Finite Group Databasebeta

← Group #100516

Character table — Group #100516

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size1111111122222222222244444488888888888888888888888881616161616161616161616163232
order12222222444444444444444444444444444888888888888888888888888888844
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
χ5111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1
χ6111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ7111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111
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
χ911111111-1-1111-1-1-1-11-1-111-1-1-1-111111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iii−i−iii−i−i11-1-11-1
χ1011111111-1-1111-1-1-1-11-1-111-1-1-1-111111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−i-1-111-11
χ1111111111-1-1111-1-1-1-11-1-111-1-1-1-111111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iii-1-111-11
χ1211111111-1-1111-1-1-1-11-1-111-1-1-1-111111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−iii−i−iii11-1-11-1
χ1311111111-1-1111-1-1-1-11-1-111-1-1-1-11-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i−i−iii−i−iii11-1-1-11
χ1411111111-1-1111-1-1-1-11-1-111-1-1-1-11-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iii-1-1111-1
χ1511111111-1-1111-1-1-1-11-1-111-1-1-1-11-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−i-1-1111-1
χ1611111111-1-1111-1-1-1-11-1-111-1-1-1-11-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiiiii−i−iii−i−i11-1-1-11
χ172222222222222-2-2222-2-2-2-22-2-22-222-2-222-2-2000000000000000000000000000000
χ182222222222222-2-2222-2-2-2-22-2-22-2-2-222-2-222000000000000000000000000000000
χ192222222222-2-2-22222-22222-2-2-2-2-20000000022-2-222-2-20000000000000000000000
χ202222222222-2-2-22222-22222-2-2-2-2-200000000-2-222-2-2220000000000000000000000
χ212222222222-2-2-2-2-222-2-2-2-2-2-222-2200000000000000000000000000002i−2i2i−2i000000
χ222222222222-2-2-2-2-222-2-2-2-2-2-222-220000000000000000000000000000−2i2i−2i2i000000
χ2322222222-2-222222-2-2222-2-2-222-2-222-2-2-2-222000000000000000000000000000000
χ2422222222-2-222222-2-2222-2-2-222-2-2-2-22222-2-2000000000000000000000000000000
χ2522222222-2-2-2-2-222-2-2-222-2-22-2-22200000000000000000000000000002-2-22000000
χ2622222222-2-2-2-2-222-2-2-222-2-22-2-2220000000000000000000000000000-222-2000000
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
χ2922-22-2-2-222i−2i0002i−2i2i−2i02i−2i2-20000000000000002ζ3−2ζ3002ζ−2ζ1−i1−i−1+i−1+i1+i1+i−1−i−1−i000000002−2i2−i200
χ3022-22-2-2-222i−2i0002i−2i2i−2i02i−2i2-20000000000000002ζ3−2ζ3002ζ−2ζ−1+i−1+i1−i1−i−1−i−1−i1+i1+i00000000−22−i2i200
χ3122-22-2-2-222i−2i0002i−2i2i−2i02i−2i2-2000000000000000−2ζ32ζ300−2ζ2ζ1−i1−i−1+i−1+i1+i1+i−1−i−1−i00000000−22−i2i200
χ3222-22-2-2-222i−2i0002i−2i2i−2i02i−2i2-2000000000000000−2ζ32ζ300−2ζ2ζ−1+i−1+i1−i1−i−1−i−1−i1+i1+i000000002−2i2−i200
χ3322-22-2-2-22−2i2i000−2i2i−2i2i0−2i2i2-20000000000000002ζ−2ζ002ζ3−2ζ31+i1+i−1−i−1−i1−i1−i−1+i−1+i00000000−22i2−i200
