Finite Group Databasebeta

← Group #150412

Character table — Group #150412

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47
size1111222244444448888888881616161616161616161616161616161616161616163232
order12222222244444444444444424444888888888888888888
χ111111111111111111111111111111111111111111111111
χ211111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111
χ3111111111111111111111111-1-11-1-111111111-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-111111111-1-1
χ511111111111-1-1-1-1111-1-1-1-1-1-111111iiii−i−i−i−iiiii−i−i−i−i-1-1
χ611111111111-1-1-1-1111-1-1-1-1-1-111111−i−i−i−iiiii−i−i−i−iiiii-1-1
χ711111111111-1-1-1-1111-1-1-1-1-1-1-1-11-1-1iiii−i−i−i−i−i−i−i−iiiii11
χ811111111111-1-1-1-1111-1-1-1-1-1-1-1-11-1-1−i−i−i−iiiiiiiii−i−i−i−i11
χ911111-1-11-1111111-1-1-11-1-1-1-111-11-1111-1-111-1-111-1-111-1-11-1
χ1011111-1-11-1111111-1-1-11-1-1-1-111-11-11-1-111-1-111-1-111-1-1111-1
χ1111111-1-11-1111111-1-1-11-1-1-1-11-1111-111-1-111-1-1-1-111-1-111-11
χ1211111-1-11-1111111-1-1-11-1-1-1-11-1111-1-1-111-1-11111-1-111-1-1-11
χ1311111-1-11-111-1-1-1-1-1-1-1-11111-11-11-11ii−i−i−i−iiiii−i−i−i−iii-11
χ1411111-1-11-111-1-1-1-1-1-1-1-11111-11-11-11−i−iiiii−i−i−i−iiiii−i−i-11
χ1511111-1-11-111-1-1-1-1-1-1-1-11111-1-1111-1ii−i−i−i−iii−i−iiiii−i−i1-1
χ1611111-1-11-111-1-1-1-1-1-1-1-11111-1-1111-1−i−iiiii−i−iii−i−i−i−iii1-1
χ17222222222222222-2-22-2-2-222-200-200000000000000000000
χ1822222222222-2-2-2-2-2-22222-2-2200-200000000000000000000
χ1922222-2-22-222222222-2-222-2-2-200-200000000000000000000
χ2022222-2-22-222-2-2-2-222-22-2-222200-200000000000000000000
χ212-2-22200-202-22i2i−2i−2i2i−2i002-200000000000000001+i−1−i1−i−1+i1−i−1+i1+i−1−i00
χ222-2-22200-202-22i2i−2i−2i2i−2i002-20000000000000000−1−i1+i−1+i1−i−1+i1−i−1−i1+i00
χ232-2-22200-202-22i2i−2i−2i−2i2i00-2200000000000000001+i−1−i−1+i1−i1−i−1+i−1−i1+i00
χ242-2-22200-202-22i2i−2i−2i−2i2i00-220000000000000000−1−i1+i1−i−1+i−1+i1−i1+i−1−i00
χ252-2-22200-202-2−2i−2i2i2i2i−2i00-2200000000000000001−i−1+i−1−i1+i1+i−1−i−1+i1−i00
χ262-2-22200-202-2−2i−2i2i2i2i−2i00-220000000000000000−1+i1−i1+i−1−i−1−i1+i1−i−1+i00
χ272-2-22200-202-2−2i−2i2i2i−2i2i002-200000000000000001−i−1+i1+i−1−i1+i−1−i1−i−1+i00
χ282-2-22200-202-2−2i−2i2i2i−2i2i002-20000000000000000−1+i1−i−1−i1+i−1−i1+i−1+i1−i00
χ29444444444-4-4000000-400000000000000000000000000000
χ3044444-4-44-4-4-4000000400000000000000000000000000000
χ314444-444-4-40000000000000002-202-2000000000000000000
χ324444-444-4-4000000000000000-220-22000000000000000000
χ334444-4-4-4-44000000000000000220-2-2000000000000000000
χ344444-4-4-4-44000000000000000-2-2022000000000000000000
χ354-44-404-400002i−2i2i−2i0000002i−2i0000001+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000
χ364-44-404-400002i−2i2i−2i0000002i−2i000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000
χ374-44-404-40000−2i2i−2i2i000000−2i2i0000001−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000
χ384-44-404-40000−2i2i−2i2i000000−2i2i000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000
χ394-44-40-4400002i−2i2i−2i000000−2i2i0000001+i−1−i−1−i1+i1−i−1+i−1+i1−i0000000000
χ404-44-40-4400002i−2i2i−2i000000−2i2i000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i0000000000
χ414-44-40-440000−2i2i−2i2i0000002i−2i0000001−i−1+i−1+i1−i1+i−1−i−1−i1+i0000000000
χ424-44-40-440000−2i2i−2i2i0000002i−2i000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i0000000000
χ434-4-44400-40-44000000040000-400000000000000000000000
χ444-4-44400-40-440000000-40000400000000000000000000000
χ4588-8-800000004-4-4400000000000000000000000000000000
χ4688-8-80000000-444-400000000000000000000000000000000
χ478-8-88-8008000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).