Finite Group Databasebeta

← Group #100552

Character table — Group #100552

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size1111111122222222222244444488888888888888888888888881616161616161616161616163232
order12222222444444444444224444444444444888888888888888888888888888824
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ311111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ5111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1-1-1
χ6111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ7111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111
χ8111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1
χ91111111111-1-1-1-111-1-1-1-1-1-111-1-111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iii−i−i11-1-1ii−i−i1-1
χ101111111111-1-1-1-111-1-1-1-1-1-111-1-111111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii−i−iii-1-111ii−i−i-11
χ111111111111-1-1-1-111-1-1-1-1-1-111-1-111111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−iii−i−i-1-111−i−iii-11
χ121111111111-1-1-1-111-1-1-1-1-1-111-1-111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−iii11-1-1−i−iii1-1
χ131111111111-1-1-1-111-1-1-1-1-1-111-1-11-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i−i−iii11-1-1−i−iii-11
χ141111111111-1-1-1-111-1-1-1-1-1-111-1-11-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiiiii−i−i-1-111−i−iii1-1
χ151111111111-1-1-1-111-1-1-1-1-1-111-1-11-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i−i−iii-1-111ii−i−i1-1
χ161111111111-1-1-1-111-1-1-1-1-1-111-1-11-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiiiii−i−i11-1-1ii−i−i-11
χ17222222222222-2-22222-2-2-2-2-2-222-222-2-222-2-2000000000000000000000000000000
χ18222222222222-2-22222-2-2-2-2-2-222-2-2-222-2-222000000000000000000000000000000
χ192222222222-2-22222-2-22222-2-2-2-2-222-2-2-2-222000000000000000000000000000000
χ202222222222-2-22222-2-22222-2-2-2-2-2-2-22222-2-2000000000000000000000000000000
χ2122222222-2-22222-2-22222-2-222-2-2-20000000022-2-222-2-20000000000000000000000
χ2222222222-2-22222-2-22222-2-222-2-2-200000000-2-222-2-2220000000000000000000000
χ2322222222-2-222-2-2-2-222-2-222-2-2-2-22000000000000000000000000000000002i−2i2i−2i00
χ2422222222-2-222-2-2-2-222-2-222-2-2-2-2200000000000000000000000000000000−2i2i−2i2i00
χ2522222222-2-2-2-222-2-2-2-222-2-2-2-2222000000000000000000000000000000002-2-2200
χ2622222222-2-2-2-222-2-2-2-222-2-2-2-222200000000000000000000000000000000-222-200
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2222222-2000000002i2i−2i−2i−2i−2i2i2i0000000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-2222222-200000000−2i−2i2i2i2i2i−2i−2i0000000000000000000000
χ292222-2-2-2-2002i−2i2i−2i002i−2i2i−2i002-200000000000002ζ3−2ζ3002ζ−2ζ1−i1−i−1+i−1+i1+i1+i−1−i−1−i00002−2i2−i2000000
χ302222-2-2-2-2002i−2i2i−2i002i−2i2i−2i002-200000000000002ζ3−2ζ3002ζ−2ζ−1+i−1+i1−i1−i−1−i−1−i1+i1+i0000−22−i2i2000000
χ312222-2-2-2-2002i−2i2i−2i002i−2i2i−2i002-20000000000000−2ζ32ζ300−2ζ2ζ1−i1−i−1+i−1+i1+i1+i−1−i−1−i0000−22−i2i2000000
χ322222-2-2-2-2002i−2i2i−2i002i−2i2i−2i002-20000000000000−2ζ32ζ300−2ζ2ζ−1+i−1+i1−i1−i−1−i−1−i1+i1+i00002−2i2−i2000000
χ332222-2-2-2-200−2i2i−2i2i00−2i2i−2i2i002-200000000000002ζ−2ζ002ζ3−2ζ31+i1+i−1−i−1−i1−i1−i−1+i−1+i0000−22i2−i2000000
