Finite Group Databasebeta

← Group #13138748

Character table — Group #13138748

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size111122222222224444446666666612121212121212121212121212121212121212121212121212121212181818183636363636363636363636363636363636367272727272727272
order12223446661212121288242424243366666636661212121212121212242424242424242424242424242424244444444444448812121212242424241212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-11111-1-1-1-111-1-111-1-1
χ611111111111111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-11111-1-1-1-1-1-111-1-111
χ711111111111111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-1-1-111
χ811111111111111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-11111-1-1
χ91-1-1111-11-1-111-1-11-111-1-111-1-11-1-111-1-11-1-1-1-1111111111111-1-1-1-1-1-1-1-1ii−i−ii−ii−i1-11-1i−iii−i−iii−i−ii−ii−i1-11-1
χ101-1-1111-11-1-111-1-11-111-1-111-1-11-1-111-1-11-1-1-1-1111111111111-1-1-1-1-1-1-1-1ii−i−i−ii−ii-11-11i−iii−i−iii−i−i−ii−ii-11-11
χ111-1-1111-11-1-111-1-11-111-1-111-1-11-1-111-1-11-1-1-1-1111111111111-1-1-1-1-1-1-1-1−i−iiii−ii−i-11-11−ii−i−iii−i−iiii−ii−i-11-11
χ121-1-1111-11-1-111-1-11-111-1-111-1-11-1-111-1-11-1-1-1-1111111111111-1-1-1-1-1-1-1-1−i−iii−ii−ii1-11-1−ii−i−iii−i−iii−ii−ii1-11-1
χ131-1-1111-11-1-111-1-1-11-1-11111-1-11-1-111-1-11-1-1-1-11111-1-1-1-1-1-1-1-111111111ii−i−ii−i−ii1-1-11−iiii−i−i−i−iiii−i−ii1-1-11
χ141-1-1111-11-1-111-1-1-11-1-11111-1-11-1-111-1-11-1-1-1-11111-1-1-1-1-1-1-1-111111111ii−i−i−iii−i-111-1−iiii−i−i−i−iii−iii−i-111-1
χ151-1-1111-11-1-111-1-1-11-1-11111-1-11-1-111-1-11-1-1-1-11111-1-1-1-1-1-1-1-111111111−i−iiii−i−ii-111-1i−i−i−iiiii−i−ii−i−ii-111-1
χ161-1-1111-11-1-111-1-1-11-1-11111-1-11-1-111-1-11-1-1-1-11111-1-1-1-1-1-1-1-111111111−i−iii−iii−i1-1-11i−i−i−iiiii−i−i−iii−i1-1-11
χ17222222222222222222222-122-1-1-12-1-1-1-1-12-1-1-12-1-122-1-1-1-1-1-122-1-1-1-1-1-10000222200000000000000-1-1-1-10000
χ18222222222222222222222-122-1-1-12-1-1-1-1-12-1-1-12-1-122-1-1-1-1-1-122-1-1-1-1-1-10000-2-2-2-20000000000000011110000
χ1922222222222222222222-12-1-1222-1-1-1-1-12-1-1-12-1-1-1-1-122-1-1-1-1-1-122-1-1-1-100000000222200000000000000-1-1-1-1
χ2022222222222222222222-12-1-1222-1-1-1-1-12-1-1-12-1-1-1-1-122-1-1-1-1-1-122-1-1-1-100000000-2-2-2-2000000000000001111
χ2122222222222222-2-2-2-2-2-22-122-1-1-12-1-1-1-1-12-1-1-12-1-1-2-2111111-2-2111111000022-2-200000000000000-1-1110000
χ2222222222222222-2-2-2-2-2-22-122-1-1-12-1-1-1-1-12-1-1-12-1-1-2-2111111-2-21111110000-2-2220000000000000011-1-10000
