Finite Group Databasebeta

← Group #10590178

Character table — Group #10590178

Order 576.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60
size11112222224444444444444444444444444444444499991818181818183636363636363636
order12442488883366666612121212121212122424242424242424242424242424242488884444881616161616161616
χ1111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii
χ5111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1
χ6111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-111
χ7111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1ii−i−i−i−iii
χ8111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1−i−iiiii−i−i
χ911-1-1-1111-1-111-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1ii−i−iii−i−ii−iζ−ζζ−ζζ3−ζ3ζ3−ζ3
χ1011-1-1-1111-1-111-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1ii−i−iii−i−ii−i−ζζ−ζζ−ζ3ζ3−ζ3ζ3
χ1111-1-1-1111-1-111-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1−i−iii−i−iii−iiζ3−ζ3ζ3−ζ3ζ−ζζ−ζ
χ1211-1-1-1111-1-111-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1−i−iii−i−iii−ii−ζ3ζ3−ζ3ζ3−ζζ−ζζ
χ1311-1-1-11-1-11111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111ii−i−i−i−iiii−iζ−ζ−ζζζ3−ζ3−ζ3ζ3
χ1411-1-1-11-1-11111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111ii−i−i−i−iiii−i−ζζζ−ζ−ζ3ζ3ζ3−ζ3
χ1511-1-1-11-1-11111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111−i−iiiii−i−i−iiζ3−ζ3−ζ3ζ3ζ−ζ−ζζ
χ1611-1-1-11-1-11111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111−i−iiiii−i−i−ii−ζ3ζ3ζ3−ζ3−ζζζ−ζ
χ172222-2-2000022-2-2-2-2222222-2-2-2-2000000000000000022220000-2-200000000
χ182222-2-2000022-2-2-2-2222222-2-2-2-20000000000000000-2-2-2-200002200000000
χ1922-2-22-2000022222222-2-2-2-2-2-2-2-200000000000000002i2i−2i−2i0000−2i2i00000000
χ2022-2-22-2000022222222-2-2-2-2-2-2-2-20000000000000000−2i−2i2i2i00002i−2i00000000
χ212-22i−2i00i2−i22−2220000-2-22i2i−2i−2i0000i2i2i2i2−i2−i2−i2−i22222−2−2−2−22ζ−2ζ2ζ3−2ζ31−i−1+i1+i−1−i0000000000
χ222-22i−2i00i2−i22−2220000-2-22i2i−2i−2i0000i2i2i2i2−i2−i2−i2−i22222−2−2−2−2−2ζ2ζ−2ζ32ζ3−1+i1−i−1−i1+i0000000000
