Finite Group Databasebeta

← Group #264805

Character table — Group #264805

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11112222222222222244444444444444444444444488888888161616161616161616161616161616163232
order12222244444444888844888888888888888888888844444444224444448888888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-11-1-11-1-1-1-11111-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-111-1-1-111-1-1-1-1-1-1-1-111
χ511111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-111-1111111-1-1-1-1-1-1-1-1
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
χ711111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1111-1-1-1-111-1-1-1-111
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
χ911111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-11-1-11-11-1-1-11111-1-11-1
χ1011111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-11-1-11-11-1-111-1-111-11
χ1111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11-1111-1-1111-1-111-1-1-11
χ1211111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11-111-111-1-1-1-1111-1
χ1311111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-111-111-11-1-1-1-1-1-1-111-11
χ1411111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1111-111-11-11-1-1-1-111-1-11-1
χ1511111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1-11-11-1-111111-1-1111-1
χ1611111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-11-1-1-111-1111111-1-1-11
χ17222222-2-2-22222-22222-2-20000000022-2-2-2-200000000000022220000-2-2000000000000
χ18222222-2-2-22222-22222-2-20000000022-2-2-2-2000000000000-2-2-2-2000022000000000000
χ19222222-2-2-22222-2-2-2-2-2-2-200000000-2-2222200000000000022-2-20000-22000000000000
χ20222222-2-2-22222-2-2-2-2-2-2-200000000-2-22222000000000000-2-22200002-2000000000000
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
χ252222-2-22-2-222-2-220000-22000000000000002222-2-2-2-222-2-20000200-200000000000000
χ262222-2-22-2-222-2-220000-22000000000000002222-2-2-2-2-2-2220000-200200000000000000
χ272222-2-22-2-222-2-220000-2200000000000000-2-2-2-2222222-2-20000-200200000000000000
χ282222-2-22-2-222-2-220000-2200000000000000-2-2-2-22222-2-2220000200-200000000000000
χ292222-2-22-2-2-2-222222222-200000000-2-222-2-20000000000000000022000-2-20000000000
χ302222-2-22-2-2-2-222222222-200000000-2-222-2-200000000000000000-2-2000220000000000
χ312222-2-22-2-2-2-2222-2-2-2-22-20000000022-2-222000000000000000002-2000-220000000000
χ322222-2-22-2-2-2-2222-2-2-2-22-20000000022-2-22200000000000000000-220002-20000000000
χ332222-2-2-222-2-222-22222-2200000000-2-2-2-222000000002-2-220000000000002-200000000
χ342222-2-2-222-2-222-22222-2200000000-2-2-2-22200000000-222-2000000000000-2200000000
χ352222-2-2-222-2-222-2-2-2-2-2-22000000002222-2-2000000002-2-22000000000000-2200000000
χ362222-2-2-222-2-222-2-2-2-2-2-22000000002222-2-200000000-222-20000000000002-200000000
χ372-22-22-20002-22-202i2i−2i−2i0022−2−222−2−22i−2i0000i2i2−i2−i2i2i2−i2−i200002i−2i2-2000000000000i2−i22−200
χ382-22-22-20002-22-202i2i−2i−2i0022−2−222−2−22i−2i0000i2i2−i2−i2i2i2−i2−i20000−2i2i-22000000000000−i2i2−2200
χ392-22-22-20002-22-202i2i−2i−2i00−2−222−2−2222i−2i0000−i2−i2i2i2−i2−i2i2i200002i−2i2-2000000000000−i2i2−2200
