Finite Group Databasebeta

← Group #100295

Character table — Group #100295

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size1111111122222222222244444488888888888888888888888881616161616161616161616163232
order12222222444444444444444444224444444888888888888888888888888888844
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
χ511111111111111111111111111-1-11-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1-1-1
χ611111111111111111111111111-1-11-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ711111111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111
χ811111111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1
χ91111111111-1-1-1-111-1-1-1-111-1-1-1-111111-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iii−i−i11-1-1ii−i−i1-1
χ101111111111-1-1-1-111-1-1-1-111-1-1-1-111111-1-1-1-1ii−i−iii−i−i−i−i−i−iiiii−i−iii-1-111ii−i−i-11
χ111111111111-1-1-1-111-1-1-1-111-1-1-1-111111-1-1-1-1−i−iii−i−iiiiiii−i−i−i−iii−i−i-1-111−i−iii-11
χ121111111111-1-1-1-111-1-1-1-111-1-1-1-111111-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−iii11-1-1−i−iii1-1
χ131111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-11-1-11111ii−i−iii−i−iiiii−i−i−i−i−i−iii11-1-1−i−iii-11
χ141111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-11-1-11111ii−i−iii−i−i−i−i−i−iiiiiii−i−i-1-111−i−iii1-1
χ151111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-11-1-11111−i−iii−i−iiiiiii−i−i−i−i−i−iii-1-111ii−i−i1-1
χ161111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-11-1-11111−i−iii−i−iii−i−i−i−iiiiiii−i−i11-1-1ii−i−i-11
χ17222222222222-2-22222-2-2-2-2-2-22222-2-2-2-2-222000000000000000000000000000000
χ18222222222222-2-22222-2-2-2-2-2-222-2-2-22222-2-2000000000000000000000000000000
χ192222222222-2-22222-2-222-2-222-2-222-2-2-222-2-2000000000000000000000000000000
χ202222222222-2-22222-2-222-2-222-2-2-2-2-222-2-222000000000000000000000000000000
χ2122222222-2-22222-2-2222222-2-2-2-200-20000002222-2-2-2-20000000000000000000000
χ2222222222-2-22222-2-2222222-2-2-2-200-2000000-2-2-2-222220000000000000000000000
χ2322222222-2-222-2-2-2-222-2-2-2-222-2-20020000000000000000000000000000002i−2i2i−2i00
χ2422222222-2-222-2-2-2-222-2-2-2-222-2-2002000000000000000000000000000000−2i2i−2i2i00
χ2522222222-2-2-2-222-2-2-2-222-2-2-2-2220020000000000000000000000000000002-2-2200
χ2622222222-2-2-2-222-2-2-2-222-2-2-2-222002000000000000000000000000000000-222-200
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-222222200-20000002i2i−2i−2i−2i−2i2i2i0000000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-222222200-2000000−2i−2i2i2i2i2i−2i−2i0000000000000000000000
χ29222-2-2-2-222-2002i−2i2-2002i−2i002i−2i002-20002i−2i00000000001−i1−i−1+i−1+i1+i1+i−1−i−1−i1−i−1+i1+i−1−i0000000000
χ30222-2-2-2-222-2002i−2i2-2002i−2i002i−2i002-20002i−2i0000000000−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1+i1−i−1−i1+i0000000000
χ31222-2-2-2-222-2002i−2i2-2002i−2i002i−2i00-22000−2i2i00000000001−i1−i−1+i−1+i1+i1+i−1−i−1−i−1+i1−i−1−i1+i0000000000
χ32222-2-2-2-222-2002i−2i2-2002i−2i002i−2i00-22000−2i2i0000000000−1+i−1+i1−i1−i−1−i−1−i1+i1+i1−i−1+i1+i−1−i0000000000
χ33222-2-2-2-222-200−2i2i2-200−2i2i00−2i2i002-2000−2i2i00000000001+i1+i−1−i−1−i1−i1−i−1+i−1+i1+i−1−i1−i−1+i0000000000
