Finite Group Databasebeta

← Group #470972

Character table — Group #470972

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222222222444444444444444444444444161616161616161616161616161616161616161616161616
order12224444222222444444444444448888888888888888244444448888888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1
χ51111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-111-1-111-1-1
χ61111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-11111-1-1-1-111-1-111
χ71111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-11111-1-1
χ81111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-111
χ911111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-111-1-111
χ1011111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-111-1-111-1-111-1-1
χ1111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-111
χ1211111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-11111-1-1
χ1311111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1111111-1-11111-1-1-1-1-1-1-1-1
χ1411111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111
χ1511111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111111-1-111-1-1-1-11111-1-1-1-1
χ1611111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1111111-1-1-1-1-1-11111
χ17222222222-2-22-2-222-2-2-2-200000000000000002222-2-2-2-200000000000000002i−2i2i−2i0000
χ18222222222-2-22-2-222-2-2-2-200000000000000002222-2-2-2-20000000000000000−2i2i−2i2i0000
χ19222222222-2-22-2-222-2-2-2-20000000000000000-2-2-2-2222200000000000000002i−2i−2i2i0000
χ20222222222-2-22-2-222-2-2-2-20000000000000000-2-2-2-222220000000000000000−2i2i2i−2i0000
χ2122222222-22-2-22-2-2-222-2-22222-2-2-2-20000000000000000002i−2i00000000002i−2i00000000
χ2222222222-22-2-22-2-2-222-2-22222-2-2-2-2000000000000000000−2i2i0000000000−2i2i00000000
χ2322222222-22-2-22-2-2-222-2-2-2-2-2-222220000000000000000002i−2i0000000000−2i2i00000000
χ2422222222-22-2-22-2-2-222-2-2-2-2-2-22222000000000000000000−2i2i00000000002i−2i00000000
χ252222-2-2-2-22-2-22-2-2-2-222222i2i−2i−2i2i2i−2i−2i00000000000000002-2000000002i−2i000000000000
χ262222-2-2-2-22-2-22-2-2-2-222222i2i−2i−2i2i2i−2i−2i0000000000000000-2200000000−2i2i000000000000
χ272222-2-2-2-22-2-22-2-2-2-22222−2i−2i2i2i−2i−2i2i2i00000000000000002-200000000−2i2i000000000000
χ282222-2-2-2-22-2-22-2-2-2-22222−2i−2i2i2i−2i−2i2i2i0000000000000000-22000000002i−2i000000000000
χ292222-2-2-2-2-22-2-22-222-2-222000000000000000022-2-222-2-2000000002i−2i002i−2i0000000000
χ302222-2-2-2-2-22-2-22-222-2-222000000000000000022-2-222-2-200000000−2i2i00−2i2i0000000000
χ312222-2-2-2-2-22-2-22-222-2-2220000000000000000-2-222-2-222000000002i−2i00−2i2i0000000000
χ322222-2-2-2-2-22-2-22-222-2-2220000000000000000-2-222-2-22200000000−2i2i002i−2i0000000000
χ332222-2-2-2-2-2-22-2-222222-2-22i2i−2i−2i−2i−2i2i2i2i2i2i2i−2i−2i−2i−2i22-2-2-2-222000000000000000000000000
χ342222-2-2-2-2-2-22-2-222222-2-22i2i−2i−2i−2i−2i2i2i−2i−2i−2i−2i2i2i2i2i-2-22222-2-2000000000000000000000000
χ352222-2-2-2-2-2-22-2-222222-2-2−2i−2i2i2i2i2i−2i−2i2i2i2i2i−2i−2i−2i−2i-2-22222-2-2000000000000000000000000
χ362222-2-2-2-2-2-22-2-222222-2-2−2i−2i2i2i2i2i−2i−2i−2i−2i−2i−2i2i2i2i2i22-2-2-2-222000000000000000000000000
χ372-2-2222-2-2-2-2222-22-22-22-20000000022-2-222-2-2000000000000002i−2i0000000000002i−2i00
χ382-2-2222-2-2-2-2222-22-22-22-20000000022-2-222-2-200000000000000−2i2i000000000000−2i2i00
χ392-2-2222-2-2-2-2222-22-22-22-200000000-2-222-2-222000000000000002i−2i000000000000−2i2i00
χ402-2-2222-2-2-2-2222-22-22-22-200000000-2-222-2-22200000000000000−2i2i0000000000002i−2i00
