Finite Group Databasebeta

← Group #264804

Character table — Group #264804

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11112222222222222244444444444444444444444488888888161616161616161616161616161616163232
order12222244444444888844888888888888888888888822444444224444448888888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-111111-1-1-11-1-1-1-1-1-1-11111-1-1
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-11-1-1-1111-1-1-1-1-1-1-1-111
χ511111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1111-1111-1-1-1-111-1-1-1-1
χ611111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11-1111-1-1-1-1-1-1-1-1-11111
χ711111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-111
χ811111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-111-1-1
χ911111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-11-1-111-111-1-1-1-1111-1
χ1011111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111-11-1-1111-1-111-1-1-11
χ1111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-11-11-1-1-11-1-111-1-111-11
χ1211111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11-1-11111-1-1-11111-1-11-1
χ1311111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111111-11-1111-1-1-111-1-1-1-1-11
χ1411111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-111-1-1-1-11-1-11111111-1
χ1511111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111111111-111-1-1111-1-1-1-1-1-11-1
χ1611111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-1-11-111-111-1-11111-11
χ17222222-2-222-2-2222222-2-20000000022-2-2-2-2000000002222000000-2-200000000000000
χ18222222-2-222-2-2222222-2-20000000022-2-2-2-200000000-2-2-2-20000002200000000000000
χ19222222-2-222-2-222-2-2-2-2-2-200000000-2-222220000000022-2-2000000-2200000000000000
χ20222222-2-222-2-222-2-2-2-2-2-200000000-2-2222200000000-2-2220000002-200000000000000
χ21222222-2-2-2-2-2-2-2-20000222i2i2i2i−2i−2i−2i−2i00000000000000000022-2-2000000000000002i−2i00
χ22222222-2-2-2-2-2-2-2-20000222i2i2i2i−2i−2i−2i−2i000000000000000000-2-22200000000000000−2i2i00
χ23222222-2-2-2-2-2-2-2-2000022−2i−2i−2i−2i2i2i2i2i00000000000000000022-2-200000000000000−2i2i00
χ24222222-2-2-2-2-2-2-2-2000022−2i−2i−2i−2i2i2i2i2i000000000000000000-2-222000000000000002i−2i00
χ252222-2-222-2-2-2-2222222-2200000000-2-222-2-20000000000002-22-20000000000002-20000
χ262222-2-222-2-2-2-2222222-2200000000-2-222-2-2000000000000-22-22000000000000-220000
χ272222-2-222-2-2-2-222-2-2-2-2-220000000022-2-2220000000000002-22-2000000000000-220000
χ282222-2-222-2-2-2-222-2-2-2-2-220000000022-2-222000000000000-22-220000000000002-20000
χ292222-2-2-2-22222-2-20000-22000000000000002222-2-2-2-200002-2-222000-20000000000000
χ302222-2-2-2-22222-2-20000-22000000000000002222-2-2-2-20000-222-2-200020000000000000
χ312222-2-2-2-22222-2-20000-2200000000000000-2-2-2-2222200002-2-22-200020000000000000
χ322222-2-2-2-22222-2-20000-2200000000000000-2-2-2-222220000-222-22000-20000000000000
χ332222-2-2-2-2-2-2222222222-200000000-2-2-2-2220000000000000000020002-2-20000000000
χ342222-2-2-2-2-2-2222222222-200000000-2-2-2-22200000000000000000-2000-2220000000000
χ352222-2-2-2-2-2-22222-2-2-2-22-2000000002222-2-2000000000000000002000-22-20000000000
χ362222-2-2-2-2-2-22222-2-2-2-22-2000000002222-2-200000000000000000-20002-220000000000
χ3722-2-22-2002-2002-22i2i−2i−2i0022−2−222−2−22i−2i0000i2i2−i2−i2i2i2−i2−i22-22i−2i0000000000002−2i2−i2000000
χ3822-2-22-2002-2002-22i2i−2i−2i0022−2−222−2−22i−2i0000i2i2−i2−i2i2i2−i2−i2-22−2i2i000000000000−22−i2i2000000
