Finite Group Databasebeta

← Group #10590691

Character table — Group #10590691

Order 576.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size1111222222222244444444444444444444444444444412121212121212121818181824242424242424243636
order12223344666666366688121212121212121224242424242424242424242424242424444444442244121212121212121288
χ1111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-111-1-111-1-1-1-1
χ311111111111111111111111111111111111111111111-1-111-1-111-1-1-1-1-1-111-1-111-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111
χ5111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1
χ6111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-111-1-1-1-11111
χ7111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111
χ8111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1
χ91-1-11111-1-1-1-1-1111-1-11i−i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−ii−ii−i1-11-11-11-1i−ii−i1-11-1i−i
χ101-1-11111-1-1-1-1-1111-1-11i−i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−ii−i−ii1-1-11-11-11i−i−ii1-1-11−ii
χ111-1-11111-1-1-1-1-1111-1-11i−i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i−iii−i-111-1-11-11−iii−i-111-1−ii
χ121-1-11111-1-1-1-1-1111-1-11i−i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i−ii−ii-11-111-11-1−ii−ii-11-11i−i
χ131-1-11111-1-1-1-1-1111-1-11−ii1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiiii−ii−i-11-111-11-1i−ii−i-11-11−ii
χ141-1-11111-1-1-1-1-1111-1-11−ii1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiiii−i−ii-111-1-11-11i−i−ii-111-1i−i
χ151-1-11111-1-1-1-1-1111-1-11−ii1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii−iii−i1-1-11-11-11−iii−i1-1-11i−i
χ161-1-11111-1-1-1-1-1111-1-11−ii1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii−ii−ii1-11-11-11-1−ii−ii1-11-1−ii
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
χ1922222-1222-12-12-1-1-1-1-1222-1-1-12-1-1-122-1-1-1-1-1-122-1-1-1-1-1-100220022000000-1-100-1-100
χ2022222-1222-12-12-1-1-1-1-1222-1-1-12-1-1-122-1-1-1-1-1-122-1-1-1-1-1-100-2-200-2-200000011001100
χ2122222-1222-12-12-1-1-1-1-1-2-22-1-1-12-1-1-1-2-2111111-2-2111111002200-2-2000000-1-1001100
χ2222222-1222-12-12-1-1-1-1-1-2-22-1-1-12-1-1-1-2-2111111-2-211111100-2-200220000001100-1-100
χ232222-1222-12-12-12-1-1-1-122-12-1-1-12-1-1-1-122-1-1-1-1-1-122-1-1-1-1220022000000-1-100-1-10000
χ242222-1222-12-12-12-1-1-1-122-12-1-1-12-1-1-1-122-1-1-1-1-1-122-1-1-1-1-2-200-2-20000001100110000
χ252222-1222-12-12-12-1-1-1-1-2-2-12-1-1-12-1-111-2-2111111-2-211112200-2-2000000-1-100110000
χ262222-1222-12-12-12-1-1-1-1-2-2-12-1-1-12-1-111-2-2111111-2-21111-2-200220000001100-1-10000
χ272-2-2222-22-2-2-2-2222-2-2200-2-2-2-222220000000000000000000000002-2-220000000000
χ282-2-2222-22-2-2-2-2222-2-2200-2-2-2-22222000000000000000000000000-222-20000000000
χ292-2-222-12-2-21-212-1-111-12i−2i2-1-1-1-21112i2i−i−i−i−i−i−i−2i−2iiiiiii002i−2i002-2000000−ii00-1100
χ302-2-222-12-2-21-212-1-111-12i−2i2-1-1-1-21112i2i−i−i−i−i−i−i−2i−2iiiiiii00−2i2i00-22000000i−i001-100
χ312-2-222-12-2-21-212-1-111-1−2i2i2-1-1-1-2111−2i−2iiiiiii2i2i−i−i−i−i−i−i002i−2i00-22000000−ii001-100
χ322-2-222-12-2-21-212-1-111-1−2i2i2-1-1-1-2111−2i−2iiiiiii2i2i−i−i−i−i−i−i00−2i2i002-2000000i−i00-1100
χ332-2-22-122-21-21-2-12-111-12i−2i-12-1-11-211−i−i2i2i−i−i−i−iii−2i−2iiiii2i−2i002-2000000−ii00-110000
χ342-2-22-122-21-21-2-12-111-12i−2i-12-1-11-211−i−i2i2i−i−i−i−iii−2i−2iiiii−2i2i00-22000000i−i001-10000
