Finite Group Databasebeta

← Group #101705

Character table — Group #101705

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size1111111122222222222244444488888888888888888888888881616161616161616161616163232
order12222222444444444444444444488888888888888888888888824448888888844
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
χ911111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1ii−i−iii−i−iiiii−i−i−i−i1111-1-1-1-11-11-1ii−i−iii−i−i1-1
χ1011111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1ii−i−iii−i−iiiii−i−i−i−i-1-1-1-111111-11-1−i−iii−i−iii-11
χ1111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1ii−i−iii−i−i−i−i−i−iiiii1111-1-1-1-1-11-11ii−i−i−i−iii-11
χ1211111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1ii−i−iii−i−i−i−i−i−iiiii-1-1-1-11111-11-11−i−iiiii−i−i1-1
χ1311111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1−i−iii−i−iiiiiii−i−i−i−i1111-1-1-1-1-11-11−i−iiiii−i−i-11
χ1411111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1−i−iii−i−iiiiiii−i−i−i−i-1-1-1-11111-11-11ii−i−i−i−iii1-1
χ1511111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1−i−iii−i−iii−i−i−i−iiiii1111-1-1-1-11-11-1−i−iii−i−iii1-1
χ1611111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1−i−iii−i−iii−i−i−i−iiiii-1-1-1-111111-11-1ii−i−iii−i−i-11
χ17222222222222-2-22222-2-2-2-2-2-222-200000000000000000000000022-2-20000000000
χ18222222222222-2-22222-2-2-2-2-2-222-2000000000000000000000000-2-2220000000000
χ192222222222-2-22222-2-22222-2-2-2-2-20000000022-2-222-2-20000000000000000000000
χ202222222222-2-22222-2-22222-2-2-2-2-200000000-2-222-2-2220000000000000000000000
χ212222222222-2-2-2-222-2-2-2-2-2-222-2-222i2i−2i−2i−2i−2i2i2i000000000000000000000000000000
χ222222222222-2-2-2-222-2-2-2-2-2-222-2-22−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000
χ2322222222-2-22222-2-22222-2-222-2-2-22222-2-2-2-2000000000000000000000000000000
χ2422222222-2-22222-2-22222-2-222-2-2-2-2-2-2-22222000000000000000000000000000000
χ2522222222-2-222-2-2-2-222-2-222-2-2-2-22000000002i2i−2i−2i−2i−2i2i2i0000000000000000000000
χ2622222222-2-222-2-2-2-222-2-222-2-2-2-2200000000−2i−2i2i2i2i2i−2i−2i0000000000000000000000
χ2722222222-2-2-2-222-2-2-2-222-2-2-2-22220000000000000000000000002-2-220000000000
χ2822222222-2-2-2-222-2-2-2-222-2-2-2-2222000000000000000000000000-222-20000000000
χ29222-2-2-22-22i−2i002i−2i2i−2i002i−2i2-20000000000000002ζ−2ζ002ζ3−2ζ3i2i2−i2−i222−2−2000000001−i−1+i1+i−1−i00
χ30222-2-2-22-22i−2i002i−2i2i−2i002i−2i2-20000000000000002ζ−2ζ002ζ3−2ζ3−i2−i2i2i2−2−22200000000−1+i1−i−1−i1+i00
χ31222-2-2-22-22i−2i002i−2i2i−2i002i−2i2-2000000000000000−2ζ2ζ00−2ζ32ζ3i2i2−i2−i222−2−200000000−1+i1−i−1−i1+i00
χ32222-2-2-22-22i−2i002i−2i2i−2i002i−2i2-2000000000000000−2ζ2ζ00−2ζ32ζ3−i2−i2i2i2−2−222000000001−i−1+i1+i−1−i00
χ33222-2-2-22-2−2i2i00−2i2i−2i2i00−2i2i2-20000000000000002ζ3−2ζ3002ζ−2ζi2i2−i2−i2−2−222000000001+i−1−i1−i−1+i00
