Finite Group Databasebeta

← Group #152694

Character table — Group #152694

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
χ911111-1-11-11111111-1-1111-1-1-11-1-1-1111-1-111-1-111-1-111-1-11-1
χ1011111-1-11-11111111-1-1111-1-1-11-1-1-11-1-111-1-111-1-111-1-1111-1
χ1111111-1-11-11111111-1-1111-1-1-1-111-1-111-1-111-1-1-1-111-1-111-11
χ1211111-1-11-11111111-1-1111-1-1-1-111-1-1-1-111-1-11111-1-111-1-1-11
χ1311111-1-11-111-1-1-1-1-111-111-1111-1-1-11ii−i−i−i−iiiii−i−i−i−iii-11
χ1411111-1-11-111-1-1-1-1-111-111-1111-1-1-11−i−iiiii−i−i−i−iiiii−i−i-11
χ1511111-1-11-111-1-1-1-1-111-111-111-111-1-1ii−i−i−i−iii−i−iiiii−i−i1-1
χ1611111-1-11-111-1-1-1-1-111-111-111-111-1-1−i−iiiii−i−iii−i−i−i−iii1-1
χ17222222222222222-2-2-2-2-2-2222000-20000000000000000000
χ1822222222222-2-2-2-22222-2-22-2-2000-20000000000000000000
χ1922222-2-22-2222222-222-2-2-2-2-2-200020000000000000000000
χ2022222-2-22-222-2-2-2-22-2-22-2-2-22200020000000000000000000
χ212-2-22-200202-222-2-2200-22-200000000002i−2i002i−2i0000000000
χ222-2-22-200202-222-2-2200-22-20000000000−2i2i00−2i2i0000000000
χ232-2-22-200202-222-2-2-2002-22000000002-2002-2000000000000
χ242-2-22-200202-222-2-2-2002-2200000000-2200-22000000000000
χ252-2-22-200202-2-2-222200-2-22000000002i−2i00−2i2i000000000000
χ262-2-22-200202-2-2-222200-2-2200000000−2i2i002i−2i000000000000
χ272-2-22-200202-2-2-222-20022-200000000002-200-220000000000
χ282-2-22-200202-2-2-222-20022-20000000000-22002-20000000000
χ29444444444-4-40000000000-40000000000000000000000000
χ3044444-4-44-4-4-4000000000040000000000000000000000000
χ314444-444-4-400000000000000022-20-2000000000000000000
χ324444-444-4-4000000000000000-2-2202000000000000000000
χ334444-4-4-4-440000000000000002-220-2000000000000000000
χ344444-4-4-4-44000000000000000-22-202000000000000000000
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
χ434-4-44-40040-44000004-400000000000000000000000000000
χ444-4-44-40040-4400000-4400000000000000000000000000000
χ458-88-800000004i−4i−4i4i00000000000000000000000000000000
χ468-88-80000000−4i4i4i−4i00000000000000000000000000000000
χ478-8-88800-8000000000000000000000000000000000000000

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