χ232-22i−2i00−i2i2−22220000-2-22i2i−2i−2i0000−i2−i2−i2−i2i2i2i2i2−2−2−2−222222ζ−2ζ2ζ3−2ζ3−1+i1−i−1−i1+i0000000000
χ242-22i−2i00−i2i2−22220000-2-22i2i−2i−2i0000−i2−i2−i2−i2i2i2i2i2−2−2−2−22222−2ζ2ζ−2ζ32ζ31−i−1+i1+i−1−i0000000000
χ252-2−2i2i00i2−i2−22220000-2-2−2i−2i2i2i0000i2i2i2i2−i2−i2−i2−i2−2−2−2−222222ζ3−2ζ32ζ−2ζ1+i−1−i1−i−1+i0000000000
χ262-2−2i2i00i2−i2−22220000-2-2−2i−2i2i2i0000i2i2i2i2−i2−i2−i2−i2−2−2−2−22222−2ζ32ζ3−2ζ2ζ−1−i1+i−1+i1−i0000000000
χ272-2−2i2i00−i2i22−2220000-2-2−2i−2i2i2i0000−i2−i2−i2−i2i2i2i2i22222−2−2−2−22ζ3−2ζ32ζ−2ζ−1−i1+i−1+i1−i0000000000
χ282-2−2i2i00−i2i22−2220000-2-2−2i−2i2i2i0000−i2−i2−i2−i2i2i2i2i22222−2−2−2−2−2ζ32ζ3−2ζ2ζ1+i−1−i1−i−1+i0000000000
χ2944444444441-211-2-21-21-21-211-2-211-2-211-2-211-2-211-2-2000000000000000000
χ304444444444-21-2-211-21-21-21-2-211-2-211-2-211-2-211-2-211000000000000000000
χ31444444-4-4-4-41-211-2-21-21-21-211-2-2-1-122-1-122-1-122-1-122000000000000000000
χ32444444-4-4-4-4-21-2-211-21-21-21-2-21122-1-122-1-122-1-122-1-1000000000000000000
χ334444-4-400001-2-1-1221-21-21-2-1-1223i−3i003i−3i003i−3i003i−3i00000000000000000000
χ344444-4-400001-2-1-1221-21-21-2-1-122−3i3i00−3i3i00−3i3i00−3i3i00000000000000000000
χ354444-4-40000-2122-1-1-21-21-2122-1-1003i−3i003i−3i003i−3i003i−3i000000000000000000
χ364444-4-40000-2122-1-1-21-21-2122-1-100−3i3i00−3i3i00−3i3i00−3i3i000000000000000000
χ3744-4-44-400001-211-2-21-2-12-12-1-1223i−3i003i−3i00−3i3i00−3i3i00000000000000000000
χ3844-4-44-400001-211-2-21-2-12-12-1-122−3i3i00−3i3i003i−3i003i−3i00000000000000000000
χ3944-4-44-40000-21-2-211-212-12-122-1-1003i−3i003i−3i00−3i3i00−3i3i000000000000000000
χ4044-4-44-40000-21-2-211-212-12-122-1-100−3i3i00−3i3i003i−3i003i−3i000000000000000000
χ4144-4-4-4444-4-41-2-1-1221-2-12-1211-2-211-2-211-2-2-1-122-1-122000000000000000000
χ4244-4-4-4444-4-4-2122-1-1-212-12-1-2-211-2-211-2-21122-1-122-1-1000000000000000000
χ4344-4-4-44-4-4441-2-1-1221-2-12-1211-2-2-1-122-1-12211-2-211-2-2000000000000000000
χ4444-4-4-44-4-444-2122-1-1-212-12-1-2-21122-1-122-1-1-2-211-2-211000000000000000000