χ3422-22-2-2-22−2i2i000−2i2i−2i2i0−2i2i2-20000000000000002ζ−2ζ002ζ3−2ζ3−1−i−1−i1+i1+i−1+i−1+i1−i1−i000000002−2−i2i200
χ3522-22-2-2-22−2i2i000−2i2i−2i2i0−2i2i2-2000000000000000−2ζ2ζ00−2ζ32ζ31+i1+i−1−i−1−i1−i1−i−1+i−1+i000000002−2−i2i200
χ3622-22-2-2-22−2i2i000−2i2i−2i2i0−2i2i2-2000000000000000−2ζ2ζ00−2ζ32ζ3−1−i−1−i1+i1+i−1+i−1+i1−i1−i00000000−22i2−i200
χ372-2-2-22-222002-2-222002-2-20002-2002-200002-200000000i2−i2i2−i2i2−i2i2−i2i2−i2i2−i20000000000
χ382-2-2-22-222002-2-222002-2-20002-2002-200002-200000000−i2i2−i2i2−i2i2−i2i2−i2i2−i2i20000000000
χ392-2-2-22-222002-2-222002-2-20002-200-220000-2200000000i2−i2i2−i2i2−i2i2−i2−i2i2−i2i20000000000
χ402-2-2-22-222002-2-222002-2-20002-200-220000-2200000000−i2i2−i2i2−i2i2−i2i2i2−i2i2−i20000000000
χ412-2-2-22-222002-2-2-2-200222000-22002-20000-22000000002−22−2−22−222−2−220000000000
χ422-2-2-22-222002-2-2-2-200222000-22002-20000-2200000000−22−222−22−2−222−20000000000
χ432-2-2-22-222002-2-2-2-200222000-2200-2200002-2000000002−22−2−22−22−222−20000000000
χ442-2-2-22-222002-2-2-2-200222000-2200-2200002-200000000−22−222−22−22−2−220000000000
χ4544-44-4-4-444i−4i000−4i4i4i−4i0−4i4i-440000000000000000000000000000000000000000000
χ4644-44-4-4-44−4i4i0004i−4i−4i4i04i−4i-440000000000000000000000000000000000000000000
χ4744-4-444-4-40044-40000-4000000000004-40000000000000000000000000000000000
χ4844-4-444-4-40044-40000-400000000000-440000000000000000000000000000000000
χ4944-4-444-4-400-4-440000400000000000004i−4i00000000000000000000000000000000
χ5044-4-444-4-400-4-44000040000000000000−4i4i00000000000000000000000000000000
χ514-4444-4-4-4444-4400-4-4-40000-4004000000000000000000000000000000000000000
χ524-4444-4-4-444-44-400-4-440000400-4000000000000000000000000000000000000000
χ534-4444-4-4-4-4-44-440044-40000400-4000000000000000000000000000000000000000
χ544-4444-4-4-4-4-4-44-4004440000-4004000000000000000000000000000000000000000
χ554-44-4-44-44000004i−4i000−4i4i000000000000000000000002ζ−2ζ−2ζ2ζ2ζ3−2ζ3−2ζ32ζ300000000000000
χ564-44-4-44-44000004i−4i000−4i4i00000000000000000000000−2ζ2ζ2ζ−2ζ−2ζ32ζ32ζ3−2ζ300000000000000
χ574-44-4-44-4400000−4i4i0004i−4i000000000000000000000002ζ3−2ζ3−2ζ32ζ32ζ−2ζ−2ζ2ζ00000000000000
χ584-44-4-44-4400000−4i4i0004i−4i00000000000000000000000−2ζ32ζ32ζ3−2ζ3−2ζ2ζ2ζ−2ζ00000000000000
χ594-4-44-444-44i−4i00000−4i4i0000000000000000002−2i−2+2i002+2i−2−2i000000000000000000000000
χ604-4-44-444-44i−4i00000−4i4i000000000000000000−2+2i2−2i00−2−2i2+2i000000000000000000000000
χ614-4-44-444-4−4i4i000004i−4i0000000000000000002+2i−2−2i002−2i−2+2i000000000000000000000000
χ624-4-44-444-4−4i4i000004i−4i000000000000000000−2−2i2+2i00−2+2i2−2i000000000000000000000000
χ634-4-4-44-44400-4444400-4-4-4000-440000000000000000000000000000000000000000
χ644-4-4-44-44400-444-4-400-4440004-40000000000000000000000000000000000000000
χ65888-8-8-88-8000000000000000000000000000000000000000000000000000000000

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