-2002000000000000-22-2002000000000000
χ352222-2-2-222-2-2-2-2-2-2200-2200222200-20000000000000002-20-220000000000
χ362222-2-2-222-2-2-2-2-2-2200-2200222200-2000000000000000-2202-20000000000
χ37444444-4-4-4-400004400-4-4000000000000000000000000000000000000000
χ384444-4-4-4-4-4-400004-40044000000000000000000000000000000000000000
χ3944-4-44-400002222−22−220000000022−22000000000ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7000000000000000000
χ4044-4-44-400002222−22−220000000022−22000000000−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7000000000000000000
χ4144-4-44-40000−22−22222200000000−2222000000000ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7000000000000000000
χ4244-4-44-40000−22−22222200000000−2222000000000−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7000000000000000000
χ4344-4-4-4400002222−22−2200000000−2222000000000ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7000000000000000000
χ4444-4-4-4400002222−22−2200000000−2222000000000−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7000000000000000000
χ4544-4-4-440000−22−2222220000000022−22000000000ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7000000000000000000
χ4644-4-4-440000−22−2222220000000022−22000000000−ζ+ζ3−ζ5+ζ7ζ−ζ3+ζ5−ζ7ζ+ζ3−ζ5−ζ7−ζ−ζ3+ζ5+ζ7ζ−ζ3+ζ5−ζ7−ζ+ζ3−ζ5+ζ7−ζ−ζ3+ζ5+ζ7ζ+ζ3−ζ5−ζ7000000000000000000
χ474-44-40004-404-44-4000000000000000000000000000000000000022−22000000
χ484-44-40004-404-44-40000000000000000000000000000000000000−2222000000
χ494-44-40004-40-44-440000000000000000000000000000000000022−2200000000
χ504-44-40004-40-44-4400000000000000000000000000000000000−222200000000
χ514-4-4400400-422−22−2222004i−4i00000022−220002i2−2i20000000000000000000000000000
χ524-4-4400400-422−22−222200−4i4i00000022−22000−2i22i20000000000000000000000000000
χ534-4-4400400-4−222222−22004i−4i000000−2222000−2i22i20000000000000000000000000000
χ544-4-4400400-4−222222−2200−4i4i000000−22220002i2−2i20000000000000000000000000000
χ554-4-4400-400422−22−22220000004-400−22220000022−2200000000000000000000000000
χ564-4-4400-400422−22−2222000000-4400−222200000−222200000000000000000000000000
χ574-4-4400-4004−222222−220000004-40022−2200000−222200000000000000000000000000
χ584-4-4400-4004−222222−22000000-440022−220000022−2200000000000000000000000000
χ598-88-8000-8800000000000000000000000000000000000000000000000000

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