Finite Group Databasebeta

← Group #117416

Character table — Group #117416

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222222222222222244444444444444444444888888888888888816161616161616161616161616161616
order12224444222244444444444444442444444444444444444488888888888888884444888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111
χ511111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1
χ611111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ91111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-111-1iiiiiiii−i−i−i−i−i−i−i−iiiii−i−i−i−i1111-1-1-1-111-1-1i−iii−i−ii−i11-1-1
χ101111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-111-1iiiiiiii−i−i−i−i−i−i−i−iiiii−i−i−i−i1111-1-1-1-1-1-111−ii−i−iii−ii-1-111
χ111111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-111-1iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiii-1-1-1-1111111-1-1−iiii−i−i−ii-1-111
χ121111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-111-1iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiii-1-1-1-11111-1-111i−i−i−iiii−i11-1-1
χ131111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-111-1−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i-1-1-1-1111111-1-1i−i−i−iiii−i-1-111
χ141111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-111-1−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i-1-1-1-11111-1-111−iiii−i−i−ii11-1-1
χ151111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-111-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−iiiii1111-1-1-1-111-1-1−ii−i−iii−ii11-1-1
χ161111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-111-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−iiiii1111-1-1-1-1-1-111i−iii−i−ii−i-1-111
χ1722222222222222-2-2-2-2-2-2-2-222-2-2-2-222-2-2000000000000000000000000000000000000002-22-2000000
χ1822222222222222-2-2-2-2-2-2-2-222-2-2-2-222-2-200000000000000000000000000000000000000-22-22000000
χ192222222222-2-22222-2-222-2-2-2-22222-2-2-2-2000000000000000022-2-222-2-2000000000000000000000000
χ202222222222-2-22222-2-222-2-2-2-22222-2-2-2-20000000000000000-2-222-2-222000000000000000000000000
χ212222222222-2-222-2-222-2-222-2-2-2-2-2-2-2-222000000000000000000000000000000000000000000002i−2i2i−2i
χ222222222222-2-222-2-222-2-222-2-2-2-2-2-2-2-22200000000000000000000000000000000000000000000−2i2i−2i2i
χ2322222222-2-222-2-22222-2-22222-2-222-2-2-2-2000000000000000000000000000000000000220000-2-20000
χ2422222222-2-222-2-22222-2-22222-2-222-2-2-2-2000000000000000000000000000000000000-2-20000220000
χ2522222222-2-222-2-2-2-2-2-222-2-22222-2-2-2-22200000000000000000000000022-2-222-2-20000000000000000
χ2622222222-2-222-2-2-2-2-2-222-2-22222-2-2-2-222000000000000000000000000-2-222-2-2220000000000000000
χ2722222222-2-2-2-2-2-222-2-2-2-2-2-2-2-2-2-2222222000000000000000000000000000000002-22-2000000000000
χ2822222222-2-2-2-2-2-222-2-2-2-2-2-2-2-2-2-222222200000000000000000000000000000000-22-22000000000000
χ2922222222-2-2-2-2-2-2-2-2222222-2-222-2-222-2-22222-2-2-2-22222-2-2-2-200000000000000000000000000000000
χ3022222222-2-2-2-2-2-2-2-2222222-2-222-2-222-2-2-2-2-2-22222-2-2-2-2222200000000000000000000000000000000
