Finite Group Databasebeta

← Group #98263

Character table — Group #98263

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size1111111122222222222244444444448888888888888888888888888881616161616161616161616161616
order12222222444444444444444444444422224444444888888888888888822444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111-1-111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111-1-1-1-11111-1-1111-1-1-1-1111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1
χ61111111111111111111111-1-1-1-11111-1-1111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111
χ71111111111111111111111-1-1-1-11111-1-1-1-11-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-11111
χ81111111111111111111111-1-1-1-11111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1111111-1-1-1-1
χ9111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-11-111ii−i−iii−i−i
χ10111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-11-111−i−iii−i−iii
χ11111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-11-1-1-1-111iiii−i−i−i−i−i−i−i−iiiii11-11-1-1ii−i−i−i−iii
χ12111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-11-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i11-11-1-1−i−iiiii−i−i
χ13111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111111-1-1iiii−i−i−i−iiiii−i−i−i−i111-1-1-1−i−iii−i−iii
χ14111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111111-1-1−i−i−i−iiiii−i−i−i−iiiii111-1-1-1ii−i−iii−i−i
χ15111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111iiii−i−i−i−i−i−i−i−iiiii-1-1-1111−i−iiiii−i−i
χ16111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111−i−i−i−iiiiiiiii−i−i−i−i-1-1-1111ii−i−i−i−iii
χ1722222222222222-2-222-2-2-2-2222222-2-2-2-200-222-2-200000000000000000000000000000000
χ1822222222222222-2-222-2-2-2-2-2-2-2-222-2-22200-2-2-22200000000000000000000000000000000
χ19222222222222-2-222-2-222-2-22222-2-222-2-200-2-2-22200000000000000000000000000000000
χ20222222222222-2-222-2-222-2-2-2-2-2-2-2-2222200-222-2-200000000000000000000000000000000
χ2122222222-2-2-2-222222222220000-2-2-2-20022-2000022000000000000000000-2-20000000000
χ2222222222-2-2-2-222222222220000-2-2-2-200-2-2-20000-2-2000000000000000000220000000000
χ2322222222-2-2-2-222-2-222-2-2-2-20000-2-2220000200000000000000000000002-2002-200000000
χ2422222222-2-2-2-222-2-222-2-2-2-20000-2-222000020000000000000000000000-2200-2200000000
χ2522222222-2-2-2-2-2-222-2-222-2-2000022-2-20000200000000000000000000002-200-2200000000
χ2622222222-2-2-2-2-2-222-2-222-2-2000022-2-2000020000000000000000000000-22002-200000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-222000022220022-20000-2-2000000000000000000-220000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-2220000222200-2-2-20000220000000000000000002-20000000000
χ2922-222-2-2-222-2-2002i−2i002i−2i002i2i−2i−2i002i−2i00000002-2001+i1+i−1−i−1−i1−i1−i−1+i−1+i000000000000001−i−1+i1+i−1−i0000
χ3022-222-2-2-222-2-2002i−2i002i−2i002i2i−2i−2i002i−2i00000002-200−1−i−1−i1+i1+i−1+i−1+i1−i1−i00000000000000−1+i1−i−1−i1+i0000
χ3122-222-2-2-222-2-2002i−2i002i−2i00−2i−2i2i2i002i−2i0000000-22001+i1+i−1−i−1−i1−i1−i−1+i−1+i00000000000000−1+i1−i−1−i1+i0000
χ3222-222-2-2-222-2-2002i−2i002i−2i00−2i−2i2i2i002i−2i0000000-2200−1−i−1−i1+i1+i−1+i−1+i1−i1−i000000000000001−i−1+i1+i−1−i0000
χ3322-222-2-2-222-2-200−2i2i00−2i2i002i2i−2i−2i00−2i2i0000000-22001−i1−i−1+i−1+i1+i1+i−1−i−1−i00000000000000−1−i1+i−1+i1−i0000
χ3422-222-2-2-222-2-200−2i2i00−2i2i002i2i−2i−2i00−2i2i0000000-2200−1+i−1+i1−i1−i−1−i−1−i1+i1+i000000000000001+i−1−i1−i−1+i0000
χ3522-222-2-2-222-2-200−2i2i00−2i2i00−2i−2i2i2i00−2i2i00000002-2001−i1−i−1+i−1+i1+i1+i−1−i−1−i000000000000001+i−1−i1−i−1+i0000
χ3622-222-2-2-222-2-200−2i2i00−2i2i00−2i−2i2i2i00−2i2i00000002-200−1+i−1+i1−i1−i−1−i−1−i1+i1+i00000000000000−1−i1+i−1+i1−i0000
χ372-222-22-2-22-22-22i−2i002i−2i00002i−2i2i−2i2i−2i00000002-20000000000001+i1+i−1−i−1−i1−i1−i−1+i−1+i00000000001−i−1+i1+i−1−i
