Finite Group Databasebeta

← Group #150405

Character table — Group #150405

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47
size1111222244444448888888881616161616161616161616161616161616161616163232
order12222222244444422224444424444444444448888888888
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
χ511111111111-1-1-1-1-1-1-1-1111-1-111111iiii−i−i−i−iiiii−i−i−i−i-1-1
χ611111111111-1-1-1-1-1-1-1-1111-1-111111−i−i−i−iiiii−i−i−i−iiiii-1-1
χ711111111111-1-1-1-1-1-1-1-1111-1-1-1-1-11-1iiii−i−i−i−i−i−i−i−iiiii11
χ811111111111-1-1-1-1-1-1-1-1111-1-1-1-1-11-1−i−i−i−iiiiiiiii−i−i−i−i11
χ911111-1-11-11111111-1-11-1-1-1-1-11-111-111-1-111-1-111-1-111-1-11-1
χ1011111-1-11-11111111-1-11-1-1-1-1-11-111-1-1-111-1-111-1-111-1-1111-1
χ1111111-1-11-11111111-1-11-1-1-1-1-1-11-11111-1-111-1-1-1-111-1-111-11
χ1211111-1-11-11111111-1-11-1-1-1-1-1-11-111-1-111-1-11111-1-111-1-1-11
χ1311111-1-11-111-1-1-1-1-111-1-1-1-1111-111-1ii−i−i−i−iiiii−i−i−i−iii-11
χ1411111-1-11-111-1-1-1-1-111-1-1-1-1111-111-1−i−iiiii−i−i−i−iiiii−i−i-11
χ1511111-1-11-111-1-1-1-1-111-1-1-1-111-11-111ii−i−i−i−iii−i−iiiii−i−i1-1
χ1611111-1-11-111-1-1-1-1-111-1-1-1-111-11-111−i−iiiii−i−iii−i−i−i−iii1-1
χ17222222222222222-2-2-2-22-2-222000-20000000000000000000
χ1822222222222-2-2-2-222222-2-2-2-2000-20000000000000000000
χ1922222-2-22-2222222-222-2-222-2-2000-20000000000000000000
χ2022222-2-22-222-2-2-2-22-2-22-22222000-20000000000000000000
χ212-22-2200-202-22i2i−2i−2i02-2002i−2i00000001+i−1−i1−i−1+i1−i−1+i1+i−1−i0000000000
χ222-22-2200-202-22i2i−2i−2i02-2002i−2i0000000−1−i1+i−1+i1−i−1+i1−i−1−i1+i0000000000
χ232-22-2200-202-22i2i−2i−2i0-2200−2i2i00000001+i−1−i−1+i1−i1−i−1+i−1−i1+i0000000000
χ242-22-2200-202-22i2i−2i−2i0-2200−2i2i0000000−1−i1+i1−i−1+i−1+i1−i1+i−1−i0000000000
χ252-22-2200-202-2−2i−2i2i2i02-200−2i2i00000001−i−1+i1+i−1−i1+i−1−i1−i−1+i0000000000
χ262-22-2200-202-2−2i−2i2i2i02-200−2i2i0000000−1+i1−i−1−i1+i−1−i1+i−1+i1−i0000000000
χ272-22-2200-202-2−2i−2i2i2i0-22002i−2i00000001−i−1+i−1−i1+i1+i−1−i−1+i1−i0000000000
χ282-22-2200-202-2−2i−2i2i2i0-22002i−2i0000000−1+i1−i1+i−1−i−1−i1+i1−i−1+i0000000000
χ29444444444-4-400000000-4000000000000000000000000000
χ3044444-4-44-4-4-4000000004000000000000000000000000000
χ314444-444-4-400000000000000022-20-2000000000000000000
χ324444-444-4-4000000000000000-2-2202000000000000000000
χ334444-4-4-4-440000000000000002-2-202000000000000000000
χ344444-4-4-4-44000000000000000-2220-2000000000000000000
χ3544-4-404-400002i−2i2i−2i00000002i−2i00000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i00
χ3644-4-404-400002i−2i2i−2i00000002i−2i0000000000000−1−i1+i−1−i1+i−1+i1−i−1+i1−i00
χ3744-4-404-40000−2i2i−2i2i0000000−2i2i00000000000001−i−1+i1−i−1+i1+i−1−i1+i−1−i00
χ3844-4-404-40000−2i2i−2i2i0000000−2i2i0000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i00
χ3944-4-40-4400002i−2i2i−2i0000000−2i2i00000000000001+i−1−i−1−i1+i1−i−1+i−1+i1−i00
χ4044-4-40-4400002i−2i2i−2i0000000−2i2i0000000000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i00
χ4144-4-40-440000−2i2i−2i2i00000002i−2i00000000000001−i−1+i−1+i1−i1+i−1−i−1−i1+i00
χ4244-4-40-440000−2i2i−2i2i00000002i−2i0000000000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i00
χ434-44-4400-40-440000400-40000000000000000000000000000
χ444-44-4400-40-440000-40040000000000000000000000000000
χ458-88-8-8008000000000000000000000000000000000000000
χ468-8-8800000004-4-4400000000000000000000000000000000
χ478-8-880000000-444-400000000000000000000000000000000

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