χ312222-2-2-2-22222-2-222-2-2-2-222-2-222-2-22-2-2200000000000000002i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ322222-2-2-2-22222-2-222-2-2-2-222-2-222-2-22-2-220000000000000000−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ332222-2-2-2-22222-2-2-2-22222-2-2-2-2-2-2222-22-2000000000000000000000000000000000000000000002i−2i−2i2i
χ342222-2-2-2-22222-2-2-2-22222-2-2-2-2-2-2222-22-200000000000000000000000000000000000000000000−2i2i2i−2i
χ352222-2-2-2-222-2-2-2-2-2-2-2-2222222-2-222-22-22000000000000000000000000000000000000002i−2i−2i2i000000
χ362222-2-2-2-222-2-2-2-2-2-2-2-2222222-2-222-22-2200000000000000000000000000000000000000−2i2i2i−2i000000
χ372222-2-2-2-2-2-2222222-2-22222-2-2-2-2-2-2-222-2000000000000000000000000000000002-2-22000000000000
χ382222-2-2-2-2-2-2222222-2-22222-2-2-2-2-2-2-222-200000000000000000000000000000000-222-2000000000000
χ392222-2-2-2-2-2-22222-2-222-2-2-2-2-2-22222-22-222i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i00000000000000000000000000000000
χ402222-2-2-2-2-2-22222-2-222-2-2-2-2-2-22222-22-22−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i00000000000000000000000000000000
χ412222-2-2-2-2-2-2-2-222222222-2-222-2-2-2-22-2-220000000000000000000000000000000000002i−2i0000−2i2i0000
χ422222-2-2-2-2-2-2-2-222222222-2-222-2-2-2-22-2-22000000000000000000000000000000000000−2i2i00002i−2i0000
χ432222-2-2-2-2-2-2-2-222-2-2-2-2-2-2222222222-22-200000000000000000000000022-2-2-2-2220000000000000000
χ442222-2-2-2-2-2-2-2-222-2-2-2-2-2-2222222222-22-2000000000000000000000000-2-22222-2-20000000000000000
χ452-22-22i−2i2i−2i2-2002i−2i2-2002i−2i00002-22i−2i00001+i1+i−1−i−1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i1−i1−i−1+i−1+i002ζ3−2ζ3002ζ−2ζi2−i2i2−i22−22−20000000000000000
χ462-22-22i−2i2i−2i2-2002i−2i2-2002i−2i00002-22i−2i00001+i1+i−1−i−1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i1−i1−i−1+i−1+i00−2ζ32ζ300−2ζ2ζ−i2i2−i2i2−22−220000000000000000
χ472-22-22i−2i2i−2i2-2002i−2i2-2002i−2i00002-22i−2i0000−1−i−1−i1+i1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1+i−1+i1−i1−i002ζ3−2ζ3002ζ−2ζ−i2i2−i2i2−22−220000000000000000
χ482-22-22i−2i2i−2i2-2002i−2i2-2002i−2i00002-22i−2i0000−1−i−1−i1+i1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1+i−1+i1−i1−i00−2ζ32ζ300−2ζ2ζi2−i2i2−i22−22−20000000000000000
χ492-22-22i−2i2i−2i-2200−2i2i-22002i−2i00002-2−2i2i00001+i1+i−1−i−1−i−1−i−1−i1+i1+i1−i1−i−1+i−1+i−1+i−1+i1−i1−i2ζ3−2ζ3002ζ−2ζ00i2−i2−i2i22−2−220000000000000000
χ502-22-22i−2i2i−2i-2200−2i2i-22002i−2i00002-2−2i2i00001+i1+i−1−i−1−i−1−i−1−i1+i1+i1−i1−i−1+i−1+i−1+i−1+i1−i1−i−2ζ32ζ300−2ζ2ζ00−i2i2i2−i2−222−20000000000000000
χ512-22-22i−2i2i−2i-2200−2i2i-22002i−2i00002-2−2i2i0000−1−i−1−i1+i1+i1+i1+i−1−i−1−i−1+i−1+i1−i1−i1−i1−i−1+i−1+i2ζ3−2ζ3002ζ−2ζ00−i2i2i2−i2−222−20000000000000000
χ522-22-22i−2i2i−2i-2200−2i2i-22002i−2i00002-2−2i2i0000−1−i−1−i1+i1+i1+i1+i−1−i−1−i−1+i−1+i1−i1−i1−i1−i−1+i−1+i−2ζ32ζ300−2ζ2ζ00i2−i2−i2i22−2−220000000000000000
χ532-22-2−2i2i−2i2i2-200−2i2i2-200−2i2i00002-2−2i2i00001−i1−i−1+i−1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i1+i1+i−1−i−1−i002ζ−2ζ002ζ3−2ζ3i2−i2i2−i2−22−220000000000000000
χ542-22-2−2i2i−2i2i2-200−2i2i2-200−2i2i00002-2−2i2i00001−i1−i−1+i−1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i1+i1+i−1−i−1−i00−2ζ2ζ00−2ζ32ζ3−i2i2−i2i22−22−20000000000000000
