Finite Group Databasebeta

← Group #102343

Character table — Group #102343

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11111111222222222222222244444444444444444444448888888888888888161616161616161632323232
order12222222444444444444444422444488888888888888888888888888888888888888884444
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11-11-1
χ6111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-11-11
χ7111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-11-11
χ8111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111-11-1
χ91111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i11-1-1
χ101111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii-1-111
χ111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i-1-111
χ121111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii11-1-1
χ131111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111iiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iii1-1-11
χ141111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111iiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−i-111-1
χ151111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iii-111-1
χ161111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−i1-1-11
χ17222222222222-2-2-2-2-2-2-2-2222222-2-2-2-22222-2-2-2-22222-2-2-2-20000000000000000000000000000
χ18222222222222-2-2-2-2-2-2-2-2222222-2-2-2-2-2-2-2-22222-2-2-2-222220000000000000000000000000000
χ192222222222-2-22222222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-222220000000000000000000000000000
χ202222222222-2-22222222222-2-2-2-2-2-2-2-2-2-2-2-222222222-2-2-2-20000000000000000000000000000
χ2122222222-2-2222222-2-2-2-2-2-222-2-2-2-22200000000000000000000000022-2-222-2-2000000000000
χ2222222222-2-2222222-2-2-2-2-2-222-2-2-2-222000000000000000000000000-2-222-2-222000000000000
χ2322222222-2-222-2-2-2-22222-2-222-2-222-2-2000000000000000022-2-222-2-200000000000000000000
χ2422222222-2-222-2-2-2-22222-2-222-2-222-2-20000000000000000-2-222-2-22200000000000000000000
χ2522222222-2-2-2-22222-2-2-2-2-2-2-2-22222-2-200000000000000002i2i−2i−2i−2i−2i2i2i00000000000000000000
χ2622222222-2-2-2-22222-2-2-2-2-2-2-2-22222-2-20000000000000000−2i−2i2i2i2i2i−2i−2i00000000000000000000
χ2722222222-2-2-2-2-2-2-2-22222-2-2-2-222-2-2220000000000000000000000002i2i−2i−2i−2i−2i2i2i000000000000
χ2822222222-2-2-2-2-2-2-2-22222-2-2-2-222-2-222000000000000000000000000−2i−2i2i2i2i2i−2i−2i000000000000
χ2922-2-22-22-22-2002i2i−2i−2i2i2i−2i−2i2-20000000000002i2i−2i−2i22-2-2000000000000000000001+i−1−i1−i−1+i1−i−1+i1+i−1−i0000
χ3022-2-22-22-22-2002i2i−2i−2i2i2i−2i−2i2-20000000000002i2i−2i−2i22-2-200000000000000000000−1−i1+i−1+i1−i−1+i1−i−1−i1+i0000
χ3122-2-22-22-22-2002i2i−2i−2i2i2i−2i−2i2-2000000000000−2i−2i2i2i-2-222000000000000000000001+i−1−i1−i−1+i−1+i1−i−1−i1+i0000
χ3222-2-22-22-22-2002i2i−2i−2i2i2i−2i−2i2-2000000000000−2i−2i2i2i-2-22200000000000000000000−1−i1+i−1+i1−i1−i−1+i1+i−1−i0000
χ3322-2-22-22-22-200−2i−2i2i2i−2i−2i2i2i2-20000000000002i2i−2i−2i-2-222000000000000000000001−i−1+i1+i−1−i−1−i1+i−1+i1−i0000
χ3422-2-22-22-22-200−2i−2i2i2i−2i−2i2i2i2-20000000000002i2i−2i−2i-2-22200000000000000000000−1+i1−i−1−i1+i1+i−1−i1−i−1+i0000
χ3522-2-22-22-22-200−2i−2i2i2i−2i−2i2i2i2-2000000000000−2i−2i2i2i22-2-2000000000000000000001−i−1+i1+i−1−i1+i−1−i1−i−1+i0000
χ3622-2-22-22-22-200−2i−2i2i2i−2i−2i2i2i2-2000000000000−2i−2i2i2i22-2-200000000000000000000−1+i1−i−1−i1+i−1−i1+i−1+i1−i0000
χ372-2-2222-2-2002i−2i00002i−2i2i−2i002i−2i002-20022−2−22−22−2i2−i2i2−i2i2i2−i2−i2002ζ3−2ζ3002ζ−2ζ1−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000
χ382-2-2222-2-2002i−2i00002i−2i2i−2i002i−2i002-20022−2−22−22−2i2−i2i2−i2i2i2−i2−i200−2ζ32ζ300−2ζ2ζ−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000
χ392-2-2222-2-2002i−2i00002i−2i2i−2i002i−2i002-200−2−222−22−22−i2i2−i2i2−i2−i2i2i2002ζ3−2ζ3002ζ−2ζ−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000000000
