Finite Group Databasebeta

← Group #115111

Character table — Group #115111

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size111111112222222222222222222244444444444444444444888888888888888816161616161616161616161616161616
order12224444222244444444444444442444888888888888888888888888888888882444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ4111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ511111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ611111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111
χ91111-1-1-1-111-1-1111111-1-111-1-1-1-1-1-1-111-1iiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-1iiii−i−i−i−i1-11-111-1-1ii−i−iii−i−i
χ101111-1-1-1-111-1-1111111-1-111-1-1-1-1-1-1-111-1iiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-1iiii−i−i−i−i-11-11-1-111−i−iii−i−iii
χ111111-1-1-1-111-1-1111111-1-111-1-1-1-1-1-1-111-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-11111−i−i−i−iiiii1-11-1-1-111−i−iiiii−i−i
χ121111-1-1-1-111-1-1111111-1-111-1-1-1-1-1-1-111-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-11111−i−i−i−iiiii-11-1111-1-1ii−i−i−i−iii
χ131111-1-1-1-111-1-1111111-1-111-1-1-1-1-1-1-111-1−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-1−i−i−i−iiiii1-11-111-1-1−i−iii−i−iii
χ141111-1-1-1-111-1-1111111-1-111-1-1-1-1-1-1-111-1−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-1−i−i−i−iiiii-11-11-1-111ii−i−iii−i−i
χ151111-1-1-1-111-1-1111111-1-111-1-1-1-1-1-1-111-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-11111iiii−i−i−i−i1-11-1-1-111ii−i−i−i−iii
χ161111-1-1-1-111-1-1111111-1-111-1-1-1-1-1-1-111-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-11111iiii−i−i−i−i-11-1111-1-1−i−iiiii−i−i
χ17222222222222-2-2-2-2-2-2-2-22222-2-2-2-222-2-20000000000000000000000000000000000002-22-200000000
χ18222222222222-2-2-2-2-2-2-2-22222-2-2-2-222-2-2000000000000000000000000000000000000-22-2200000000
χ192222222222-2-22222-2-222-2-22222-2-2-2-2-2-22222-2-2-2-22222-2-2-2-200000000000000000000000000000000
χ202222222222-2-22222-2-222-2-22222-2-2-2-2-2-2-2-2-2-22222-2-2-2-2222200000000000000000000000000000000
χ212222222222-2-2-2-2-2-222-2-2-2-222-2-222-2-22200000000000000000000000000000000000000002-22-20000
χ222222222222-2-2-2-2-2-222-2-2-2-222-2-222-2-2220000000000000000000000000000000000000000-22-220000
χ2322222222-2-22222-2-2222222-2-2-2-222-2-2-2-20000000000000000000000000000000022-2-2000000000000
χ2422222222-2-22222-2-2222222-2-2-2-222-2-2-2-200000000000000000000000000000000-2-222000000000000
χ2522222222-2-222-2-222-2-2-2-222-2-222-2-2-2-222000000000000000022-2-222-2-2000000000000000000000000
χ2622222222-2-222-2-222-2-2-2-222-2-222-2-2-2-2220000000000000000-2-222-2-222000000000000000000000000
χ2722222222-2-2-2-222-2-2-2-222-2-2-2-2-2-2-2-22222000000000000000000000000000000000000000000002i−2i2i−2i
χ2822222222-2-2-2-222-2-2-2-222-2-2-2-2-2-2-2-2222200000000000000000000000000000000000000000000−2i2i−2i2i
χ2922222222-2-2-2-2-2-22222-2-2-2-2-2-2222222-2-200000000000000000000000022-2-222-2-20000000000000000
χ3022222222-2-2-2-2-2-22222-2-2-2-2-2-2222222-2-2000000000000000000000000-2-222-2-2220000000000000000
χ312222-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2222-2-222i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i00000000000000000000000000000000
