Finite Group Databasebeta

← Group #100511

Character table — Group #100511

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size1111111122222222222244444488888888888888888888888881616161616161616161616163232
order12222222444444444444444444224444444888888888888888888888888888844
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1
χ311111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ511111111111111111111111111-1-11-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1
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
χ711111111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111
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
χ911111111111-1-1-1-1-1-11-1-1-1-111-1-111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i11-1-11-1
χ1011111111111-1-1-1-1-1-11-1-1-1-111-1-111111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−i-1-111-11
χ1111111111111-1-1-1-1-1-11-1-1-1-111-1-111111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iii-1-111-11
χ1211111111111-1-1-1-1-1-11-1-1-1-111-1-111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii11-1-11-1
χ1311111111111-1-1-1-1-1-11-1-1-1-111-1-1-1-11-1-11111iiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii11-1-1-11
χ1411111111111-1-1-1-1-1-11-1-1-1-111-1-1-1-11-1-11111iiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iii-1-1111-1
χ1511111111111-1-1-1-1-1-11-1-1-1-111-1-1-1-11-1-11111−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−i-1-1111-1
χ1611111111111-1-1-1-1-1-11-1-1-1-111-1-1-1-11-1-11111−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i11-1-1-11
χ172222222222222-2-2-2-222222-2-2-2-222-2-2-222-2-2000000000000000000000000000000
χ182222222222222-2-2-2-222222-2-2-2-2-2-2-222-2-222000000000000000000000000000000
χ1922222222222-2-222222-2-2-2-2-2-22222-2-2-2-2-222000000000000000000000000000000
χ2022222222222-2-222222-2-2-2-2-2-222-2-2-22222-2-2000000000000000000000000000000
χ2122222222-2-2-2222222-222-2-222-2-200-200000022-2-222-2-20000000000000000000000
χ2222222222-2-2-2222222-222-2-222-2-200-2000000-2-222-2-2220000000000000000000000
χ2322222222-2-2-222-2-2-2-2-222-2-2-2-222002000000000000000000000000002-22-2000000
χ2422222222-2-2-222-2-2-2-2-222-2-2-2-22200200000000000000000000000000-22-22000000
χ2522222222-2-2-2-2-22222-2-2-222-2-2-2-2002000000000000000000000000002i−2i−2i2i000000
χ2622222222-2-2-2-2-22222-2-2-222-2-2-2-200200000000000000000000000000−2i2i2i−2i000000
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
χ29222-22-2-2-222-2220000-2-2-22-200002-20002-2000000000022−2−222−2−22−22−20000000000
χ30222-22-2-2-222-2220000-2-2-22-200002-20002-20000000000−2−222−2−222−22−220000000000
χ31222-22-2-2-222-2220000-2-2-22-20000-22000-22000000000022−2−222−2−2−22−220000000000
χ32222-22-2-2-222-2220000-2-2-22-20000-22000-220000000000−2−222−2−2222−22−20000000000
χ33222-22-2-2-222-2-2-20000-222-2200002-2000-220000000000i2i2−i2−i2−i2−i2i2i2i2−i2−i2i20000000000
χ34222-22-2-2-222-2-2-20000-222-2200002-2000-220000000000−i2−i2i2i2i2i2−i2−i2−i2i2i2−i20000000000
χ35222-22-2-2-222-2-2-20000-222-220000-220002-20000000000i2i2−i2−i2−i2−i2i2i2−i2i2i2−i20000000000
χ36222-22-2-2-222-2-2-20000-222-220000-220002-20000000000−i2−i2i2i2i2i2−i2−i2i2−i2−i2i20000000000
χ3722-2-2-222-20002i−2i2i−2i2i−2i02i−2i002-200000000000002ζ3−2ζ3002ζ−2ζ1−i−1+i1−i−1+i1+i−1−i1+i−1−i000000002−2i2−i200
χ3822-2-2-222-20002i−2i2i−2i2i−2i02i−2i002-200000000000002ζ3−2ζ3002ζ−2ζ−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000−22−i2i200
χ3922-2-2-222-20002i−2i2i−2i2i−2i02i−2i002-20000000000000−2ζ32ζ300−2ζ2ζ1−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000−22−i2i200
χ4022-2-2-222-20002i−2i2i−2i2i−2i02i−2i002-20000000000000−2ζ32ζ300−2ζ2ζ−1+i1−i−1+i1−i−1−i1+i−1−i1+i000000002−2i2−i200
χ4122-2-2-222-2000−2i2i−2i2i−2i2i0−2i2i002-200000000000002ζ−2ζ002ζ3−2ζ31+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000−22i2−i200
χ4222-2-2-222-2000−2i2i−2i2i−2i2i0−2i2i002-200000000000002ζ−2ζ002ζ3−2ζ3−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000002−2−i2i200
χ4322-2-2-222-2000−2i2i−2i2i−2i2i0−2i2i002-20000000000000−2ζ2ζ00−2ζ32ζ31+i−1−i1+i−1−i1−i−1+i1−i−1+i000000002−2−i2i200
χ4422-2-2-222-2000−2i2i−2i2i−2i2i0−2i2i002-20000000000000−2ζ2ζ00−2ζ32ζ3−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000−22i2−i200
χ45444-44-4-4-4-4-444400004-4-4-440000000000000000000000000000000000000000000
χ46444-44-4-4-4-4-44-4-400004444-40000000000000000000000000000000000000000000
χ4744-44-4-4-440004i−4i00000−4i4i000000000000000000000002ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ00000000000000
χ4844-44-4-4-440004i−4i00000−4i4i00000000000000000000000−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ00000000000000
χ4944-44-4-4-44000−4i4i000004i−4i000000000000000000000002ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ300000000000000
χ5044-44-4-4-44000−4i4i000004i−4i00000000000000000000000−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ300000000000000
χ5144-4-4-444-40004i−4i−4i4i−4i4i04i−4i00-4400000000000000000000000000000000000000000
χ5244-4-4-444-4000−4i4i4i−4i4i−4i0−4i4i00-4400000000000000000000000000000000000000000
χ534-444-44-4-44-44000000-4000000000004-40000000000000000000000000000000000
χ544-444-44-4-44-44000000-400000000000-440000000000000000000000000000000000
χ554-444-44-4-4-44-400000040000000000000004i−4i000000000000000000000000000000
χ564-444-44-4-4-44-40000004000000000000000−4i4i000000000000000000000000000000
χ574-44-4-4-4444-4-40044-4-44000000-44000000000000000000000000000000000000000
χ584-44-4-4-4444-4-400-4-44440000004-4000000000000000000000000000000000000000
χ594-44-4-4-444-4440044-4-4-40000004-4000000000000000000000000000000000000000
χ604-44-4-4-444-44400-4-444-4000000-44000000000000000000000000000000000000000
χ614-4-444-44-4000004i−4i−4i4i0000000000000000002+2i−2−2i002−2i−2+2i000000000000000000000000
χ624-4-444-44-4000004i−4i−4i4i000000000000000000−2−2i2+2i00−2+2i2−2i000000000000000000000000
χ634-4-444-44-400000−4i4i4i−4i0000000000000000002−2i−2+2i002+2i−2−2i000000000000000000000000
χ644-4-444-44-400000−4i4i4i−4i000000000000000000−2+2i2−2i00−2−2i2+2i000000000000000000000000
χ658-8-8-888-88000000000000000000000000000000000000000000000000000000000

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