χ402-2-2222-2-2002i−2i00002i−2i2i−2i002i−2i002-200−2−222−22−22−i2i2−i2i2−i2−i2i2i200−2ζ32ζ300−2ζ2ζ1−i−1+i1−i−1+i1+i−1−i1+i−1−i000000000000
χ412-2-2222-2-2002i−2i0000−2i2i−2i2i002i−2i00-220022−2−2−22−22i2−i2i2−i2−i2−i2i2i22ζ3−2ζ3002ζ−2ζ001−i−1+i−1+i1−i1+i−1−i−1−i1+i000000000000
χ422-2-2222-2-2002i−2i0000−2i2i−2i2i002i−2i00-220022−2−2−22−22i2−i2i2−i2−i2−i2i2i2−2ζ32ζ300−2ζ2ζ00−1+i1−i1−i−1+i−1−i1+i1+i−1−i000000000000
χ432-2-2222-2-2002i−2i0000−2i2i−2i2i002i−2i00-2200−2−2222−22−2−i2i2−i2i2i2i2−i2−i22ζ3−2ζ3002ζ−2ζ00−1+i1−i1−i−1+i−1−i1+i1+i−1−i000000000000
χ442-2-2222-2-2002i−2i0000−2i2i−2i2i002i−2i00-2200−2−2222−22−2−i2i2−i2i2i2i2−i2−i2−2ζ32ζ300−2ζ2ζ001−i−1+i−1+i1−i1+i−1−i−1−i1+i000000000000
χ452-2-2222-2-200−2i2i00002i−2i2i−2i00−2i2i00-220022−2−2−22−22−i2i2−i2i2i2i2−i2−i22ζ−2ζ002ζ3−2ζ300−1−i1+i1+i−1−i−1+i1−i1−i−1+i000000000000
χ462-2-2222-2-200−2i2i00002i−2i2i−2i00−2i2i00-220022−2−2−22−22−i2i2−i2i2i2i2−i2−i2−2ζ2ζ00−2ζ32ζ3001+i−1−i−1−i1+i1−i−1+i−1+i1−i000000000000
χ472-2-2222-2-200−2i2i00002i−2i2i−2i00−2i2i00-2200−2−2222−22−2i2−i2i2−i2−i2−i2i2i22ζ−2ζ002ζ3−2ζ3001+i−1−i−1−i1+i1−i−1+i−1+i1−i000000000000
χ482-2-2222-2-200−2i2i00002i−2i2i−2i00−2i2i00-2200−2−2222−22−2i2−i2i2−i2−i2−i2i2i2−2ζ2ζ00−2ζ32ζ300−1−i1+i1+i−1−i−1+i1−i1−i−1+i000000000000
χ492-2-2222-2-200−2i2i0000−2i2i−2i2i00−2i2i002-20022−2−22−22−2−i2i2−i2i2−i2−i2i2i2002ζ−2ζ002ζ3−2ζ3−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000
χ502-2-2222-2-200−2i2i0000−2i2i−2i2i00−2i2i002-20022−2−22−22−2−i2i2−i2i2−i2−i2i2i200−2ζ2ζ00−2ζ32ζ31+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000
χ512-2-2222-2-200−2i2i0000−2i2i−2i2i00−2i2i002-200−2−222−22−22i2−i2i2−i2i2i2−i2−i2002ζ−2ζ002ζ3−2ζ31+i−1−i1+i−1−i1−i−1+i1−i−1+i000000000000
χ522-2-2222-2-200−2i2i0000−2i2i−2i2i00−2i2i002-200−2−222−22−22i2−i2i2−i2i2i2−i2−i200−2ζ2ζ00−2ζ32ζ3−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000000000
χ534444-4-4-4-400004-44-40000000000000022−2222−220000000022−2222−220000000000000000000000000000
χ544444-4-4-4-400004-44-400000000000000−2222−222200000000−2222−22220000000000000000000000000000
χ554444-4-4-4-40000-44-440000000000000022−2222−2200000000−2222−22220000000000000000000000000000
χ564444-4-4-4-40000-44-4400000000000000−2222−22220000000022−2222−220000000000000000000000000000
χ5744-4-44-44-4-44004i4i−4i−4i−4i−4i4i4i-440000000000000000000000000000000000000000000000000000
χ5844-4-44-44-4-4400−4i−4i4i4i4i4i−4i−4i-440000000000000000000000000000000000000000000000000000
χ5944-4-4-44-44004i−4i4i−4i−4i4i000000−4i4i00004-400000000000000000000000000000000000000000000
χ6044-4-4-44-44004i−4i−4i4i4i−4i000000−4i4i0000-4400000000000000000000000000000000000000000000
χ6144-4-4-44-4400−4i4i4i−4i−4i4i0000004i−4i0000-4400000000000000000000000000000000000000000000
χ6244-4-4-44-4400−4i4i−4i4i4i−4i0000004i−4i00004-400000000000000000000000000000000000000000000
χ634-44-44-4-44000000004-4-44000000000000002i2−2i2−2i22i2−2i22i22i2−2i200000000000000000000000000000000
χ644-44-44-4-44000000004-4-4400000000000000−2i22i22i2−2i22i2−2i2−2i22i200000000000000000000000000000000
χ654-44-44-4-4400000000-444-4000000000000002i2−2i2−2i22i22i2−2i2−2i22i200000000000000000000000000000000
χ664-44-44-4-4400000000-444-400000000000000−2i22i22i2−2i2−2i22i22i2−2i200000000000000000000000000000000
χ674-44-4-444-44-44400000000-44-4-44-4000000000000000000000000000000000000000000000000
χ684-44-4-444-44-4-4-400000000-4444-44000000000000000000000000000000000000000000000000
χ694-44-4-444-4-4444000000004-4-4-4-44000000000000000000000000000000000000000000000000
χ704-44-4-444-4-44-4-4000000004-4444-4000000000000000000000000000000000000000000000000
χ714-4-44-4-444440000000000-4-4000000000000000000004i−4i−4i4i0000000000000000000000000000
χ724-4-44-4-444440000000000-4-400000000000000000000−4i4i4i−4i0000000000000000000000000000
χ734-4-44-4-444-4-4000000000044000000004-4-440000000000000000000000000000000000000000
χ744-4-44-4-444-4-400000000004400000000-444-40000000000000000000000000000000000000000

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