χ454-44i−4i002i2−2i222−221-23-300-12i−2i−i2i3i−3i002ζ−ζ3−ζ+2ζ3−i2−i2−2ζ+ζ3ζ−2ζ3i2i2−ζ−2ζ32ζ+ζ3−2−2ζ+2ζ3−2ζ−ζ322000000000000000000
χ464-44i−4i002i2−2i222−221-2-3300-12i−2i−i2i−3i3i00−ζ+2ζ32ζ−ζ3−i2−i2ζ−2ζ3−2ζ+ζ3i2i22ζ+ζ3−ζ−2ζ3−2−2−2ζ−ζ3ζ+2ζ322000000000000000000
χ474-44i−4i002i2−2i222−22-21003-32-1−2ii2i−i003i−3i−i2−i22ζ−ζ3−ζ+2ζ3i2i2−2ζ+ζ3ζ−2ζ3−2−2−ζ−2ζ32ζ+ζ322ζ+2ζ3−2ζ−ζ3000000000000000000
χ484-44i−4i002i2−2i222−22-2100-332-1−2ii2i−i00−3i3i−i2−i2−ζ+2ζ32ζ−ζ3i2i2ζ−2ζ3−2ζ+ζ3−2−22ζ+ζ3−ζ−2ζ322−2ζ−ζ3ζ+2ζ3000000000000000000
χ494-44i−4i00−2i22i2−22221-23-300-12i−2i−i2i3i−3i00−2ζ+ζ3ζ−2ζ3i2i22ζ−ζ3−ζ+2ζ3−i2−i2ζ+2ζ3−2ζ−ζ322−ζ−2ζ32ζ+ζ3−2−2000000000000000000
χ504-44i−4i00−2i22i2−22221-2-3300-12i−2i−i2i−3i3i00ζ−2ζ3−2ζ+ζ3i2i2−ζ+2ζ32ζ−ζ3−i2−i2−2ζ−ζ3ζ+2ζ3222ζ+ζ3−ζ−2ζ3−2−2000000000000000000
χ514-44i−4i00−2i22i2−2222-21003-32-1−2ii2i−i003i−3ii2i2−2ζ+ζ3ζ−2ζ3−i2−i22ζ−ζ3−ζ+2ζ322ζ+2ζ3−2ζ−ζ3−2−2−ζ−2ζ32ζ+ζ3000000000000000000
χ524-44i−4i00−2i22i2−2222-2100-332-1−2ii2i−i00−3i3ii2i2ζ−2ζ3−2ζ+ζ3−i2−i2−ζ+2ζ32ζ−ζ322−2ζ−ζ3ζ+2ζ3−2−22ζ+ζ3−ζ−2ζ3000000000000000000
χ534-4−4i4i002i2−2i2−22221-23-300-12−i2ii−2i−3i3i00−ζ+2ζ32ζ−ζ3−i2−i2ζ−2ζ3−2ζ+ζ3i2i2−2ζ−ζ3ζ+2ζ3222ζ+ζ3−ζ−2ζ3−2−2000000000000000000
χ544-4−4i4i002i2−2i2−22221-2-3300-12−i2ii−2i3i−3i002ζ−ζ3−ζ+2ζ3−i2−i2−2ζ+ζ3ζ−2ζ3i2i2ζ+2ζ3−2ζ−ζ322−ζ−2ζ32ζ+ζ3−2−2000000000000000000
χ554-4−4i4i002i2−2i2−2222-21003-32-12i−i−2ii00−3i3i−i2−i2−ζ+2ζ32ζ−ζ3i2i2ζ−2ζ3−2ζ+ζ322−2ζ−ζ3ζ+2ζ3−2−22ζ+ζ3−ζ−2ζ3000000000000000000
χ564-4−4i4i002i2−2i2−2222-2100-332-12i−i−2ii003i−3i−i2−i22ζ−ζ3−ζ+2ζ3i2i2−2ζ+ζ3ζ−2ζ322ζ+2ζ3−2ζ−ζ3−2−2−ζ−2ζ32ζ+ζ3000000000000000000
χ574-4−4i4i00−2i22i222−221-23-300-12−i2ii−2i−3i3i00ζ−2ζ3−2ζ+ζ3i2i2−ζ+2ζ32ζ−ζ3−i2−i22ζ+ζ3−ζ−2ζ3−2−2−2ζ−ζ3ζ+2ζ322000000000000000000
χ584-4−4i4i00−2i22i222−221-2-3300-12−i2ii−2i3i−3i00−2ζ+ζ3ζ−2ζ3i2i22ζ−ζ3−ζ+2ζ3−i2−i2−ζ−2ζ32ζ+ζ3−2−2ζ+2ζ3−2ζ−ζ322000000000000000000
χ594-4−4i4i00−2i22i222−22-21003-32-12i−i−2ii00−3i3ii2i2ζ−2ζ3−2ζ+ζ3−i2−i2−ζ+2ζ32ζ−ζ3−2−22ζ+ζ3−ζ−2ζ322−2ζ−ζ3ζ+2ζ3000000000000000000
χ604-4−4i4i00−2i22i222−22-2100-332-12i−i−2ii003i−3ii2i2−2ζ+ζ3ζ−2ζ3−i2−i22ζ−ζ3−ζ+2ζ3−2−2−ζ−2ζ32ζ+ζ322ζ+2ζ3−2ζ−ζ3000000000000000000

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