χ322222-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2222-2-22−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i00000000000000000000000000000000
χ332222-2-2-2-22222-2-2-2-22222-2-2-2-222-2-22-22-200000000000000000000000000000000000000002i−2i−2i2i0000
χ342222-2-2-2-22222-2-2-2-22222-2-2-2-222-2-22-22-20000000000000000000000000000000000000000−2i2i2i−2i0000
χ352222-2-2-2-222-2-2-2-2-2-2-2-22222-2-22222-22-220000000000000000000000000000000000002-2-2200000000
χ362222-2-2-2-222-2-2-2-2-2-2-2-22222-2-22222-22-22000000000000000000000000000000000000-222-200000000
χ372222-2-2-2-2-2-22222-2-2-2-2-2-2-2-2222222-222-2000000000000000000000000000000000000000000002-2-22
χ382222-2-2-2-2-2-22222-2-2-2-2-2-2-2-2222222-222-200000000000000000000000000000000000000000000-222-2
χ392222-2-2-2-2-2-222-2-2222222-2-222-2-2-2-2-22-220000000000000000000000002i2i−2i−2i−2i−2i2i2i0000000000000000
χ402222-2-2-2-2-2-222-2-2222222-2-222-2-2-2-2-22-22000000000000000000000000−2i−2i2i2i2i2i−2i−2i0000000000000000
χ412222-2-2-2-2-2-2-2-222-2-222-2-2222222-2-22-2-22000000000000000000000000000000002-2-22000000000000
χ422222-2-2-2-2-2-2-2-222-2-222-2-2222222-2-22-2-2200000000000000000000000000000000-222-2000000000000
χ432222-2-2-2-2-2-2-2-2-2-222-2-2222222-2-2222-22-2000000000000000022-2-2-2-222000000000000000000000000
χ442222-2-2-2-2-2-2-2-2-2-222-2-2222222-2-2222-22-20000000000000000-2-22222-2-2000000000000000000000000
χ452-22-22i−2i2i−2i2-2002-22-2002i−2i002i−2i2i−2i00000000002ζ32ζ3−2ζ3−2ζ300002ζ2ζ−2ζ−2ζi2−i2i2−i22−22−21+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000000000
χ462-22-22i−2i2i−2i2-2002-22-2002i−2i002i−2i2i−2i00000000002ζ32ζ3−2ζ3−2ζ300002ζ2ζ−2ζ−2ζ−i2i2−i2i2−22−22−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000000000
χ472-22-22i−2i2i−2i2-2002-22-2002i−2i002i−2i2i−2i0000000000−2ζ3−2ζ32ζ32ζ30000−2ζ−2ζ2ζ2ζi2−i2i2−i22−22−2−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000000000
χ482-22-22i−2i2i−2i2-2002-22-2002i−2i002i−2i2i−2i0000000000−2ζ3−2ζ32ζ32ζ30000−2ζ−2ζ2ζ2ζ−i2i2−i2i2−22−221+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000000000
χ492-22-22i−2i2i−2i-2200-222-200−2i2i00−2i2i2i−2i0000002ζ32ζ3−2ζ3−2ζ300002ζ2ζ−2ζ−2ζ0000i2−i2−i2i22−2−221+i−1−i−1−i1+i1−i−1+i−1+i1−i0000000000000000
χ502-22-22i−2i2i−2i-2200-222-200−2i2i00−2i2i2i−2i0000002ζ32ζ3−2ζ3−2ζ300002ζ2ζ−2ζ−2ζ0000−i2i2i2−i2−222−2−1−i1+i1+i−1−i−1+i1−i1−i−1+i0000000000000000
χ512-22-22i−2i2i−2i-2200-222-200−2i2i00−2i2i2i−2i000000−2ζ3−2ζ32ζ32ζ30000−2ζ−2ζ2ζ2ζ0000i2−i2−i2i22−2−22−1−i1+i1+i−1−i−1+i1−i1−i−1+i0000000000000000
χ522-22-22i−2i2i−2i-2200-222-200−2i2i00−2i2i2i−2i000000−2ζ3−2ζ32ζ32ζ30000−2ζ−2ζ2ζ2ζ0000−i2i2i2−i2−222−21+i−1−i−1−i1+i1−i−1+i−1+i1−i0000000000000000
χ532-22-2−2i2i−2i2i2-2002-22-200−2i2i00−2i2i−2i2i00000000002ζ2ζ−2ζ−2ζ00002ζ32ζ3−2ζ3−2ζ3i2−i2i2−i2−22−221−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000000000
χ542-22-2−2i2i−2i2i2-2002-22-200−2i2i00−2i2i−2i2i00000000002ζ2ζ−2ζ−2ζ00002ζ32ζ3−2ζ3−2ζ3−i2i2−i2i22−22−2−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000000000
χ552-22-2−2i2i−2i2i2-2002-22-200−2i2i00−2i2i−2i2i0000000000−2ζ−2ζ2ζ2ζ0000−2ζ3−2ζ32ζ32ζ3i2−i2i2−i2−22−22−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000000000
χ562-22-2−2i2i−2i2i2-2002-22-200−2i2i00−2i2i−2i2i0000000000−2ζ−2ζ2ζ2ζ0000−2ζ3−2ζ32ζ32ζ3−i2i2−i2i22−22−21−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000000000
