Finite Group Databasebeta

← Group #10593820

Character table — Group #10593820

Order 576.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48
size1111224444444444888888888888999918181818181818181818363636363636
order1222222334666666666666661212121244444488888888448888
χ1111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-1iiii−i−i−i−i-1-1i−ii−i
χ41111111111111111111111111111-1-1-1-1-1-1−i−i−i−iiiii-1-1−ii−ii
χ5111111-111-11111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1
χ6111111-111-11111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111
χ7111111-111-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i11−ii−ii
χ8111111-111-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii11i−ii−i
χ91111-1-1111-1111111-1-1-1-11111-1-1-1-11111-1-111-1-111-1-1-1111-1-1
χ101111-1-1111-1111111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-11-1-111
χ111111-1-1111-1111111-1-1-1-11111-1-1-1-1-1-1-1-111ii−i−i−i−iii1-1i−i−ii
χ121111-1-1111-1111111-1-1-1-11111-1-1-1-1-1-1-1-111−i−iiiii−i−i1-1−iii−i
χ131111-1-1-1111111111-1-1-1-1-1-1-1-111111111-1-111-1-111-1-11-1-1-111
χ141111-1-1-1111111111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1111-111-1-1
χ151111-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-111ii−i−i−i−iii-11−iii−i
χ161111-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-111−i−iiiii−i−i-11i−i−ii
χ1722-2-22-20220-2-2-2-22222-2-2000000002i−2i2i−2i2i−2i00000000000000
χ1822-2-22-20220-2-2-2-22222-2-200000000−2i2i−2i2i−2i2i00000000000000
χ1922-2-2-220220-2-2-2-222-2-222000000002i−2i2i−2i−2i2i00000000000000
χ2022-2-2-220220-2-2-2-222-2-22200000000−2i2i−2i2i2i−2i00000000000000
χ212-22-200022022-2-2-2-20000000000002i−2i−2i2i002ζ3−2ζ3002ζ−2ζ00000000
χ222-22-200022022-2-2-2-20000000000002i−2i−2i2i00−2ζ32ζ300−2ζ2ζ00000000
χ232-22-200022022-2-2-2-2000000000000−2i2i2i−2i002ζ−2ζ002ζ3−2ζ300000000
χ242-22-200022022-2-2-2-2000000000000−2i2i2i−2i00−2ζ2ζ00−2ζ32ζ300000000
χ252-2-22000220-2-222-2-200000000000022-2-200002i−2i002i−2i000000
χ262-2-22000220-2-222-2-200000000000022-2-20000−2i2i00−2i2i000000
χ272-2-22000220-2-222-2-2000000000000-2-22200002-200-22000000
χ282-2-22000220-2-222-2-2000000000000-2-2220000-22002-2000000
χ2944444441-241-21-21-21-21-211-2-211-2-200000000000000000000
χ304444444-214-21-21-21-21-21-2-211-2-21100000000000000000000
χ31444444-41-2-41-21-21-21-21-2-1-122-1-12200000000000000000000
χ32444444-4-21-4-21-21-21-21-2122-1-122-1-100000000000000000000
χ334444-4-441-2-41-21-21-2-12-1211-2-2-1-12200000000000000000000
χ344444-4-44-21-4-21-21-212-12-1-2-21122-1-100000000000000000000
χ354444-4-4-41-241-21-21-2-12-12-1-12211-2-200000000000000000000
χ364444-4-4-4-214-21-21-212-12-122-1-1-2-21100000000000000000000
χ3744-4-44-401-20-12-121-21-2-123-3003-30000000000000000000000
χ3844-4-44-401-20-12-121-21-2-12-3300-330000000000000000000000
χ3944-4-44-40-2102-12-1-21-212-1003-3003-300000000000000000000
χ4044-4-44-40-2102-12-1-21-212-100-3300-3300000000000000000000
χ4144-4-4-4401-20-12-121-2-121-23-300-330000000000000000000000
χ4244-4-4-4401-20-12-121-2-121-2-33003-30000000000000000000000
χ4344-4-4-440-2102-12-1-212-1-21003-300-3300000000000000000000
χ4444-4-4-440-2102-12-1-212-1-2100-33003-300000000000000000000
χ458-88-80002-402-4-24-2400000000000000000000000000000000
χ468-88-8000-420-424-24-200000000000000000000000000000000
χ478-8-880002-40-242-4-2400000000000000000000000000000000
χ488-8-88000-4204-2-424-200000000000000000000000000000000

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