Finite Group Databasebeta

← Group #264792

Character table — Group #264792

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11112222222222222244444444444444444444444488888888161616161616161616161616161616163232
order12222244444444888844888888888888888888888822444444224444448888888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111
χ511111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111111111-1-1111111-1-1-1-1-1-1-1-1
χ611111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111
χ711111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111-1-1-1-111
χ811111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1111111-1-1
χ911111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11-1-1-11-11-1-1-11111-1-11-1
χ1011111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-11-1-1-11-11-1-111-1-111-11
χ1111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-11111-1-1111-1-111-1-1-11
χ1211111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-111-111-111-1-1-1-1111-1
χ1311111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-11-1111-11-1-1-1-1-1-1-111-11
χ1411111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1111-11-11-1-1-1-111-1-11-1
χ1511111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-11-1-11-1-111111-1-1111-1
χ1611111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111-1-1-1-111-1111111-1-1-11
χ17222222-22-2-222-222222-2-20000000022-2-2-2-200000000000022220000-2-2000000000000
χ18222222-22-2-222-222222-2-20000000022-2-2-2-2000000000000-2-2-2-2000022000000000000
χ19222222-22-2-222-22-2-2-2-2-2-200000000-2-2222200000000000022-2-20000-22000000000000
χ20222222-22-2-222-22-2-2-2-2-2-200000000-2-22222000000000000-2-22200002-2000000000000
χ21222222-2-2-2-2-2-2-2-20000222i2i2i2i−2i−2i−2i−2i000000000000002-22-2000000000000002i−2i000000
χ22222222-2-2-2-2-2-2-2-20000222i2i2i2i−2i−2i−2i−2i00000000000000-22-2200000000000000−2i2i000000
χ23222222-2-2-2-2-2-2-2-2000022−2i−2i−2i−2i2i2i2i2i000000000000002-22-200000000000000−2i2i000000
χ24222222-2-2-2-2-2-2-2-2000022−2i−2i−2i−2i2i2i2i2i00000000000000-22-22000000000000002i−2i000000
χ252222-2-222-2-2-2-2220000-22000000000000002222-2-2-2-222-2-20000002-200000000000000
χ262222-2-222-2-2-2-2220000-22000000000000002222-2-2-2-2-2-222000000-2200000000000000
χ272222-2-222-2-2-2-2220000-2200000000000000-2-2-2-2222222-2-2000000-2200000000000000
χ282222-2-222-2-2-2-2220000-2200000000000000-2-2-2-22222-2-2220000002-200000000000000
χ292222-2-22-2-2-2222-222222-200000000-2-222-2-20000000000000000220000-2-20000000000
χ302222-2-22-2-2-2222-222222-200000000-2-222-2-20000000000000000-2-20000220000000000
χ312222-2-22-2-2-2222-2-2-2-2-22-20000000022-2-22200000000000000002-20000-220000000000
χ322222-2-22-2-2-2222-2-2-2-2-22-20000000022-2-2220000000000000000-2200002-20000000000
χ332222-2-2-2-22222-2-22222-2200000000-2-2-2-222000000002-2-220000000000002-200000000
χ342222-2-2-2-22222-2-22222-2200000000-2-2-2-22200000000-222-2000000000000-2200000000
χ352222-2-2-2-22222-2-2-2-2-2-2-22000000002222-2-2000000002-2-22000000000000-2200000000
χ362222-2-2-2-22222-2-2-2-2-2-2-22000000002222-2-200000000-222-20000000000002-200000000
χ372-2-222-202002-20-222-2-200i2i2−i2−i2i2i2−i2−i22-20000i2i2−i2−i2i2i2−i2−i200002-22-2000000000000i2−i2i2−i200
χ382-2-222-202002-20-222-2-200i2i2−i2−i2i2i2−i2−i22-20000i2i2−i2−i2i2i2−i2−i20000-22-22000000000000−i2i2−i2i200