χ552-22-2−2i2i−2i2i2-200−2i2i2-200−2i2i00002-2−2i2i0000−1+i−1+i1−i1−i−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1−i−1−i1+i1+i002ζ−2ζ002ζ3−2ζ3−i2i2−i2i22−22−20000000000000000
χ562-22-2−2i2i−2i2i2-200−2i2i2-200−2i2i00002-2−2i2i0000−1+i−1+i1−i1−i−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1−i−1−i1+i1+i00−2ζ2ζ00−2ζ32ζ3i2−i2i2−i2−22−220000000000000000
χ572-22-2−2i2i−2i2i-22002i−2i-2200−2i2i00002-22i−2i00001−i1−i−1+i−1+i−1+i−1+i1−i1−i1+i1+i−1−i−1−i−1−i−1−i1+i1+i2ζ−2ζ002ζ3−2ζ300i2−i2−i2i2−222−20000000000000000
χ582-22-2−2i2i−2i2i-22002i−2i-2200−2i2i00002-22i−2i00001−i1−i−1+i−1+i−1+i−1+i1−i1−i1+i1+i−1−i−1−i−1−i−1−i1+i1+i−2ζ2ζ00−2ζ32ζ300−i2i2i2−i22−2−220000000000000000
χ592-22-2−2i2i−2i2i-22002i−2i-2200−2i2i00002-22i−2i0000−1+i−1+i1−i1−i1−i1−i−1+i−1+i−1−i−1−i1+i1+i1+i1+i−1−i−1−i2ζ−2ζ002ζ3−2ζ300−i2i2i2−i22−2−220000000000000000
χ602-22-2−2i2i−2i2i-22002i−2i-2200−2i2i00002-22i−2i0000−1+i−1+i1−i1−i1−i1−i−1+i−1+i−1−i−1−i1+i1+i1+i1+i−1−i−1−i−2ζ2ζ00−2ζ32ζ300i2−i2−i2i2−222−20000000000000000
χ6144-4-444-4-4004-400000000004-4000000002-22-22-22-22-22-22-22-200000000000000000000000000000000
χ6244-4-444-4-4004-400000000004-400000000-22-22-22-22-22-22-22-2200000000000000000000000000000000
χ6344-4-444-4-400-440000000000-44000000002-22-2-22-222-22-2-22-2200000000000000000000000000000000
χ6444-4-444-4-400-440000000000-4400000000-22-222-22-2-22-222-22-200000000000000000000000000000000
χ6544-4-4-4-444004-40000000000-44000000002i−2i2i−2i−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i00000000000000000000000000000000
χ6644-4-4-4-444004-40000000000-4400000000−2i2i−2i2i2i−2i2i−2i2i−2i2i−2i−2i2i−2i2i00000000000000000000000000000000
χ6744-4-4-4-44400-4400000000004-4000000002i−2i2i−2i2i−2i2i−2i−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000000
χ6844-4-4-4-44400-4400000000004-400000000−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000
χ694-44-44i−4i4i−4i4-4004i−4i-4400−4i4i0000-44−4i4i0000000000000000000000000000000000000000000000000000
χ704-44-44i−4i4i−4i-4400−4i4i4-400−4i4i0000-444i−4i0000000000000000000000000000000000000000000000000000
χ714-44-4−4i4i−4i4i4-400−4i4i-44004i−4i0000-444i−4i0000000000000000000000000000000000000000000000000000
χ724-44-4−4i4i−4i4i-44004i−4i4-4004i−4i0000-44−4i4i0000000000000000000000000000000000000000000000000000
χ734-4-444i−4i−4i4i000000004-4004i−4i000000000000002+2i−2−2i−2−2i2+2i00002−2i−2+2i−2+2i2−2i00000000000000000000000000000000
χ744-4-444i−4i−4i4i000000004-4004i−4i00000000000000−2−2i2+2i2+2i−2−2i0000−2+2i2−2i2−2i−2+2i00000000000000000000000000000000
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χ764-4-444i−4i−4i4i00000000-4400−4i4i0000000000−2−2i2+2i2+2i−2−2i0000−2+2i2−2i2−2i−2+2i000000000000000000000000000000000000
χ774-4-44−4i4i4i−4i000000004-400−4i4i000000000000002−2i−2+2i−2+2i2−2i00002+2i−2−2i−2−2i2+2i00000000000000000000000000000000
χ784-4-44−4i4i4i−4i000000004-400−4i4i00000000000000−2+2i2−2i2−2i−2+2i0000−2−2i2+2i2+2i−2−2i00000000000000000000000000000000
χ794-4-44−4i4i4i−4i00000000-44004i−4i00000000002−2i−2+2i−2+2i2−2i00002+2i−2−2i−2−2i2+2i000000000000000000000000000000000000
χ804-4-44−4i4i4i−4i00000000-44004i−4i0000000000−2+2i2−2i2−2i−2+2i0000−2−2i2+2i2+2i−2−2i000000000000000000000000000000000000

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