Finite Group Databasebeta

← Group #100522

Character table — Group #100522

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size1111111122222222222244444488888888888888888888888881616161616161616161616163232
order12222222444444444444444444444444444888888888888888888888888888824
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1
χ411111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1
χ6111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ7111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111
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
χ911111111-1-1111-1-1-1-1-1-1111-1-1-1-111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i11-1-11-1
χ1011111111-1-1111-1-1-1-1-1-1111-1-1-1-111111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iii-1-111-11
χ1111111111-1-1111-1-1-1-1-1-1111-1-1-1-111111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−i-1-111-11
χ1211111111-1-1111-1-1-1-1-1-1111-1-1-1-111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii11-1-11-1
χ1311111111-1-1111-1-1-1-1-1-1111-1-1-1-11-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii11-1-1-11
χ1411111111-1-1111-1-1-1-1-1-1111-1-1-1-11-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−i-1-1111-1
χ1511111111-1-1111-1-1-1-1-1-1111-1-1-1-11-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iii-1-1111-1
χ1611111111-1-1111-1-1-1-1-1-1111-1-1-1-11-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i11-1-1-11
χ17222222222222222-2-2-2-22-2-22-2-22-222-2-222-2-2000000000000000000000000000000
χ18222222222222222-2-2-2-22-2-22-2-22-2-2-222-2-222000000000000000000000000000000
χ192222222222-2-2-2222222-222-2-2-2-2-20000000022-2-222-2-20000000000000000000000
χ202222222222-2-2-2222222-222-2-2-2-2-200000000-2-222-2-2220000000000000000000000
χ212222222222-2-2-222-2-2-2-2-2-2-2-222-220000000000000000000000002i−2i2i−2i0000000000
χ222222222222-2-2-222-2-2-2-2-2-2-2-222-22000000000000000000000000−2i2i−2i2i0000000000
χ2322222222-2-2222-2-222222-2-2-222-2-222-2-2-2-222000000000000000000000000000000
χ2422222222-2-2222-2-222222-2-2-222-2-2-2-22222-2-2000000000000000000000000000000
χ2522222222-2-2-2-2-2-2-22222-2-2-22-2-2220000000000000000000000002-2-220000000000
χ2622222222-2-2-2-2-2-2-22222-2-2-22-2-222000000000000000000000000-222-20000000000
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
χ2922-2-222-2-22i−2i0002i−2i2i2i−2i−2i02-20000000000000002ζ3−2ζ3002ζ−2ζ1−i1−i−1+i−1+i1+i1+i−1−i−1−i000000002−2i2−i200
χ3022-2-222-2-22i−2i0002i−2i2i2i−2i−2i02-20000000000000002ζ3−2ζ3002ζ−2ζ−1+i−1+i1−i1−i−1−i−1−i1+i1+i00000000−22−i2i200
χ3122-2-222-2-22i−2i0002i−2i2i2i−2i−2i02-2000000000000000−2ζ32ζ300−2ζ2ζ1−i1−i−1+i−1+i1+i1+i−1−i−1−i00000000−22−i2i200
χ3222-2-222-2-22i−2i0002i−2i2i2i−2i−2i02-2000000000000000−2ζ32ζ300−2ζ2ζ−1+i−1+i1−i1−i−1−i−1−i1+i1+i000000002−2i2−i200
χ3322-2-222-2-2−2i2i000−2i2i−2i−2i2i2i02-20000000000000002ζ−2ζ002ζ3−2ζ31+i1+i−1−i−1−i1−i1−i−1+i−1+i00000000−22i2−i200
χ3422-2-222-2-2−2i2i000−2i2i−2i−2i2i2i02-20000000000000002ζ−2ζ002ζ3−2ζ3−1−i−1−i1+i1+i−1+i−1+i1−i1−i000000002−2−i2i200
