Finite Group Databasebeta

← Group #398733

Character table — Group #398733

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444488888888888888888888888888888888161616161616161616161616
order12224444222222224444444422244444444444888888888888888888888888888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ411111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ5111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ6111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ91111111111111-1-111-1-111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-111-1-1
χ101111111111111-1-111-1-111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-111-1-111
χ111111111111111-1-111-1-111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-111-1-11111-1-1
χ121111111111111-1-111-1-111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-111
χ131111111111111-1-111-1-111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-111
χ141111111111111-1-111-1-111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-11111-1-1
χ151111111111111-1-111-1-111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-1-1-111-1-111
χ161111111111111-1-111-1-111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-11111-1-111-1-1
χ172222222222-2-2-222-2222-2-22-2-22-2-22-2-20000000000000000000000000000000000002i−2i2i−2i0000
χ182222222222-2-2-222-2222-2-22-2-22-2-22-2-2000000000000000000000000000000000000−2i2i−2i2i0000
χ192222222222-2-2-2-2-2-22-2-2-2-22-2-2-222-2220000000000000000000000000000000000002i−2i−2i2i0000
χ202222222222-2-2-2-2-2-22-2-2-2-22-2-2-222-222000000000000000000000000000000000000−2i2i2i−2i0000
χ2122222222-2-222-222-2-22222-2-2-2-22-2-22-200000000000000002i2i−2i−2i2i2i−2i−2i00000000000000000000
χ2222222222-2-222-222-2-22222-2-2-2-22-2-22-20000000000000000−2i−2i2i2i−2i−2i2i2i00000000000000000000
χ2322222222-2-222-2-2-2-2-2-2-222-2-2-22-222-2200000000000000002i2i−2i−2i−2i−2i2i2i00000000000000000000
χ2422222222-2-222-2-2-2-2-2-2-222-2-2-22-222-220000000000000000−2i−2i2i2i2i2i−2i−2i00000000000000000000
χ2522222222-2-2-2-22222-222-2-2-222-2-22-2-2200000000000000000000000000000000000000002-22-2
χ2622222222-2-2-2-22222-222-2-2-222-2-22-2-220000000000000000000000000000000000000000-22-22
χ2722222222-2-2-2-22-2-22-2-2-2-2-2-22222-222-200000000000000000000000000000000000000002-2-22
χ2822222222-2-2-2-22-2-22-2-2-2-2-2-22222-222-20000000000000000000000000000000000000000-222-2
χ292222-2-2-2-222222222-2-2-2-2-2-2-2-2222-2-2-222-2-222-2-2000000000000000000000000000000000000
χ302222-2-2-2-222222222-2-2-2-2-2-2-2-2222-2-2-2-2-222-2-222000000000000000000000000000000000000
χ312222-2-2-2-222222-2-22-222-2-2-2-2-2-2-2-222222-2-2-2-222000000000000000000000000000000000000
χ322222-2-2-2-222222-2-22-222-2-2-2-2-2-2-2-2222-2-22222-2-2000000000000000000000000000000000000
χ332222-2-2-2-222-2-2-222-2-2-2-222-2222-2-2-222000000000000000000000000000000002i−2i2i−2i00000000
χ342222-2-2-2-222-2-2-222-2-2-2-222-2222-2-2-22200000000000000000000000000000000−2i2i−2i2i00000000
χ352222-2-2-2-222-2-2-2-2-2-2-22222-222-2222-2-2000000000000000000000000000000002i−2i−2i2i00000000
χ362222-2-2-2-222-2-2-2-2-2-2-22222-222-2222-2-200000000000000000000000000000000−2i2i2i−2i00000000
χ372222-2-2-2-2-2-222-222-22-2-2-2-2222-22-22-22000000002i2i−2i−2i2i2i−2i−2i0000000000000000000000000000
χ382222-2-2-2-2-2-222-222-22-2-2-2-2222-22-22-2200000000−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000
χ392222-2-2-2-2-2-222-2-2-2-2222-2-22222-22-22-2000000002i2i−2i−2i−2i−2i2i2i0000000000000000000000000000