χ342222-2-2-2-200−2i2i−2i2i00−2i2i−2i2i002-200000000000002ζ−2ζ002ζ3−2ζ3−1−i−1−i1+i1+i−1+i−1+i1−i1−i00002−2−i2i2000000
χ352222-2-2-2-200−2i2i−2i2i00−2i2i−2i2i002-20000000000000−2ζ2ζ00−2ζ32ζ31+i1+i−1−i−1−i1−i1−i−1+i−1+i00002−2−i2i2000000
χ362222-2-2-2-200−2i2i−2i2i00−2i2i−2i2i002-20000000000000−2ζ2ζ00−2ζ32ζ3−1−i−1−i1+i1+i−1+i−1+i1−i1−i0000−22i2−i2000000
χ3722-2-22-2-22-2-200222200-2-22-2000002-200002-200000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i20000000000
χ3822-2-22-2-22-2-200222200-2-22-2000002-200002-200000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i20000000000
χ3922-2-22-2-22-2-200222200-2-22-200000-220000-2200000000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i20000000000
χ4022-2-22-2-22-2-200222200-2-22-200000-220000-2200000000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i20000000000
χ4122-2-22-2-22-2-200-2-2220022-22000002-20000-22000000002−22−2−22−222−2−220000000000
χ4222-2-22-2-22-2-200-2-2220022-22000002-20000-2200000000−22−222−22−2−222−20000000000
χ4322-2-22-2-22-2-200-2-2220022-2200000-2200002-2000000002−22−2−22−22−222−20000000000
χ4422-2-22-2-22-2-200-2-2220022-2200000-2200002-200000000−22−222−22−22−2−220000000000
χ454444-4-4-4-4004i−4i−4i4i004i−4i−4i4i00-4400000000000000000000000000000000000000000
χ464444-4-4-4-400−4i4i4i−4i00−4i4i4i−4i00-4400000000000000000000000000000000000000000
χ4744-4-44-4-44440044-4-400-4-4-440000000000000000000000000000000000000000000
χ4844-4-44-4-444400-4-4-4-400444-40000000000000000000000000000000000000000000
χ4944-4-4-444-400004i−4i0000−4i4i000000000000000000000002ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ300000000000000
χ5044-4-4-444-400004i−4i0000−4i4i00000000000000000000000−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ300000000000000
χ5144-4-4-444-40000−4i4i00004i−4i000000000000000000000002ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ00000000000000
χ5244-4-4-444-40000−4i4i00004i−4i00000000000000000000000−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ00000000000000
χ534-44-444-4-44-400004-40000000000000004i−4i00000000000000000000000000000000
χ544-44-444-4-44-400004-4000000000000000−4i4i00000000000000000000000000000000
χ554-44-444-4-4-440000-4400000000000004i−4i0000000000000000000000000000000000
χ564-44-444-4-4-440000-440000000000000−4i4i0000000000000000000000000000000000
χ574-4-444-44-44-44i−4i00-44−4i4i0000004i−4i000000000000000000000000000000000000000
χ584-4-444-44-44-4−4i4i00-444i−4i000000−4i4i000000000000000000000000000000000000000
χ594-4-444-44-4-444i−4i004-4−4i4i000000−4i4i000000000000000000000000000000000000000
χ604-4-444-44-4-44−4i4i004-44i−4i0000004i−4i000000000000000000000000000000000000000
χ614-4-44-44-4400440000-4-4000000000000000002i2−2i2002i2−2i2000000000000000000000000
χ624-4-44-44-4400440000-4-400000000000000000−2i22i200−2i22i2000000000000000000000000
χ634-4-44-44-4400-4-40000440000000000000000022−2200−2222000000000000000000000000
χ644-4-44-44-4400-4-400004400000000000000000−22220022−22000000000000000000000000
χ658-88-8-8-888000000000000000000000000000000000000000000000000000000000

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