Finite Group Databasebeta

← Group #149831

Character table — Group #149831

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size1111222244444444488888888888888881616161616161616161616161632323232
order12222222244444444222244444444444448888888888888888
χ111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ3111111111111111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-11111
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
χ7111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i1111−i−iii
χ8111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1−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
χ1111111-1-11-11-1-11111111-1-1-1-111-1-111-1-111-111-1-111-1-1-1-111-11-11
χ1211111-1-11-11-1-11111111-1-1-1-111-1-111-1-111-1-1-111-1-111-1-1111-11-1
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
χ1511111-1-11-11-1-1-1-1-1-1111-1-1-1-111-1-11111-1-11ii−i−i−i−iii11-1-1−iii−i
χ1611111-1-11-11-1-1-1-1-1-1111-1-1-1-111-1-11111-1-11−i−iiiii−i−i11-1-1i−i−ii
χ1722222222222222222-2-2-2-20000000022-2-2-20000000000000000
χ18222222222222-2-2-2-22-2-2-2-200000000-2-22220000000000000000
χ1922222-2-22-22-2-222222-2-22200000000-2-2-2-220000000000000000
χ2022222-2-22-22-2-2-2-2-2-22-2-222000000002222-20000000000000000
χ2122-2-2200-20-2002i2i−2i−2i22-200002i−2i002i−2i002i−2i000000000002-20000
χ2222-2-2200-20-2002i2i−2i−2i22-20000−2i2i00−2i2i002i−2i00000000000-220000
χ2322-2-2200-20-2002i2i−2i−2i2-22002i−2i002i−2i0000−2i2i0000000002-2000000
χ2422-2-2200-20-2002i2i−2i−2i2-2200−2i2i00−2i2i0000−2i2i000000000-22000000
χ2522-2-2200-20-200−2i−2i2i2i22-200002i−2i002i−2i00−2i2i00000000000-220000
χ2622-2-2200-20-200−2i−2i2i2i22-20000−2i2i00−2i2i00−2i2i000000000002-20000
χ2722-2-2200-20-200−2i−2i2i2i2-22002i−2i002i−2i00002i−2i000000000-22000000
χ2822-2-2200-20-200−2i−2i2i2i2-2200−2i2i00−2i2i00002i−2i0000000002-2000000
χ29444444444-4-4-40000-4000000000000000000000000000000000
χ3044444-4-44-4-4440000-4000000000000000000000000000000000
χ314444-444-4-40000000000002222-2-2-2-2000000000000000000000
χ324444-444-4-4000000000000-2-2-2-22222000000000000000000000
χ334444-4-4-4-4400000000000022-2-2-2-222000000000000000000000
χ344444-4-4-4-44000000000000-2-22222-2-2000000000000000000000
χ3544-4-4400-404000000-4004-400000000000000000000000000000
χ3644-4-4400-404000000-400-4400000000000000000000000000000
χ3744-4-4-4004004-40000000002i−2i2i−2i−2i2i−2i2i000000000000000000000
χ3844-4-4-4004004-4000000000−2i2i−2i2i2i−2i2i−2i000000000000000000000
χ3944-4-4-400400-440000000002i−2i−2i2i−2i2i2i−2i000000000000000000000
χ4044-4-4-400400-44000000000−2i2i2i−2i2i−2i−2i2i000000000000000000000
χ414-44-404-4000002i−2i2i−2i00000000000002i−2i0001+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000
χ424-44-404-4000002i−2i2i−2i00000000000002i−2i000−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000
χ434-44-404-400000−2i2i−2i2i0000000000000−2i2i0001−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000
χ444-44-404-400000−2i2i−2i2i0000000000000−2i2i000−1+i1−i−1+i1−i−1−i1+i−1−i1+i00000000
χ454-44-40-44000002i−2i2i−2i0000000000000−2i2i0001+i−1−i−1−i1+i1−i−1+i−1+i1−i00000000
χ464-44-40-44000002i−2i2i−2i0000000000000−2i2i000−1−i1+i1+i−1−i−1+i1−i1−i−1+i00000000
χ474-44-40-4400000−2i2i−2i2i00000000000002i−2i0001−i−1+i−1+i1−i1+i−1−i−1−i1+i00000000
χ484-44-40-4400000−2i2i−2i2i00000000000002i−2i000−1+i1−i1−i−1+i−1−i1+i1+i−1−i00000000
χ498-8-88000000004-4-440000000000000000000000000000000000
χ508-8-8800000000-444-40000000000000000000000000000000000

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