χ34222-2-2-2-222-200−2i2i2-200−2i2i00−2i2i002-2000−2i2i0000000000−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1−i1+i−1+i1−i0000000000
χ35222-2-2-2-222-200−2i2i2-200−2i2i00−2i2i00-220002i−2i00000000001+i1+i−1−i−1−i1−i1−i−1+i−1+i−1−i1+i−1+i1−i0000000000
χ36222-2-2-2-222-200−2i2i2-200−2i2i00−2i2i00-220002i−2i0000000000−1−i−1−i1+i1+i−1+i−1+i1−i1−i1+i−1−i1−i−1+i0000000000
χ3722-2-22-22-2002i−2i2i−2i002i−2i−2i2i2-2000000000000000002ζ3−2ζ32ζ−2ζ1−i−1+i1−i−1+i1+i−1−i1+i−1−i00002−2i2−i2000000
χ3822-2-22-22-2002i−2i2i−2i002i−2i−2i2i2-2000000000000000002ζ3−2ζ32ζ−2ζ−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000−22−i2i2000000
χ3922-2-22-22-2002i−2i2i−2i002i−2i−2i2i2-200000000000000000−2ζ32ζ3−2ζ2ζ1−i−1+i1−i−1+i1+i−1−i1+i−1−i0000−22−i2i2000000
χ4022-2-22-22-2002i−2i2i−2i002i−2i−2i2i2-200000000000000000−2ζ32ζ3−2ζ2ζ−1+i1−i−1+i1−i−1−i1+i−1−i1+i00002−2i2−i2000000
χ4122-2-22-22-200−2i2i−2i2i00−2i2i2i−2i2-2000000000000000002ζ−2ζ2ζ3−2ζ31+i−1−i1+i−1−i1−i−1+i1−i−1+i0000−22i2−i2000000
χ4222-2-22-22-200−2i2i−2i2i00−2i2i2i−2i2-2000000000000000002ζ−2ζ2ζ3−2ζ3−1−i1+i−1−i1+i−1+i1−i−1+i1−i00002−2−i2i2000000
χ4322-2-22-22-200−2i2i−2i2i00−2i2i2i−2i2-200000000000000000−2ζ2ζ−2ζ32ζ31+i−1−i1+i−1−i1−i−1+i1−i−1+i00002−2−i2i2000000
χ4422-2-22-22-200−2i2i−2i2i00−2i2i2i−2i2-200000000000000000−2ζ2ζ−2ζ32ζ3−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000−22i2−i2000000
χ45444-4-4-4-44-44004i−4i-44004i−4i00−4i4i00000000000000000000000000000000000000000
χ46444-4-4-4-44-4400−4i4i-4400−4i4i004i−4i00000000000000000000000000000000000000000
χ4744-44-44-4-40000440000-4-4000000000000000000000002-2-222-2-2200000000000000
χ4844-44-44-4-40000440000-4-400000000000000000000000-222-2-222-200000000000000
χ4944-44-44-4-40000-4-4000044000000000000000000000002i−2i−2i2i−2i2i2i−2i00000000000000
χ5044-44-44-4-40000-4-400004400000000000000000000000−2i2i2i−2i2i−2i−2i2i00000000000000
χ5144-4-44-44-4004i−4i−4i4i004i−4i4i−4i-440000000000000000000000000000000000000000000
χ5244-4-44-44-400−4i4i4i−4i00−4i4i−4i4i-440000000000000000000000000000000000000000000
χ534-4444-4-4-4440000-4-400000000000004-40000000000000000000000000000000000
χ544-4444-4-4-4440000-4-40000000000000-440000000000000000000000000000000000
χ554-4444-4-4-4-4-4000044000000000000000004i−4i000000000000000000000000000000
χ564-4444-4-4-4-4-400004400000000000000000−4i4i000000000000000000000000000000
χ574-44-4-444-44-44i−4i00-44−4i4i0000004i−4i000000000000000000000000000000000000000
χ584-44-4-444-44-4−4i4i00-444i−4i000000−4i4i000000000000000000000000000000000000000
χ594-44-4-444-4-444i−4i004-4−4i4i000000−4i4i000000000000000000000000000000000000000
χ604-44-4-444-4-44−4i4i004-44i−4i0000004i−4i000000000000000000000000000000000000000
χ614-4-44-4-44400440000-4-4000000000000000002i2−2i22i2−2i200000000000000000000000000
χ624-4-44-4-44400440000-4-400000000000000000−2i22i2−2i22i200000000000000000000000000
χ634-4-44-4-44400-4-40000440000000000000000022−22−222200000000000000000000000000
χ644-4-44-4-44400-4-400004400000000000000000−222222−2200000000000000000000000000
χ658-8-8-888-88000000000000000000000000000000000000000000000000000000000

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