χ3522-2-222-2-2−2i2i000−2i2i−2i−2i2i2i02-2000000000000000−2ζ2ζ00−2ζ32ζ31+i1+i−1−i−1−i1−i1−i−1+i−1+i000000002−2−i2i200
χ3622-2-222-2-2−2i2i000−2i2i−2i−2i2i2i02-2000000000000000−2ζ2ζ00−2ζ32ζ3−1−i−1−i1+i1+i−1+i−1+i1−i1−i00000000−22i2−i200
χ372-22-22-2-220022-2002-22-2-20002-200002i−2i2i−2i0000000000i2−i2i2−i2i2−i2i2−i200002−22−2000000
χ382-22-22-2-220022-2002-22-2-20002-200002i−2i2i−2i0000000000−i2i2−i2i2−i2i2−i2i20000−22−22000000
χ392-22-22-2-220022-2002-22-2-20002-20000−2i2i−2i2i0000000000i2−i2i2−i2i2−i2i2−i20000−22−22000000
χ402-22-22-2-220022-2002-22-2-20002-20000−2i2i−2i2i0000000000−i2i2−i2i2−i2i2−i2i200002−22−2000000
χ412-22-22-2-220022-200-22-22-2000-2200002i−2i−2i2i00000000002−22−2−22−220000−i2i2i2−i2000000
χ422-22-22-2-220022-200-22-22-2000-2200002i−2i−2i2i0000000000−22−222−22−20000i2−i2−i2i2000000
χ432-22-22-2-220022-200-22-22-2000-220000−2i2i2i−2i00000000002−22−2−22−220000i2−i2−i2i2000000
χ442-22-22-2-220022-200-22-22-2000-220000−2i2i2i−2i0000000000−22−222−22−20000−i2i2i2−i2000000
χ4544-4-444-4-44i−4i0004i−4i−4i−4i4i4i0-440000000000000000000000000000000000000000000
χ4644-4-444-4-4−4i4i000−4i4i4i4i−4i−4i0-440000000000000000000000000000000000000000000
χ4744-4-4-4-444004-44000000-400000004i−4i000000000000000000000000000000000000
χ4844-4-4-4-444004-44000000-40000000−4i4i000000000000000000000000000000000000
χ4944-4-4-4-44400-44-4000000400000000000004-4000000000000000000000000000000
χ5044-4-4-4-44400-44-400000040000000000000-44000000000000000000000000000000
χ514-44-44-4-4400-4-44004-44-44000-440000000000000000000000000000000000000000
χ524-44-44-4-4400-4-4400-44-4440004-40000000000000000000000000000000000000000
χ534-44-4-444-44i−4i000−4i4i000000000000000000002+2i−2−2i002−2i−2+2i000000000000000000000000
χ544-44-4-444-44i−4i000−4i4i00000000000000000000−2−2i2+2i00−2+2i2−2i000000000000000000000000
χ554-44-4-444-4−4i4i0004i−4i000000000000000000002−2i−2+2i002+2i−2−2i000000000000000000000000
χ564-44-4-444-4−4i4i0004i−4i00000000000000000000−2+2i2−2i00−2−2i2+2i000000000000000000000000
χ574-4-444-44-400000004i−4i−4i4i0000000000000000000000002ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ300000000000000
χ584-4-444-44-400000004i−4i−4i4i000000000000000000000000−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ300000000000000
χ594-4-444-44-40000000−4i4i4i−4i0000000000000000000000002ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ00000000000000
χ604-4-444-44-40000000−4i4i4i−4i000000000000000000000000−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ00000000000000
χ614-4-44-44-44444-4-4-4-40000400-4004000000000000000000000000000000000000000
χ624-4-44-44-4444-444-4-40000-400400-4000000000000000000000000000000000000000
χ634-4-44-44-44-4-44-4-4440000400400-4000000000000000000000000000000000000000
χ644-4-44-44-44-4-4-444440000-400-4004000000000000000000000000000000000000000
χ658888-8-8-8-8000000000000000000000000000000000000000000000000000000000

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