Finite Group Databasebeta

← Group #10593742

Character table — Group #10593742

Order 576.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48
size1111224444444444888888888888999918181818181818181818363636363636
order12224423346666666666121212121212121244444488888888248888
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
χ5111111-111-1111111-1-1-1-11111-1-1-1-111111111111111-1-1-1-1-1-1
χ6111111-111-1111111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111
χ7111111-111-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1ii−i−iii−i−i11−i−iii
χ8111111-111-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1−i−iii−i−iii11ii−i−i
χ91111-1-1111-11111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-111-11-1
χ101111-1-1111-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-11-11-11
χ111111-1-1111-11111111111-1-1-1-1-1-1-1-1-1-1-1-111ii−i−i−i−iii1-1i−i−ii
χ121111-1-1111-11111111111-1-1-1-1-1-1-1-1-1-1-1-111−i−iiiii−i−i1-1−iii−i
χ131111-1-1-1111111111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-11-1-11-11
χ141111-1-1-1111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111111-11-11-1
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
χ1722-2-2000220-2-222-2-20000000000002i−2i2i−2i002ζ−2ζ2ζ3−2ζ30000000000
χ1822-2-2000220-2-222-2-20000000000002i−2i2i−2i00−2ζ2ζ−2ζ32ζ30000000000
χ1922-2-2000220-2-222-2-2000000000000−2i2i−2i2i002ζ3−2ζ32ζ−2ζ0000000000
χ2022-2-2000220-2-222-2-2000000000000−2i2i−2i2i00−2ζ32ζ3−2ζ2ζ0000000000
χ212-22-22i−2i022022-2-2-2-200002i2i−2i−2i00002i−2i−2i2i2-200000000000000
χ222-22-22i−2i022022-2-2-2-200002i2i−2i−2i0000−2i2i2i−2i-2200000000000000
χ232-22-2−2i2i022022-2-2-2-20000−2i−2i2i2i00002i−2i−2i2i-2200000000000000
χ242-22-2−2i2i022022-2-2-2-20000−2i−2i2i2i0000−2i2i2i−2i2-200000000000000
χ252-2-22000220-2-2-2-22200000000000022-2-20000002i−2i2i−2i000000
χ262-2-22000220-2-2-2-22200000000000022-2-2000000−2i2i−2i2i000000
χ272-2-22000220-2-2-2-222000000000000-2-2220000002-2-22000000
χ282-2-22000220-2-2-2-222000000000000-2-222000000-222-2000000
χ2944444441-241-21-21-211-2-21-21-211-2-200000000000000000000
χ304444444-214-21-21-21-2-211-21-21-2-21100000000000000000000
χ31444444-41-2-41-21-21-2-1-1221-21-2-1-12200000000000000000000
χ32444444-4-21-4-21-21-2122-1-1-21-2122-1-100000000000000000000
χ334444-4-441-2-41-21-21-211-2-2-12-12-1-12200000000000000000000
χ344444-4-44-21-4-21-21-21-2-2112-12-122-1-100000000000000000000
χ354444-4-4-41-241-21-21-2-1-122-12-1211-2-200000000000000000000
χ364444-4-4-4-214-21-21-2122-1-12-12-1-2-21100000000000000000000
χ374-44-44i−4i01-201-2-12-123-300i−2i−i2i3i−3i0000000000000000000000
χ384-44-44i−4i01-201-2-12-12-3300i−2i−i2i−3i3i0000000000000000000000
χ394-44-44i−4i0-210-212-12-1003-3−2ii2i−i003i−3i00000000000000000000
χ404-44-44i−4i0-210-212-12-100-33−2ii2i−i00−3i3i00000000000000000000
χ414-44-4−4i4i01-201-2-12-123-300−i2ii−2i−3i3i0000000000000000000000
χ424-44-4−4i4i01-201-2-12-12-3300−i2ii−2i3i−3i0000000000000000000000
χ434-44-4−4i4i0-210-212-12-1003-32i−i−2ii00−3i3i00000000000000000000
χ444-44-4−4i4i0-210-212-12-100-332i−i−2ii003i−3i00000000000000000000
χ4588-8-80002-40-242-4-2400000000000000000000000000000000
χ4688-8-8000-4204-2-424-200000000000000000000000000000000
χ478-8-880002-40-24-242-400000000000000000000000000000000
χ488-8-88000-4204-24-2-4200000000000000000000000000000000

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