χ34222-2-2-22-2−2i2i00−2i2i−2i2i00−2i2i2-20000000000000002ζ3−2ζ3002ζ−2ζ−i2−i2i2i222−2−200000000−1−i1+i−1+i1−i00
χ35222-2-2-22-2−2i2i00−2i2i−2i2i00−2i2i2-2000000000000000−2ζ32ζ300−2ζ2ζi2i2−i2−i2−2−22200000000−1−i1+i−1+i1−i00
χ36222-2-2-22-2−2i2i00−2i2i−2i2i00−2i2i2-2000000000000000−2ζ32ζ300−2ζ2ζ−i2−i2i2i222−2−2000000001+i−1−i1−i−1+i00
χ372-2-2-2-222200222200-2-2-2-2002-200000002i−2i2i−2i000000002−22−22−22−20000i2−i2i2−i2000000
χ382-2-2-2-222200222200-2-2-2-2002-200000002i−2i2i−2i00000000−22−22−22−220000−i2i2−i2i2000000
χ392-2-2-2-222200222200-2-2-2-2002-20000000−2i2i−2i2i000000002−22−22−22−20000−i2i2−i2i2000000
χ402-2-2-2-222200222200-2-2-2-2002-20000000−2i2i−2i2i00000000−22−22−22−220000i2−i2i2−i2000000
χ412-2-2-2-222200-2-2-2-2002222002-200000002-2-22000000002−22−2−22−2200002−2−22000000
χ422-2-2-2-222200-2-2-2-2002222002-200000002-2-2200000000−22−222−22−20000−222−2000000
χ432-2-2-2-222200-2-2-2-2002222002-20000000-222-2000000002−22−2−22−220000−222−2000000
χ442-2-2-2-222200-2-2-2-2002222002-20000000-222-200000000−22−222−22−200002−2−22000000
χ45444-4-4-44-44i−4i00−4i4i4i−4i00−4i4i-440000000000000000000000000000000000000000000
χ46444-4-4-44-4−4i4i004i−4i−4i4i004i−4i-440000000000000000000000000000000000000000000
χ4744-44-44-4-4440000-4-4000000000000000000022−220022−22000000000000000000000000
χ4844-44-44-4-4440000-4-40000000000000000000−222200−2222000000000000000000000000
χ4944-44-44-4-4-4-400004400000000000000000002i2−2i200−2i22i2000000000000000000000000
χ5044-44-44-4-4-4-40000440000000000000000000−2i22i2002i2−2i2000000000000000000000000
χ5144-4-44-4-444i−4i4i−4i00−4i4i4i−4i0000004-4000000000000000000000000000000000000000
χ5244-4-44-4-444i−4i−4i4i00−4i4i−4i4i000000-44000000000000000000000000000000000000000
χ5344-4-44-4-44−4i4i4i−4i004i−4i4i−4i000000-44000000000000000000000000000000000000000
χ5444-4-44-4-44−4i4i−4i4i004i−4i−4i4i0000004-4000000000000000000000000000000000000000
χ554-444-4-4-44004i−4i0000−4i4i0000000002+2i−2−2i2−2i−2+2i0000000000000000000000000000000000
χ564-444-4-4-44004i−4i0000−4i4i000000000−2−2i2+2i−2+2i2−2i0000000000000000000000000000000000
χ574-444-4-4-4400−4i4i00004i−4i0000000002−2i−2+2i2+2i−2−2i0000000000000000000000000000000000
χ584-444-4-4-4400−4i4i00004i−4i000000000−2+2i2−2i−2−2i2+2i0000000000000000000000000000000000
χ594-4-444-44-400004i−4i0000−4i4i000000000000000000000002i−2i−2i2i2-2-2200000000000000
χ604-4-444-44-400004i−4i0000−4i4i00000000000000000000000−2i2i2i−2i-222-200000000000000
χ614-4-444-44-40000−4i4i00004i−4i000000000000000000000002i−2i−2i2i-222-200000000000000
χ624-4-444-44-40000−4i4i00004i−4i00000000000000000000000−2i2i2i−2i2-2-2200000000000000
χ634-4-4-4-44440044-4-400-4-44400-4400000000000000000000000000000000000000000
χ644-4-4-4-444400-4-4440044-4-400-4400000000000000000000000000000000000000000
χ658-88-888-8-8000000000000000000000000000000000000000000000000000000000

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