χ402-22-22-20002-22-202i2i−2i−2i00−2−222−2−2222i−2i0000−i2−i2i2i2−i2−i2i2i20000−2i2i-22000000000000i2−i22−200
χ412-22-22-20002-22-20−2i−2i2i2i0022−2−222−2−2−2i2i0000−i2−i2i2i2−i2−i2i2i200002i−2i-22000000000000i2−i2−2200
χ422-22-22-20002-22-20−2i−2i2i2i0022−2−222−2−2−2i2i0000−i2−i2i2i2−i2−i2i2i20000−2i2i2-2000000000000−i2i22−200
χ432-22-22-20002-22-20−2i−2i2i2i00−2−222−2−222−2i2i0000i2i2−i2−i2i2i2−i2−i200002i−2i-22000000000000−i2i22−200
χ442-22-22-20002-22-20−2i−2i2i2i00−2−222−2−222−2i2i0000i2i2−i2−i2i2i2−i2−i20000−2i2i2-2000000000000i2−i2−2200
χ45444444444-4-4-4-440000-4-4000000000000000000000000000000000000000000000000
χ464444-4-4-44444-4-4-400004-4000000000000000000000000000000000000000000000000
χ4744-4-4004000000-422−2222−22002-22-22-22-20022−220022−2222−22000000000000000000000000000000
χ4844-4-4004000000-422−2222−2200-22-22-22-220022−2200−2222−2222000000000000000000000000000000
χ4944-4-4004000000-4−2222−2222002-22-22-22-200−222200−2222−2222000000000000000000000000000000
χ5044-4-4004000000-4−2222−222200-22-22-22-2200−22220022−2222−22000000000000000000000000000000
χ5144-4-400-4000000422−2222−22002i−2i2i−2i−2i2i−2i2i00−22220000002i2−2i22i2−2i200000000000000000000000000
χ5244-4-400-4000000422−2222−2200−2i2i−2i2i2i−2i2i−2i00−2222000000−2i22i2−2i22i200000000000000000000000000
χ5344-4-400-40000004−2222−2222002i−2i2i−2i−2i2i−2i2i0022−22000000−2i22i2−2i22i200000000000000000000000000
χ5444-4-400-40000004−2222−222200−2i2i−2i2i2i−2i2i−2i0022−220000002i2−2i22i2−2i200000000000000000000000000
χ554-44-44-4000-44-4400000002i22i2−2i2−2i2−2i2−2i22i22i20000000000000000000000000000000000000000
χ564-44-44-4000-44-440000000−2i2−2i22i22i22i22i2−2i2−2i20000000000000000000000000000000000000000
χ574-44-4-440004-4-440000000000000000000002i22i2−2i2−2i2−2i2−2i22i22i200000000000000000000000000
χ584-44-4-440004-4-44000000000000000000000−2i2−2i22i22i22i22i2−2i2−2i200000000000000000000000000
χ594-44-4-44000-444-404i4i−4i−4i0000000000−4i4i00000000000000000000000000000000000000
χ604-44-4-44000-444-40−4i−4i4i4i00000000004i−4i00000000000000000000000000000000000000
χ614-4-440004i−4i000002i2−2i2−2i22i2002ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ3000022−222i−2i−2i2i-222-200000000000000000000000000
χ624-4-440004i−4i000002i2−2i2−2i22i200−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ3000022−22−2i2i2i−2i2-2-2200000000000000000000000000
χ634-4-440004i−4i00000−2i22i22i2−2i2002ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ30000−2222−2i2i2i−2i2-2-2200000000000000000000000000
χ644-4-440004i−4i00000−2i22i22i2−2i200−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ30000−22222i−2i−2i2i-222-200000000000000000000000000
χ654-4-44000−4i4i000002i2−2i2−2i22i2002ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ0000−2222−2i2i2i−2i-222-200000000000000000000000000
χ664-4-44000−4i4i000002i2−2i2−2i22i200−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ0000−22222i−2i−2i2i2-2-2200000000000000000000000000
χ674-4-44000−4i4i00000−2i22i22i2−2i2002ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ000022−222i−2i−2i2i2-2-2200000000000000000000000000
χ684-4-44000−4i4i00000−2i22i22i2−2i200−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ000022−22−2i2i2i−2i-222-200000000000000000000000000

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