Finite Group Databasebeta

← Group #10590743

Character table — Group #10590743

Order 576.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size1111222222222244444444444444444444444444444412121212121212121818181824242424242424243636
order122233446666663666881212121212121212242424242424242424242424242424242244444444446612121212121288
χ1111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-11111-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ5111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111
χ6111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-111-1-1-1-1
χ7111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-111-1-111-1-1
χ8111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-111
χ911-1-111-11-1-11-1-111-1-11i−i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i1-11-1i−ii−ii−ii−i1-1i−ii−i1-11-1
χ1011-1-111-11-1-11-1-111-1-11i−i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i1-1-11i−i−ii−ii−ii1-1i−i−ii-11-11
χ1111-1-111-11-1-11-1-111-1-11i−i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-111-1−iii−i−ii−ii-11−iii−i1-1-11
χ1211-1-111-11-1-11-1-111-1-11i−i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-11-11−ii−iii−ii−i-11−ii−ii-111-1
χ1311-1-111-11-1-11-1-111-1-11−ii1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii1-11-1−ii−ii−ii−ii1-1−ii−ii1-11-1
χ1411-1-111-11-1-11-1-111-1-11−ii1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii1-1-11−iii−ii−ii−i1-1−iii−i-11-11
χ1511-1-111-11-1-11-1-111-1-11−ii1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-111-1i−i−iii−ii−i-11i−i−ii1-1-11
χ1611-1-111-11-1-11-1-111-1-11−ii1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-11-11i−ii−i−ii−ii-11i−ii−i-111-1
χ17222222-2-2222222222200-2-2-2-2-2-2-2-200000000000000000000000022-2-20000000000
χ18222222-2-2222222222200-2-2-2-2-2-2-2-2000000000000000000000000-2-2220000000000
χ1922222-1222-1-12-12-1-1-1-122-12-1-1-12-1-122-1-1-1-1-1-122-1-1-1-1-1-1220022000000-1-1-1-1000000
χ2022222-1222-1-12-12-1-1-1-122-12-1-1-12-1-122-1-1-1-1-1-122-1-1-1-1-1-1-2-200-2-20000001111000000
χ2122222-1222-1-12-12-1-1-1-1-2-2-12-1-1-12-1-1-2-2111111-2-21111112200-2-2000000-1-111000000
χ2222222-1222-1-12-12-1-1-1-1-2-2-12-1-1-12-1-1-2-2111111-2-2111111-2-2002200000011-1-1000000
χ232222-1222-122-12-1-1-1-1-1222-1-1-12-1-1-1-1-122-1-1-1-1-1-122-1-1-1-10022002200000000-1-1-1-100
χ242222-1222-122-12-1-1-1-1-1222-1-1-12-1-1-1-1-122-1-1-1-1-1-122-1-1-1-100-2-200-2-200000000111100
χ252222-1222-122-12-1-1-1-1-1-2-22-1-1-12-1-1-111-2-2111111-2-21111002200-2-20000000011-1-100
χ262222-1222-122-12-1-1-1-1-1-2-22-1-1-12-1-1-111-2-2111111-2-2111100-2-2002200000000-1-11100
χ2722-2-2222-2-2-22-2-222-2-2200-2-2-2-222220000000000000000000000002i−2i−2i2i0000000000
χ2822-2-2222-2-2-22-2-222-2-2200-2-2-2-22222000000000000000000000000−2i2i2i−2i0000000000
χ2922-2-22-1-22-21-1-212-111-12i−2i-12-1-11-2112i2i−i−i−i−i−i−i−2i−2iiiiiii2-2002i−2i000000-11−ii000000
χ3022-2-22-1-22-21-1-212-111-12i−2i-12-1-11-2112i2i−i−i−i−i−i−i−2i−2iiiiiii-2200−2i2i0000001-1i−i000000
χ3122-2-22-1-22-21-1-212-111-1−2i2i-12-1-11-211−2i−2iiiiiii2i2i−i−i−i−i−i−i2-200−2i2i000000-11i−i000000
χ3222-2-22-1-22-21-1-212-111-1−2i2i-12-1-11-211−2i−2iiiiiii2i2i−i−i−i−i−i−i-22002i−2i0000001-1−ii000000
χ3322-2-2-12-221-221-2-1-111-12i−2i2-1-1-1-2111−i−i2i2i−i−i−i−iii−2i−2iiiii002-2002i−2i00000000−ii-1100
χ3422-2-2-12-221-221-2-1-111-12i−2i2-1-1-1-2111−i−i2i2i−i−i−i−iii−2i−2iiiii00-2200−2i2i00000000i−i1-100
χ3522-2-2-12-221-221-2-1-111-1−2i2i2-1-1-1-2111ii−2i−2iiiii−i−i2i2i−i−i−i−i002-200−2i2i00000000i−i-1100
χ3622-2-2-12-221-221-2-1-111-1−2i2i2-1-1-1-2111ii−2i−2iiiii−i−i2i2i−i−i−i−i00-22002i−2i00000000−ii1-100
