Finite Group Databasebeta

← Group #121554

Character table — Group #121554

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11111111222244444444444488888888161616161616161616161616161616161616161616161616
order12224444444422244444444488888888888888888888888888888888
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ6111111111111111111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-1
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111
χ91111-1-1-1-1-1-1111-1-1111-1-1-111-1iiii−i−i−i−ii−ii−ii−ii−iii−i−i11-1-111-1-111-1-1
χ101111-1-1-1-1-1-1111-1-1111-1-1-111-1iiii−i−i−i−ii−i−iii−i−ii−i−iii11-1-1-1-111-1-111
χ111111-1-1-1-1-1-1111-1-1111-1-1-111-1iiii−i−i−i−i−iii−i−iii−i−i−iii-1-11111-1-1-1-111
χ121111-1-1-1-1-1-1111-1-1111-1-1-111-1iiii−i−i−i−i−ii−ii−ii−iiii−i−i-1-111-1-11111-1-1
χ131111-1-1-1-1-1-1111-1-1111-1-1-111-1−i−i−i−iiiiii−ii−ii−ii−i−i−iii-1-111-1-11111-1-1
χ141111-1-1-1-1-1-1111-1-1111-1-1-111-1−i−i−i−iiiiii−i−iii−i−iiii−i−i-1-11111-1-1-1-111
χ151111-1-1-1-1-1-1111-1-1111-1-1-111-1−i−i−i−iiiii−iii−i−iii−iii−i−i11-1-1-1-111-1-111
χ161111-1-1-1-1-1-1111-1-1111-1-1-111-1−i−i−i−iiiii−ii−ii−ii−ii−i−iii11-1-111-1-111-1-1
χ172222222222222-2-22-2-22-2-2-2-22000000000000000000002-22-200000000
χ182222222222222-2-22-2-22-2-2-2-2200000000000000000000-22-2200000000
χ19222222222222-22-2-22-2-22-22-2-200000000000000002-22-2000000000000
χ20222222222222-22-2-22-2-22-22-2-20000000000000000-22-22000000000000
χ21222222222222-2-22-2-22-2-22-22-200000000002200-2-20000000000000000
χ22222222222222-2-22-2-22-2-22-22-20000000000-2-200220000000000000000
χ2322222222-2-2-2-2222-2-22-2-2-22-220000000000000000000000002-22-20000
χ2422222222-2-2-2-2222-2-22-2-2-22-22000000000000000000000000-22-220000
χ2522222222-2-2-2-22-2-2-22-2-222-22200000000000000000000000000002-22-2
χ2622222222-2-2-2-22-2-2-22-2-222-2220000000000000000000000000000-22-22
χ2722222222-2-2-2-2-22-22-2-22-2222-2000000002200-2-2000000000000000000
χ2822222222-2-2-2-2-22-22-2-22-2222-200000000-2-20022000000000000000000
χ2922222222-2-2-2-2-2-2222222-2-2-2-22i2i−2i−2i2i2i−2i−2i000000000000000000000000
χ3022222222-2-2-2-2-2-2222222-2-2-2-2−2i−2i2i2i−2i−2i2i2i000000000000000000000000
χ312222-2-2-2-222-2-2222-22-22-2-2-22-200000000000000000000000000002-2-22
χ322222-2-2-2-222-2-2222-22-22-2-2-22-20000000000000000000000000000-222-2
χ332222-2-2-2-222-2-22-2-2-2-222222-2-20000000000000000000000002-2-220000
χ342222-2-2-2-222-2-22-2-2-2-222222-2-2000000000000000000000000-222-20000
χ352222-2-2-2-222-2-2-22-2222-2-22-2-2222-2-2-2-222000000000000000000000000
χ362222-2-2-2-222-2-2-22-2222-2-22-2-22-2-22222-2-2000000000000000000000000
χ372222-2-2-2-222-2-2-2-222-2-2-22-2222000000002i−2i00−2i2i000000000000000000
χ382222-2-2-2-222-2-2-2-222-2-2-22-222200000000−2i2i002i−2i000000000000000000
χ392222-2-2-2-2-2-2222222-2-2-222-2-2-2000000000000000000002-2-2200000000
χ402222-2-2-2-2-2-2222222-2-2-222-2-2-200000000000000000000-222-200000000
χ412222-2-2-2-2-2-222-22-2-2-2222-2-22200000000002i−2i00−2i2i0000000000000000
χ422222-2-2-2-2-2-222-22-2-2-2222-2-2220000000000−2i2i002i−2i0000000000000000
χ432222-2-2-2-2-2-222-2-22-22-22-222-2200000000000000002i−2i−2i2i000000000000
χ442222-2-2-2-2-2-222-2-22-22-22-222-220000000000000000−2i2i2i−2i000000000000
χ4544-4-44i−4i4i−4i4i−4i4-40000000000002ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ3000000000000000000000000
χ4644-4-44i−4i4i−4i4i−4i4-4000000000000−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ3000000000000000000000000
χ4744-4-44i−4i4i−4i−4i4i-440000000000002ζ3−2ζ3−2ζ32ζ3−2ζ2ζ2ζ−2ζ000000000000000000000000
χ4844-4-44i−4i4i−4i−4i4i-44000000000000−2ζ32ζ32ζ3−2ζ32ζ−2ζ−2ζ2ζ000000000000000000000000
χ4944-4-4−4i4i−4i4i4i−4i-440000000000002ζ−2ζ−2ζ2ζ−2ζ32ζ32ζ3−2ζ3000000000000000000000000
χ5044-4-4−4i4i−4i4i4i−4i-44000000000000−2ζ2ζ2ζ−2ζ2ζ3−2ζ3−2ζ32ζ3000000000000000000000000
χ5144-4-4−4i4i−4i4i−4i4i4-40000000000002ζ3−2ζ32ζ3−2ζ32ζ−2ζ2ζ−2ζ000000000000000000000000
χ5244-4-4−4i4i−4i4i−4i4i4-4000000000000−2ζ32ζ3−2ζ32ζ3−2ζ2ζ−2ζ2ζ000000000000000000000000
χ538-88-888-8-8000000000000000000000000000000000000000000000000
χ548-88-8-8-888000000000000000000000000000000000000000000000000
χ558-8-888i−8i−8i8i000000000000000000000000000000000000000000000000
χ568-8-88−8i8i8i−8i000000000000000000000000000000000000000000000000

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