χ382-222-22-2-22-22-22i−2i002i−2i00002i−2i2i−2i2i−2i00000002-2000000000000−1−i−1−i1+i1+i−1+i−1+i1−i1−i0000000000−1+i1−i−1−i1+i
χ392-222-22-2-22-22-22i−2i002i−2i0000−2i2i−2i2i2i−2i0000000-220000000000001+i1+i−1−i−1−i1−i1−i−1+i−1+i0000000000−1+i1−i−1−i1+i
χ402-222-22-2-22-22-22i−2i002i−2i0000−2i2i−2i2i2i−2i0000000-22000000000000−1−i−1−i1+i1+i−1+i−1+i1−i1−i00000000001−i−1+i1+i−1−i
χ412-222-22-2-22-22-2−2i2i00−2i2i00002i−2i2i−2i−2i2i0000000-220000000000001−i1−i−1+i−1+i1+i1+i−1−i−1−i0000000000−1−i1+i−1+i1−i
χ422-222-22-2-22-22-2−2i2i00−2i2i00002i−2i2i−2i−2i2i0000000-22000000000000−1+i−1+i1−i1−i−1−i−1−i1+i1+i00000000001+i−1−i1−i−1+i
χ432-222-22-2-22-22-2−2i2i00−2i2i0000−2i2i−2i2i−2i2i00000002-20000000000001−i1−i−1+i−1+i1+i1+i−1−i−1−i00000000001+i−1−i1−i−1+i
χ442-222-22-2-22-22-2−2i2i00−2i2i0000−2i2i−2i2i−2i2i00000002-2000000000000−1+i−1+i1−i1−i−1−i−1−i1+i1+i0000000000−1−i1+i−1+i1−i
χ452-2-2-222-2200002222-2-2-2-22-200000000002-2000002-2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i200000000000000
χ462-2-2-222-2200002222-2-2-2-22-200000000002-2000002-2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i200000000000000
χ472-2-2-222-2200002222-2-2-2-22-20000000000-2200000-22i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i200000000000000
χ482-2-2-222-2200002222-2-2-2-22-20000000000-2200000-22−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i200000000000000
χ492-2-2-222-220000-2-2-2-222222-200000000002-200000-222−22−2−22−222−22−2−22−2200000000000000
χ502-2-2-222-220000-2-2-2-222222-200000000002-200000-22−22−222−22−2−22−222−22−200000000000000
χ512-2-2-222-220000-2-2-2-222222-20000000000-22000002-22−22−2−22−22−22−222−22−200000000000000
χ522-2-2-222-220000-2-2-2-222222-20000000000-22000002-2−22−222−22−22−22−2−22−2200000000000000
χ5344-444-4-4-4-4-444004i−4i004i−4i00000000−4i4i00000000000000000000000000000000000000000
χ5444-444-4-4-4-4-44400−4i4i00−4i4i000000004i−4i00000000000000000000000000000000000000000
χ5544-4-4-444-400004i−4i00−4i4i00000000000000000000000000000002ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ00000000000000
χ5644-4-4-444-400004i−4i00−4i4i0000000000000000000000000000000−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ00000000000000
χ5744-4-4-444-40000−4i4i004i−4i00000000000000000000000000000002ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ300000000000000
χ5844-4-4-444-40000−4i4i004i−4i0000000000000000000000000000000−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ300000000000000
χ594-444-44-4-4-44-444i−4i004i−4i00000000−4i4i0000000000000000000000000000000000000000000
χ604-444-44-4-4-44-44−4i4i00−4i4i000000004i−4i0000000000000000000000000000000000000000000
χ614-44-44-44-40000004i−4i00−4i4i0000000000000000000002ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ0000000000000000000000
χ624-44-44-44-40000004i−4i00−4i4i000000000000000000000−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ0000000000000000000000
χ634-44-44-44-4000000−4i4i004i−4i0000000000000000000002ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ30000000000000000000000
χ644-44-44-44-4000000−4i4i004i−4i000000000000000000000−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ30000000000000000000000
χ654-4-44-4-4444-4-4400000000004-4-44000000000000000000000000000000000000000000000
χ664-4-44-4-4444-4-440000000000-444-4000000000000000000000000000000000000000000000
χ674-4-44-4-444-444-40000000000000000004-4000000000000000000000000000000000000000
χ684-4-44-4-444-444-4000000000000000000-44000000000000000000000000000000000000000
χ694-4-4-444-44000044-4-4-4-444-440000000000000000000000000000000000000000000000000
χ704-4-4-444-440000-4-44444-4-4-440000000000000000000000000000000000000000000000000
χ71888-8-8-8-88000000000000000000000000000000000000000000000000000000000000000

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