χ3744444-2-4-44-2-24-24-2-2-2-2002-4222-42200000000000000000000000000000000000000
χ384444-24-4-4-244-24-2-2-2-2-200-4222-422200000000000000000000000000000000000000
χ394444-2-244-2-2-2-2-2-2111144-2-211-2-211-2-2-2-21111-2-2-2-211110000000000000000000000
χ404444-2-244-2-2-2-2-2-21111-4-4-2-211-2-2112222-1-1-1-12222-1-1-1-10000000000000000000000
χ414444-2-2-4-4-2-2-2-2-2-211110022-1-122-1-100003i3i−3i−3i00003i3i−3i−3i0000000000000000000000
χ424444-2-2-4-4-2-2-2-2-2-211110022-1-122-1-10000−3i−3i3i3i0000−3i−3i3i3i0000000000000000000000
χ4344-4-44-24-4-42-2-424-222-2002-422-24-2-200000000000000000000000000000000000000
χ4444-4-4-244-42-442-4-2-222-200-42224-2-2-200000000000000000000000000000000000000
χ4544-4-4-2-24-422-222-21-1-110022-1-1-2-211000033-3-30000-3-3330000000000000000000000
χ4644-4-4-2-24-422-222-21-1-110022-1-1-2-2110000-3-333000033-3-30000000000000000000000
χ4744-4-4-2-2-4422-222-21-1-114i−4i-2-21122-1-1−2i−2i−2i−2iiiii2i2i2i2i−i−i−i−i0000000000000000000000
χ4844-4-4-2-2-4422-222-21-1-11−4i4i-2-21122-1-12i2i2i2i−i−i−i−i−2i−2i−2i−2iiiii0000000000000000000000
χ494-44-4440044-4-4-4-444-4-4000000000000000000000000000000000000000000000000
χ504-44-44-2004-22-42-4-2-2220000000000006−66−66−6006−66−66−60000000000000000000000
χ514-44-44-2004-22-42-4-2-222000000000000−66−66−6600−66−66−660000000000000000000000
χ524-44-4-2400-24-42-42-2-2220000000000i6−i600i6−i6−i6i6i6−i600i6−i6−i6i60000000000000000000000
χ534-44-4-2400-24-42-42-2-2220000000000−i6i600−i6i6i6−i6−i6i600−i6i6i6−i60000000000000000000000
χ544-44-4-2-200-2-2222211-1-100003i−3i003i−3ii6−i66−6−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23i6−i66−6−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ230000000000000000000000
χ554-44-4-2-200-2-2222211-1-100003i−3i003i−3i−i6i6−66ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−i6i6−66ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ230000000000000000000000
χ564-44-4-2-200-2-2222211-1-10000−3i3i00−3i3ii6−i6−66−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13i6−i6−66−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ130000000000000000000000
χ574-44-4-2-200-2-2222211-1-10000−3i3i00−3i3i−i6i66−6ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−i6i66−6ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ130000000000000000000000
χ584-4-444400-4-4-444-44-44-4000000000000000000000000000000000000000000000000
χ594-4-444-200-4224-2-4-22-22000000000000i6−i6i6−i6i6−i600−i6i6−i6i6−i6i60000000000000000000000
χ604-4-444-200-4224-2-4-22-22000000000000−i6i6−i6i6−i6i600i6−i6i6−i6i6−i60000000000000000000000
χ614-4-44-24002-4-4-242-22-2200000000006−6006−6−66−6600−666−60000000000000000000000
χ624-4-44-24002-4-4-242-22-220000000000−6600−666−66−6006−6−660000000000000000000000
χ634-4-44-2-200222-2-221-11-100003i−3i00−3i3i6−6−i6i6ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−66i6−i6−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ130000000000000000000000
χ644-4-44-2-200222-2-221-11-100003i−3i00−3i3i−66i6−i6−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ136−6−i6i6ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ130000000000000000000000
χ654-4-44-2-200222-2-221-11-10000−3i3i003i−3i6−6i6−i6−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23−66−i6i6ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ230000000000000000000000
χ664-4-44-2-200222-2-221-11-10000−3i3i003i−3i−66−i6i6ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ236−6i6−i6−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ230000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.