χ352-2-22-122-21-21-2-12-111-1−2i2i-12-1-11-211ii−2i−2iiiii−i−i2i2i−i−i−i−i2i−2i00-22000000−ii001-10000
χ362-2-22-122-21-21-2-12-111-1−2i2i-12-1-11-211ii−2i−2iiiii−i−i2i2i−i−i−i−i−2i2i002-2000000i−i00-110000
χ3744444-2-4-44-24-24-2-2-2-2-200-4222-422200000000000000000000000000000000000000
χ384444-24-4-4-24-24-24-2-2-2-2002-4222-42200000000000000000000000000000000000000
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
χ4344-4-444004-4-44-4-444-4-4000000000000000000000000000000000000000000000000
χ4444-4-44-20042-4-2-42-2-2220000000000006−66−66−6006−66−66−60000000000000000000000
χ4544-4-44-20042-4-2-42-2-222000000000000−66−66−6600−66−66−660000000000000000000000
χ4644-4-4-2400-2-4242-4-2-2220000000000i6−i600i6−i6−i6i6i6−i600i6−i6−i6i60000000000000000000000
χ4744-4-4-2400-2-4242-4-2-2220000000000−i6i600−i6i6i6−i6−i6i600−i6i6i6−i60000000000000000000000
χ4844-4-4-2-200-222-22211-1-100003i−3i003i−3ii6−i66−6−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23i6−i66−6−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ230000000000000000000000
χ4944-4-4-2-200-222-22211-1-100003i−3i003i−3i−i6i6−66ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−i6i6−66ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ230000000000000000000000
χ5044-4-4-2-200-222-22211-1-10000−3i3i00−3i3ii6−i6−66−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13i6−i6−66−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ130000000000000000000000
χ5144-4-4-2-200-222-22211-1-10000−3i3i00−3i3i−i6i66−6ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−i6i66−6ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ130000000000000000000000
χ524-44-44400-444-4-4-44-44-4000000000000000000000000000000000000000000000000
χ534-44-44-200-4-242-42-22-22000000000000i6−i6i6−i6i6−i600−i6i6−i6i6−i6i60000000000000000000000
χ544-44-44-200-4-242-42-22-22000000000000−i6i6−i6i6−i6i600i6−i6i6−i6i6−i60000000000000000000000
χ554-44-4-240024-2-42-4-22-2200000000006−6006−6−66−6600−666−60000000000000000000000
χ564-44-4-240024-2-42-4-22-220000000000−6600−666−66−6006−6−660000000000000000000000
χ574-44-4-2-2002-2-22221-11-100003i−3i00−3i3i6−6−i6i6ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13−66i6−i6−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ130000000000000000000000
χ584-44-4-2-2002-2-22221-11-100003i−3i00−3i3i−66i6−i6−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ136−6−i6i6ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ130000000000000000000000
χ594-44-4-2-2002-2-22221-11-10000−3i3i003i−3i6−6i6−i6−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23−66−i6i6ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ230000000000000000000000
χ604-44-4-2-2002-2-22221-11-10000−3i3i003i−3i−66−i6i6ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ236−6i6−i6−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ230000000000000000000000
χ614-4-444-2-44-42-424-2-222-200-42224-2-2-200000000000000000000000000000000000000
χ624-4-44-24-442-42-4-24-222-2002-422-24-2-200000000000000000000000000000000000000
χ634-4-44-2-24-42222-2-21-1-114i−4i-2-21122-1-1−2i−2i−2i−2iiiii2i2i2i2i−i−i−i−i0000000000000000000000
χ644-4-44-2-24-42222-2-21-1-11−4i4i-2-21122-1-12i2i2i2i−i−i−i−i−2i−2i−2i−2iiiii0000000000000000000000
χ654-4-44-2-2-442222-2-21-1-110022-1-1-2-211000033-3-30000-3-3330000000000000000000000
χ664-4-44-2-2-442222-2-21-1-110022-1-1-2-2110000-3-333000033-3-30000000000000000000000

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