χ412-2-22-2-222222-2-2-22-22-2-22000000002i2i−2i−2i−2i−2i2i2i0000000000002i−2i00000000000000002-2
χ422-2-22-2-222222-2-2-22-22-2-22000000002i2i−2i−2i−2i−2i2i2i000000000000−2i2i0000000000000000-22
χ432-2-22-2-222222-2-2-22-22-2-2200000000−2i−2i2i2i2i2i−2i−2i0000000000002i−2i0000000000000000-22
χ442-2-22-2-222222-2-2-22-22-2-2200000000−2i−2i2i2i2i2i−2i−2i000000000000−2i2i00000000000000002-2
χ4544444444-4-44-4-44-4-4-4-444000000000000000000000000000000000000000000000000
χ464444-4-4-4-4444444-4-4-4-4-4-4000000000000000000000000000000000000000000000000
χ4744-4-44i−4i4i−4i00000000000000002+2i−2−2i2−2i−2+2i2ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ3000022−222i2−2i2000000000000000000000000
χ4844-4-44i−4i4i−4i00000000000000002+2i−2−2i2−2i−2+2i−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ30000−2222−2i22i2000000000000000000000000
χ4944-4-44i−4i4i−4i0000000000000000−2−2i2+2i−2+2i2−2i2ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ30000−2222−2i22i2000000000000000000000000
χ5044-4-44i−4i4i−4i0000000000000000−2−2i2+2i−2+2i2−2i−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ3000022−222i2−2i2000000000000000000000000
χ5144-4-4−4i4i−4i4i00000000000000002−2i−2+2i2+2i−2−2i2ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ0000−22222i2−2i2000000000000000000000000
χ5244-4-4−4i4i−4i4i00000000000000002−2i−2+2i2+2i−2−2i−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ000022−22−2i22i2000000000000000000000000
χ5344-4-4−4i4i−4i4i0000000000000000−2+2i2−2i−2−2i2+2i2ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ000022−22−2i22i2000000000000000000000000
χ5444-4-4−4i4i−4i4i0000000000000000−2+2i2−2i−2−2i2+2i−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ0000−22222i2−2i2000000000000000000000000
χ554-44-44i−4i−4i4i0000000000002−2i−2+2i2+2i−2−2i00002ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ32i2−2i222−220000000000000000000000000000
χ564-44-44i−4i−4i4i0000000000002−2i−2+2i2+2i−2−2i0000−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ3−2i22i2−22220000000000000000000000000000
χ574-44-44i−4i−4i4i000000000000−2+2i2−2i−2−2i2+2i00002ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ3−2i22i2−22220000000000000000000000000000
χ584-44-44i−4i−4i4i000000000000−2+2i2−2i−2−2i2+2i0000−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ32i2−2i222−220000000000000000000000000000
χ594-44-4−4i4i4i−4i0000000000002+2i−2−2i2−2i−2+2i00002ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ2i2−2i2−22220000000000000000000000000000
χ604-44-4−4i4i4i−4i0000000000002+2i−2−2i2−2i−2+2i0000−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ−2i22i222−220000000000000000000000000000
χ614-44-4−4i4i4i−4i000000000000−2−2i2+2i−2+2i2−2i00002ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ−2i22i222−220000000000000000000000000000
χ624-44-4−4i4i4i−4i000000000000−2−2i2+2i−2+2i2−2i0000−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ2i2−2i2−22220000000000000000000000000000
χ634-4-4444-4-4444-4-4-4-44-444-4000000000000000000000000000000000000000000000000
χ644-4-4444-4-44-4-4-444-444-4-44000000000000000000000000000000000000000000000000
χ654-4-4444-4-4-44-44-444-4-44-44000000000000000000000000000000000000000000000000
χ664-4-44-4-4444-4-4-4444-4-444-4000000000000000000000000000000000000000000000000
χ674-4-44-4-444-44-44-44-444-44-4000000000000000000000000000000000000000000000000
χ684-4-44-4-444-4-4444-4-44-44-44000000000000000000000000000000000000000000000000

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