χ392-2-222-202002-20-222-2-200−i2−i2i2i2−i2−i2i2i22-20000−i2−i2i2i2−i2−i2i2i200002-22-2000000000000−i2i2−i2i200
χ402-2-222-202002-20-222-2-200−i2−i2i2i2−i2−i2i2i22-20000−i2−i2i2i2−i2−i2i2i20000-22-22000000000000i2−i2i2−i200
χ412-2-222-202002-20-2-2-22200i2i2−i2−i2i2i2−i2−i2-220000−i2−i2i2i2−i2−i2i2i200002-2-22000000000000i2−i2−i2i200
χ422-2-222-202002-20-2-2-22200i2i2−i2−i2i2i2−i2−i2-220000−i2−i2i2i2−i2−i2i2i20000-222-2000000000000−i2i2i2−i200
χ432-2-222-202002-20-2-2-22200−i2−i2i2i2−i2−i2i2i2-220000i2i2−i2−i2i2i2−i2−i200002-2-22000000000000−i2i2i2−i200
χ442-2-222-202002-20-2-2-22200−i2−i2i2i2−i2−i2i2i2-220000i2i2−i2−i2i2i2−i2−i20000-222-2000000000000i2−i2−i2i200
χ454444444-444-4-44-40000-4-4000000000000000000000000000000000000000000000000
χ464444-4-4-4444-4-4-4400004-4000000000000000000000000000000000000000000000000
χ4744-4-400400000-4022−2222−22002-22-22-22-20022−220022−2222−22000000000000000000000000000000
χ4844-4-400400000-4022−2222−2200-22-22-22-220022−2200−2222−2222000000000000000000000000000000
χ4944-4-400400000-40−2222−2222002-22-22-22-200−222200−2222−2222000000000000000000000000000000
χ5044-4-400400000-40−2222−222200-22-22-22-2200−22220022−2222−22000000000000000000000000000000
χ5144-4-400-4000004022−2222−22002i−2i2i−2i−2i2i−2i2i00−22220000002i2−2i22i2−2i200000000000000000000000000
χ5244-4-400-4000004022−2222−2200−2i2i−2i2i2i−2i2i−2i00−2222000000−2i22i2−2i22i200000000000000000000000000
χ5344-4-400-40000040−2222−2222002i−2i2i−2i−2i2i−2i2i0022−22000000−2i22i2−2i22i200000000000000000000000000
χ5444-4-400-40000040−2222−222200−2i2i−2i2i2i−2i2i−2i0022−220000002i2−2i22i2−2i200000000000000000000000000
χ554-44-400004i−4i000022−22−2222002ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ300002i2−2i22i−2i−2i2i2-2-2200000000000000000000000000
χ564-44-400004i−4i000022−22−222200−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ300002i2−2i2−2i2i2i−2i-222-200000000000000000000000000
χ574-44-400004i−4i0000−222222−22002ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ30000−2i22i2−2i2i2i−2i-222-200000000000000000000000000
χ584-44-400004i−4i0000−222222−2200−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ30000−2i22i22i−2i−2i2i2-2-2200000000000000000000000000
χ594-44-40000−4i4i000022−22−2222002ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ0000−2i22i22i−2i−2i2i-222-200000000000000000000000000
χ604-44-40000−4i4i000022−22−222200−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ0000−2i22i2−2i2i2i−2i2-2-2200000000000000000000000000
χ614-44-40000−4i4i0000−222222−22002ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ00002i2−2i2−2i2i2i−2i2-2-2200000000000000000000000000
χ624-44-40000−4i4i0000−222222−2200−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ00002i2−2i22i−2i−2i2i-222-200000000000000000000000000
χ634-4-444-40-400-44040000002222−22−22−22−2222220000000000000000000000000000000000000000
χ644-4-444-40-400-4404000000−22−2222222222−22−220000000000000000000000000000000000000000
χ654-4-44-440400-440-4000000000000000000002i22i2−2i2−2i2−2i2−2i22i22i200000000000000000000000000
χ664-4-44-440400-440-400000000000000000000−2i2−2i22i22i22i22i2−2i2−2i200000000000000000000000000
χ674-4-44-440-4004-40444-4-40000000000-4400000000000000000000000000000000000000
χ684-4-44-440-4004-404-4-44400000000004-400000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.