χ3922-2-22-2002-2002-22i2i−2i−2i00−2−222−2−2222i−2i0000−i2−i2i2i2−i2−i2i2i22-22i−2i000000000000−22−i2i2000000
χ4022-2-22-2002-2002-22i2i−2i−2i00−2−222−2−2222i−2i0000−i2−i2i2i2−i2−i2i2i2-22−2i2i0000000000002−2i2−i2000000
χ4122-2-22-2002-2002-2−2i−2i2i2i0022−2−222−2−2−2i2i0000−i2−i2i2i2−i2−i2i2i22-2−2i2i0000000000002−2−i2i2000000
χ4222-2-22-2002-2002-2−2i−2i2i2i0022−2−222−2−2−2i2i0000−i2−i2i2i2−i2−i2i2i2-222i−2i000000000000−22i2−i2000000
χ4322-2-22-2002-2002-2−2i−2i2i2i00−2−222−2−222−2i2i0000i2i2−i2−i2i2i2−i2−i22-2−2i2i000000000000−22i2−i2000000
χ4422-2-22-2002-2002-2−2i−2i2i2i00−2−222−2−222−2i2i0000i2i2−i2−i2i2i2−i2−i2-222i−2i0000000000002−2−i2i2000000
χ4544444444-4-444-4-40000-4-4000000000000000000000000000000000000000000000000
χ464444-4-44444-4-4-4-400004-4000000000000000000000000000000000000000000000000
χ4744-4-44-400-4400-440000002i22i2−2i2−2i2−2i2−2i22i22i20000000000000000000000000000000000000000
χ4844-4-44-400-4400-44000000−2i2−2i22i22i22i22i2−2i2−2i20000000000000000000000000000000000000000
χ4944-4-4-44004-400-44000000000000000000002i22i2−2i2−2i2−2i2−2i22i22i200000000000000000000000000
χ5044-4-4-44004-400-4400000000000000000000−2i2−2i22i22i22i22i2−2i2−2i200000000000000000000000000
χ5144-4-4-4400-44004-44i4i−4i−4i0000000000−4i4i00000000000000000000000000000000000000
χ5244-4-4-4400-44004-4−4i−4i4i4i00000000004i−4i00000000000000000000000000000000000000
χ534-44-40000004-4002i2−2i22i2−2i2002-22-22-22-200002i2−2i200002i2−2i22i2−2i200000000000000000000000000
χ544-44-40000004-4002i2−2i22i2−2i200-22-22-22-2200002i2−2i20000−2i22i2−2i22i200000000000000000000000000
χ554-44-40000004-400−2i22i2−2i22i2002-22-22-22-20000−2i22i20000−2i22i2−2i22i200000000000000000000000000
χ564-44-40000004-400−2i22i2−2i22i200-22-22-22-220000−2i22i200002i2−2i22i2−2i200000000000000000000000000
χ574-44-4000000-44002i2−2i22i2−2i2002i−2i2i−2i−2i2i−2i2i0000−2i22i222−2222−22000000000000000000000000000000
χ584-44-4000000-44002i2−2i22i2−2i200−2i2i−2i2i2i−2i2i−2i0000−2i22i2−2222−2222000000000000000000000000000000
χ594-44-4000000-4400−2i22i2−2i22i2002i−2i2i−2i−2i2i−2i2i00002i2−2i2−2222−2222000000000000000000000000000000
χ604-44-4000000-4400−2i22i2−2i22i200−2i2i−2i2i2i−2i2i−2i00002i2−2i222−2222−22000000000000000000000000000000
χ614-4-44004i−4i00000022−22−2222002ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ3002i2−2i200−2i2i2i−2i2-2-2200000000000000000000000000
χ624-4-44004i−4i00000022−22−222200−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ3002i2−2i2002i−2i−2i2i-222-200000000000000000000000000
χ634-4-44004i−4i000000−222222−22002ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ300−2i22i2002i−2i−2i2i-222-200000000000000000000000000
χ644-4-44004i−4i000000−222222−2200−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ300−2i22i200−2i2i2i−2i2-2-2200000000000000000000000000
χ654-4-4400−4i4i00000022−22−2222002ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ00−2i22i200−2i2i2i−2i-222-200000000000000000000000000
χ664-4-4400−4i4i00000022−22−222200−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ00−2i22i2002i−2i−2i2i2-2-2200000000000000000000000000
χ674-4-4400−4i4i000000−222222−22002ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ002i2−2i2002i−2i−2i2i2-2-2200000000000000000000000000
χ684-4-4400−4i4i000000−222222−2200−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ002i2−2i200−2i2i2i−2i-222-200000000000000000000000000

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