χ572-22-2−2i2i−2i2i-2200-222-2002i−2i002i−2i−2i2i0000002ζ2ζ−2ζ−2ζ00002ζ32ζ3−2ζ3−2ζ30000i2−i2−i2i2−222−21−i−1+i−1+i1−i1+i−1−i−1−i1+i0000000000000000
χ582-22-2−2i2i−2i2i-2200-222-2002i−2i002i−2i−2i2i0000002ζ2ζ−2ζ−2ζ00002ζ32ζ3−2ζ3−2ζ30000−i2i2i2−i22−2−22−1+i1−i1−i−1+i−1−i1+i1+i−1−i0000000000000000
χ592-22-2−2i2i−2i2i-2200-222-2002i−2i002i−2i−2i2i000000−2ζ−2ζ2ζ2ζ0000−2ζ3−2ζ32ζ32ζ30000i2−i2−i2i2−222−2−1+i1−i1−i−1+i−1−i1+i1+i−1−i0000000000000000
χ602-22-2−2i2i−2i2i-2200-222-2002i−2i002i−2i−2i2i000000−2ζ−2ζ2ζ2ζ0000−2ζ3−2ζ32ζ32ζ30000−i2i2i2−i22−2−221−i−1+i−1+i1−i1+i−1−i−1−i1+i0000000000000000
χ6144-4-444-4-4004-4000000004-400000000002-22-22-22-22-22-22-22-200000000000000000000000000000000
χ6244-4-444-4-4004-4000000004-40000000000-22-22-22-22-22-22-22-2200000000000000000000000000000000
χ6344-4-444-4-400-4400000000-4400000000002-22-2-22-222-22-2-22-2200000000000000000000000000000000
χ6444-4-444-4-400-4400000000-440000000000-22-222-22-2-22-222-22-200000000000000000000000000000000
χ6544-4-4-4-444004-400000000-4400000000002i−2i2i−2i−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i00000000000000000000000000000000
χ6644-4-4-4-444004-400000000-440000000000−2i2i−2i2i2i−2i2i−2i2i−2i2i−2i−2i2i−2i2i00000000000000000000000000000000
χ6744-4-4-4-44400-44000000004-400000000002i−2i2i−2i2i−2i2i−2i−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000000
χ6844-4-4-4-44400-44000000004-40000000000−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000
χ694-44-44i−4i4i−4i4-400-44-4400−4i4i004i−4i−4i4i000000000000000000000000000000000000000000000000000000
χ704-44-44i−4i4i−4i-44004-4-44004i−4i00−4i4i−4i4i000000000000000000000000000000000000000000000000000000
χ714-44-4−4i4i−4i4i4-400-44-44004i−4i00−4i4i4i−4i000000000000000000000000000000000000000000000000000000
χ724-44-4−4i4i−4i4i-44004-4-4400−4i4i004i−4i4i−4i000000000000000000000000000000000000000000000000000000
χ734-4-444i−4i−4i4i000000004-4000000004i−4i00002ζ3−2ζ3−2ζ32ζ32ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ2ζ−2ζ−2ζ2ζ00000000000000000000000000000000
χ744-4-444i−4i−4i4i000000004-4000000004i−4i0000−2ζ32ζ32ζ3−2ζ3−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ−2ζ2ζ2ζ−2ζ00000000000000000000000000000000
χ754-4-444i−4i−4i4i00000000-4400000000−4i4i00002ζ3−2ζ3−2ζ32ζ3−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ−2ζ2ζ2ζ−2ζ00000000000000000000000000000000
χ764-4-444i−4i−4i4i00000000-4400000000−4i4i0000−2ζ32ζ32ζ3−2ζ32ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ2ζ−2ζ−2ζ2ζ00000000000000000000000000000000
χ774-4-44−4i4i4i−4i000000004-400000000−4i4i00002ζ−2ζ−2ζ2ζ2ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ32ζ3−2ζ3−2ζ32ζ300000000000000000000000000000000
χ784-4-44−4i4i4i−4i000000004-400000000−4i4i0000−2ζ2ζ2ζ−2ζ−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ3−2ζ32ζ32ζ3−2ζ300000000000000000000000000000000
χ794-4-44−4i4i4i−4i00000000-44000000004i−4i00002ζ−2ζ−2ζ2ζ−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ3−2ζ32ζ32ζ3−2ζ300000000000000000000000000000000
χ804-4-44−4i4i4i−4i00000000-44000000004i−4i0000−2ζ2ζ2ζ−2ζ2ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ32ζ3−2ζ3−2ζ32ζ300000000000000000000000000000000

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