Finite Group Databasebeta

← Group #149889

Character table — Group #149889

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47
size1111222244444448888888881616161616161616161616161616161616161616163232
order12222222244444444444444424444888888888888888888
χ111111111111111111111111111111111111111111111111
χ211111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111
χ3111111111111111111111111-1-1-11-111111111-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111-1-1-11-1-1-1-1-1-1-1-1-111111111-1-1
χ511111111111-1-1-1-1-1-1111-1-1-1-111111iiii−i−i−i−iiiii−i−i−i−i-1-1
χ611111111111-1-1-1-1-1-1111-1-1-1-111111−i−i−i−iiiii−i−i−i−iiiii-1-1
χ711111111111-1-1-1-1-1-1111-1-1-1-1-1-1-11-1iiii−i−i−i−i−i−i−i−iiiii11
χ811111111111-1-1-1-1-1-1111-1-1-1-1-1-1-11-1−i−i−i−iiiiiiiii−i−i−i−i11
χ911111-1-11-1111111-1-111-1-1-1111-1-1-1111-1-111-1-111-1-111-1-11-1
χ1011111-1-11-1111111-1-111-1-1-1111-1-1-11-1-111-1-111-1-111-1-1111-1
χ1111111-1-11-1111111-1-111-1-1-111-111-1-111-1-111-1-1-1-111-1-111-11
χ1211111-1-11-1111111-1-111-1-1-111-111-1-1-1-111-1-11111-1-111-1-1-11
χ1311111-1-11-111-1-1-1-11111-111-1-11-1-1-11ii−i−i−i−iiiii−i−i−i−iii-11
χ1411111-1-11-111-1-1-1-11111-111-1-11-1-1-11−i−iiiii−i−i−i−iiiii−i−i-11
χ1511111-1-11-111-1-1-1-11111-111-1-1-111-1-1ii−i−i−i−iii−i−iiiii−i−i1-1
χ1611111-1-11-111-1-1-1-11111-111-1-1-111-1-1−i−iiiii−i−iii−i−i−i−iii1-1
χ17222222222222222-2-2-2-2222-2-2000-20000000000000000000
χ1822222222222-2-2-2-222-2-22-2-222000-20000000000000000000
χ1922222-2-22-222222222-2-2-2-2-2-2-200020000000000000000000
χ2022222-2-22-222-2-2-2-2-2-2-2-2-2222200020000000000000000000
χ212-2-22200-202-22i2i−2i−2i002-20002i−2i0000000000000002ζ3−2ζ3002ζ−2ζ00
χ222-2-22200-202-22i2i−2i−2i002-20002i−2i000000000000000−2ζ32ζ300−2ζ2ζ00
χ232-2-22200-202-22i2i−2i−2i00-22000−2i2i00000000000002ζ−2ζ002ζ3−2ζ30000
χ242-2-22200-202-22i2i−2i−2i00-22000−2i2i0000000000000−2ζ2ζ00−2ζ32ζ30000
χ252-2-22200-202-2−2i−2i2i2i002-2000−2i2i0000000000000002ζ−2ζ002ζ3−2ζ300
χ262-2-22200-202-2−2i−2i2i2i002-2000−2i2i000000000000000−2ζ2ζ00−2ζ32ζ300
χ272-2-22200-202-2−2i−2i2i2i00-220002i−2i00000000000002ζ3−2ζ3002ζ−2ζ0000
χ282-2-22200-202-2−2i−2i2i2i00-220002i−2i0000000000000−2ζ32ζ300−2ζ2ζ0000
χ29444444444-4-400000000-4000000000000000000000000000
χ3044444-4-44-4-4-4000000004000000000000000000000000000
χ314444-444-4-40000000000000002-220-2000000000000000000
χ324444-444-4-4000000000000000-22-202000000000000000000
χ334444-4-4-4-4400000000000000022-20-2000000000000000000
χ344444-4-4-4-44000000000000000-2-2202000000000000000000
χ354-44-404-400002i−2i2i−2i000002i−2i00000001+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000
χ364-44-404-400002i−2i2i−2i000002i−2i0000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000
χ374-44-404-40000−2i2i−2i2i00000−2i2i00000001−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000
χ384-44-404-40000−2i2i−2i2i00000−2i2i0000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000
χ394-44-40-4400002i−2i2i−2i00000−2i2i00000001+i−1−i−1−i1+i1−i−1+i−1+i1−i0000000000
χ404-44-40-4400002i−2i2i−2i00000−2i2i0000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i0000000000
χ414-44-40-440000−2i2i−2i2i000002i−2i00000001−i−1+i−1+i1−i1+i−1−i−1−i1+i0000000000
χ424-44-40-440000−2i2i−2i2i000002i−2i0000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i0000000000
χ434-4-44400-40-4400004i−4i000000000000000000000000000000
χ444-4-44400-40-440000−4i4i000000000000000000000000000000
χ4588-8-800000004-4-4400000000000000000000000000000000
χ4688-8-80000000-444-400000000000000000000000000000000
χ478-8-88-8008000000000000000000000000000000000000000

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