χ402222-2-2-2-2-2-222-2-2-2-2222-2-22222-22-22-200000000−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000
χ412222-2-2-2-2-2-2-2-222222-2-2222-2-2-2-2222-20000000000000000000000002i2i−2i−2i2i2i−2i−2i000000000000
χ422222-2-2-2-2-2-2-2-222222-2-2222-2-2-2-2222-2000000000000000000000000−2i−2i2i2i−2i−2i2i2i000000000000
χ432222-2-2-2-2-2-2-2-22-2-22222222-2-222-2-2-220000000000000000000000002i2i−2i−2i−2i−2i2i2i000000000000
χ442222-2-2-2-2-2-2-2-22-2-22222222-2-222-2-2-22000000000000000000000000−2i−2i2i2i2i2i−2i−2i000000000000
χ452-2-2222-2-22-22-2200-2-2002-222-200000000002i−2i2i−2i00002i−2i2i−2i2-22-2000000000000000000000000
χ462-2-2222-2-22-22-2200-2-2002-222-200000000002i−2i2i−2i0000−2i2i−2i2i-22-22000000000000000000000000
χ472-2-2222-2-22-22-2200-2-2002-222-20000000000−2i2i−2i2i00002i−2i2i−2i-22-22000000000000000000000000
χ482-2-2222-2-22-22-2200-2-2002-222-20000000000−2i2i−2i2i0000−2i2i−2i2i2-22-2000000000000000000000000
χ492-2-2222-2-2-222-2-20022002-2-2-220000002-22-200002i−2i2i−2i00002i−2i−2i2i000000000000000000000000
χ502-2-2222-2-2-222-2-20022002-2-2-220000002-22-20000−2i2i−2i2i0000−2i2i2i−2i000000000000000000000000
χ512-2-2222-2-2-222-2-20022002-2-2-22000000-22-2200002i−2i2i−2i0000−2i2i2i−2i000000000000000000000000
χ522-2-2222-2-2-222-2-20022002-2-2-22000000-22-220000−2i2i−2i2i00002i−2i−2i2i000000000000000000000000
χ532-2-22-2-2222-22-2200-2200-22-2-2200000000002i−2i−2i2i2-2-22000000002i−2i2i−2i00000000000000000000
χ542-2-22-2-2222-22-2200-2200-22-2-2200000000002i−2i−2i2i-222-200000000−2i2i−2i2i00000000000000000000
χ552-2-22-2-2222-22-2200-2200-22-2-220000000000−2i2i2i−2i2-2-2200000000−2i2i−2i2i00000000000000000000
χ562-2-22-2-2222-22-2200-2200-22-2-220000000000−2i2i2i−2i-222-2000000002i−2i2i−2i00000000000000000000
χ572-2-22-2-222-222-2-2002-200-2222-20000002-2-22000000002-2-220000-222-200000000000000000000
χ582-2-22-2-222-222-2-2002-200-2222-20000002-2-2200000000-222-200002-2-2200000000000000000000
χ592-2-22-2-222-222-2-2002-200-2222-2000000-222-2000000002-2-2200002-2-2200000000000000000000
χ602-2-22-2-222-222-2-2002-200-2222-2000000-222-200000000-222-20000-222-200000000000000000000
χ6144-4-44i−4i4i−4i000004-4004i−4i000000000000000000000000000000000002ζ−2ζ2ζ3−2ζ32ζ−2ζ2ζ3−2ζ3000000000000
χ6244-4-44i−4i4i−4i000004-4004i−4i00000000000000000000000000000000000−2ζ2ζ−2ζ32ζ3−2ζ2ζ−2ζ32ζ3000000000000
χ6344-4-44i−4i4i−4i00000-4400−4i4i000000000000000000000000000000000002ζ−2ζ2ζ3−2ζ3−2ζ2ζ−2ζ32ζ3000000000000
χ6444-4-44i−4i4i−4i00000-4400−4i4i00000000000000000000000000000000000−2ζ2ζ−2ζ32ζ32ζ−2ζ2ζ3−2ζ3000000000000
χ6544-4-4−4i4i−4i4i000004-400−4i4i000000000000000000000000000000000002ζ3−2ζ32ζ−2ζ2ζ3−2ζ32ζ−2ζ000000000000
χ6644-4-4−4i4i−4i4i000004-400−4i4i00000000000000000000000000000000000−2ζ32ζ3−2ζ2ζ−2ζ32ζ3−2ζ2ζ000000000000
χ6744-4-4−4i4i−4i4i00000-44004i−4i000000000000000000000000000000000002ζ3−2ζ32ζ−2ζ−2ζ32ζ3−2ζ2ζ000000000000
χ6844-4-4−4i4i−4i4i00000-44004i−4i00000000000000000000000000000000000−2ζ32ζ3−2ζ2ζ2ζ3−2ζ32ζ−2ζ000000000000
χ694-4-4444-4-44-4-44-4004-400-444-4400000000000000000000000000000000000000000000000000
χ704-4-4444-4-4-44-44400-4400-44-44-400000000000000000000000000000000000000000000000000
χ714-4-44-4-4444-4-44-40044004-4-44-400000000000000000000000000000000000000000000000000
χ724-4-44-4-444-44-44400-4-4004-44-4400000000000000000000000000000000000000000000000000
χ738-88-88i−8i−8i8i000000000000000000000000000000000000000000000000000000000000000000
χ748-88-8−8i8i8i−8i000000000000000000000000000000000000000000000000000000000000000000

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