Finite Group Databasebeta

← Group #10593821

Character table — Group #10593821

Order 576.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48
size1111224444444444888888888888999918181818181818181818363636363636
order1222442233666666666666661212121244444488888888448888
χ1111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-1ii−i−iii−i−i-1-1ii−i−i
χ41111111111111111111111111111-1-1-1-1-1-1−i−iii−i−iii-1-1−i−iii
χ5111111-1-111111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1
χ6111111-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111
χ7111111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1ii−i−iii−i−i11−i−iii
χ8111111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1−i−iii−i−iii11ii−i−i
χ91111-1-11-1111111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11-11-11-1
χ101111-1-11-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111-1-11-11
χ111111-1-11-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111ii−i−i−i−iii-11i−i−ii
χ121111-1-11-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111−i−iiiii−i−i-11−iii−i
χ131111-1-1-1111111111-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-1-11-11-11
χ141111-1-1-1111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-111-11-1
χ151111-1-1-1111111111-1-1-1-11111-1-1-1-1-1-1-1-111ii−i−i−i−iii1-1−iii−i
χ161111-1-1-1111111111-1-1-1-11111-1-1-1-1-1-1-1-111−i−iiiii−i−i1-1i−i−ii
χ1722-2-22-20022-2-2-2-2220000000022-2-22i−2i2i−2i2i−2i00000000000000
χ1822-2-22-20022-2-2-2-2220000000022-2-2−2i2i−2i2i−2i2i00000000000000
χ1922-2-2-220022-2-2-2-22200000000-2-2222i−2i2i−2i−2i2i00000000000000
χ2022-2-2-220022-2-2-2-22200000000-2-222−2i2i−2i2i2i−2i00000000000000
χ212-22-200002222-2-2-2-20000000000002i−2i−2i2i002ζ−2ζ2ζ3−2ζ30000000000
χ222-22-200002222-2-2-2-20000000000002i−2i−2i2i00−2ζ2ζ−2ζ32ζ30000000000
χ232-22-200002222-2-2-2-2000000000000−2i2i2i−2i002ζ3−2ζ32ζ−2ζ0000000000
χ242-22-200002222-2-2-2-2000000000000−2i2i2i−2i00−2ζ32ζ3−2ζ2ζ0000000000
χ252-2-22000022-2-222-2-200000000000022-2-20000002i−2i2i−2i000000
χ262-2-22000022-2-222-2-200000000000022-2-2000000−2i2i−2i2i000000
χ272-2-22000022-2-222-2-2000000000000-2-2220000002-2-22000000
χ282-2-22000022-2-222-2-2000000000000-2-222000000-222-2000000
χ29444444441-21-21-21-211-2-211-2-21-21-200000000000000000000
χ3044444444-21-21-21-21-2-211-2-211-21-2100000000000000000000
χ31444444-4-41-21-21-21-2-1-122-1-1221-21-200000000000000000000
χ32444444-4-4-21-21-21-2122-1-122-1-1-21-2100000000000000000000
χ334444-4-44-41-21-21-21-211-2-2-1-122-12-1200000000000000000000
χ344444-4-44-4-21-21-21-21-2-21122-1-12-12-100000000000000000000
χ354444-4-4-441-21-21-21-2-1-12211-2-2-12-1200000000000000000000
χ364444-4-4-44-21-21-21-2122-1-1-2-2112-12-100000000000000000000
χ3744-4-44-4001-2-12-121-23-3003-3001-2-1200000000000000000000
χ3844-4-44-4001-2-12-121-2-3300-33001-2-1200000000000000000000
χ3944-4-44-400-212-12-1-21003-3003-3-212-100000000000000000000
χ4044-4-44-400-212-12-1-2100-3300-33-212-100000000000000000000
χ4144-4-4-44001-2-12-121-23-300-3300-121-200000000000000000000
χ4244-4-4-44001-2-12-121-2-33003-300-121-200000000000000000000
χ4344-4-4-4400-212-12-1-21003-300-332-1-2100000000000000000000
χ4444-4-4-4400-212-12-1-2100-33003-32-1-2100000000000000000000
χ458-88-800002-42-4-24-2400000000000000000000000000000000
χ468-88-80000-42-424-24-200000000000000000000000000000000
χ478-8-8800002-4-242-4-2400000000000000000000000000000000
χ488-8-880000-424-2-424-200000000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.