Finite Group Databasebeta

← Group #149833

Character table — Group #149833

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size1111222244444444488888888888888881616161616161616161616161632323232
order12222222244444444444444444444444448888888888888888
χ111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ311111111111111111-1-1-1-11111-1-1-1-11111111111111-1-1-1-1-1-1-1-1
χ411111111111111111-1-1-1-11111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111-1-1-1-11111111111111-1-1-1-1-1iiii−i−i−i−i-1-1-1-1ii−i−i
χ6111111111111-1-1-1-11111111111111-1-1-1-1-1−i−i−i−iiiii-1-1-1-1−i−iii
χ7111111111111-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1iiii−i−i−i−i1111−i−iii
χ8111111111111-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1−i−i−i−iiiii1111ii−i−i
χ911111-1-11-11-1-11111111-1-111-1-111-1-1-1-111-111-1-111-1-111-1-11-11-1
χ1011111-1-11-11-1-11111111-1-111-1-111-1-1-1-111-1-1-111-1-11111-1-1-11-11
χ1111111-1-11-11-1-111111-1-11111-1-1-1-111-1-111-111-1-111-1-1-1-111-11-11
χ1211111-1-11-11-1-111111-1-11111-1-1-1-111-1-111-1-1-111-1-111-1-1111-11-1
χ1311111-1-11-11-1-1-1-1-1-1111-1-111-1-111-1-111-1-11ii−i−i−i−iii-1-111i−i−ii
χ1411111-1-11-11-1-1-1-1-1-1111-1-111-1-111-1-111-1-11−i−iiiii−i−i-1-111−iii−i
χ1511111-1-11-11-1-1-1-1-1-11-1-11111-1-1-1-11111-1-11ii−i−i−i−iii11-1-1−iii−i
χ1611111-1-11-11-1-1-1-1-1-11-1-11111-1-1-1-11111-1-11−i−iiiii−i−i11-1-1i−i−ii
χ17222222222222222220000-2-2-2-2000022-2-2-20000000000000000
χ18222222222222-2-2-2-220000-2-2-2-20000-2-22220000000000000000
χ1922222-2-22-22-2-2222220000-2-2220000-2-2-2-220000000000000000
χ2022222-2-22-22-2-2-2-2-2-220000-2-22200002222-20000000000000000
χ212-22-2200-20-2002i2i−2i−2i2002i−2i2-200002i−2i002i−2i000000000002-20000
χ222-22-2200-20-2002i2i−2i−2i200−2i2i2-20000−2i2i002i−2i00000000000-220000
χ232-22-2200-20-2002i2i−2i−2i22i−2i00-22002i−2i0000−2i2i0000000002-2000000
χ242-22-2200-20-2002i2i−2i−2i2−2i2i00-2200−2i2i0000−2i2i000000000-22000000
χ252-22-2200-20-200−2i−2i2i2i2002i−2i2-200002i−2i00−2i2i00000000000-220000
χ262-22-2200-20-200−2i−2i2i2i200−2i2i2-20000−2i2i00−2i2i000000000002-20000
χ272-22-2200-20-200−2i−2i2i2i22i−2i00-22002i−2i00002i−2i000000000-22000000
χ282-22-2200-20-200−2i−2i2i2i2−2i2i00-2200−2i2i00002i−2i0000000002-2000000
χ29444444444-4-4-40000-4000000000000000000000000000000000
χ3044444-4-44-4-4440000-4000000000000000000000000000000000
χ314444-444-4-40000000022220000-2-2-2-2000000000000000000000
χ324444-444-4-400000000-2-2-2-200002222000000000000000000000
χ334444-4-4-4-440000000022-2-20000-2-222000000000000000000000
χ344444-4-4-4-4400000000-2-222000022-2-2000000000000000000000
χ354-44-4400-404000000-40000004-40000000000000000000000000
χ364-44-4400-404000000-4000000-440000000000000000000000000
χ374-44-4-4004004-4000002i−2i2i−2i0000−2i2i−2i2i000000000000000000000
χ384-44-4-4004004-400000−2i2i−2i2i00002i−2i2i−2i000000000000000000000
χ394-44-4-400400-44000002i−2i−2i2i0000−2i2i2i−2i000000000000000000000
χ404-44-4-400400-4400000−2i2i2i−2i00002i−2i−2i2i000000000000000000000
χ414-4-4404-4000002i−2i2i−2i00000000000002i−2i0001+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000
χ424-4-4404-4000002i−2i2i−2i00000000000002i−2i000−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000
χ434-4-4404-400000−2i2i−2i2i0000000000000−2i2i0001−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000
χ444-4-4404-400000−2i2i−2i2i0000000000000−2i2i000−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000
χ454-4-440-44000002i−2i2i−2i0000000000000−2i2i0001+i−1−i−1−i1+i1−i−1+i−1+i1−i00000000
χ464-4-440-44000002i−2i2i−2i0000000000000−2i2i000−1−i1+i1+i−1−i−1+i1−i1−i−1+i00000000
χ474-4-440-4400000−2i2i−2i2i00000000000002i−2i0001−i−1+i−1+i1−i1+i−1−i−1−i1+i00000000
χ484-4-440-4400000−2i2i−2i2i00000000000002i−2i000−1+i1−i1−i−1+i−1−i1+i1+i−1−i00000000
χ4988-8-8000000004-4-440000000000000000000000000000000000
χ5088-8-800000000-444-40000000000000000000000000000000000

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