χ2322222222222222-2-2-2-2-2-2-12-1-1222-1-1-1-1-12-1-1-12-1-1-111-2-2111111-2-211110000000022-2-200000000000000-1-111
χ2422222222222222-2-2-2-2-2-2-12-1-1222-1-1-1-1-12-1-1-12-1-1-111-2-2111111-2-2111100000000-2-2220000000000000011-1-1
χ2522222-2-2222-2-2-2-2000000222222222222-2-2-2-2-2-2-2-200000000000000002-22-200000000002-22-2000000000000
χ2622222-2-2222-2-2-2-2000000222222222222-2-2-2-2-2-2-2-20000000000000000-22-220000000000-22-22000000000000
χ272-2-2222-22-2-222-2-22-222-2-22-1-2-2-1112-111-11-211-12-1-122-1-1-1-1-1-1-2-211111100002i−2i2i−2i00000000000000−ii−ii0000
χ282-2-2222-22-2-222-2-22-222-2-22-1-2-2-1112-111-11-211-12-1-122-1-1-1-1-1-1-2-21111110000−2i2i−2i2i00000000000000i−ii−i0000
χ292-2-2222-22-2-222-2-22-222-2-2-12112-2-2-1-111-1-21112-1-1-1-1-122-1-1-1-111-2-21111000000002-22-200000000000000-11-11
χ302-2-2222-22-2-222-2-22-222-2-2-12112-2-2-1-111-1-21112-1-1-1-1-122-1-1-1-111-2-2111100000000-22-22000000000000001-11-1
χ312-2-2222-22-2-222-2-2-22-2-2222-1-2-2-1112-111-11-211-12-1-1-2-211111122-1-1-1-1-1-100002i−2i−2i2i00000000000000−iii−i0000
χ322-2-2222-22-2-222-2-2-22-2-2222-1-2-2-1112-111-11-211-12-1-1-2-211111122-1-1-1-1-1-10000−2i2i2i−2i00000000000000i−i−ii0000
χ332-2-2222-22-2-222-2-2-22-2-222-12112-2-2-1-111-1-21112-1-1-111-2-21111-1-122-1-1-1-1000000002-2-2200000000000000-111-1
χ342-2-2222-22-2-222-2-2-22-2-222-12112-2-2-1-111-1-21112-1-1-111-2-21111-1-122-1-1-1-100000000-222-2000000000000001-1-11
χ352-2-222-222-2-2-2-22200000022-2-22-2-222-2-222222-2-2-2-200000000000000002i−2i−2i2i00000000002i−2i−2i2i000000000000
χ362-2-222-222-2-2-2-22200000022-2-22-2-222-2-222222-2-2-2-20000000000000000−2i2i2i−2i0000000000−2i2i2i−2i000000000000
χ3744444444444444444444-2-2-2-2-2-2-2-21111-2-211-2-211-2-2-2-21111-2-2-2-21111000000000000000000000000000000
χ3844444444444444-4-4-4-4-4-4-2-2-2-2-2-2-2-21111-2-211-2-2112222-1-1-1-12222-1-1-1-1000000000000000000000000000000
χ3944444-4-4444-4-4-4-40000004-244-2-2-24-2-2-2-22-4222-4220000000000000000000000000000000000000000000000
χ4044444-4-4444-4-4-4-4000000-24-2-2444-2-2-2-2-2-4222-42220000000000000000000000000000000000000000000000
χ4144444-4-4444-4-4-4-4000000-2-2-2-2-2-2-2-2111122-1-122-1-100003i3i−3i−3i00003i3i−3i−3i000000000000000000000000000000
χ4244444-4-4444-4-4-4-4000000-2-2-2-2-2-2-2-2111122-1-122-1-10000−3i−3i3i3i0000−3i−3i3i3i000000000000000000000000000000
χ4344-4-4400-44-40000000000444-4-44-4-444-4-4000000000000000000000000000000000000000000000000000000
χ4444-4-4400-44-400000000004-24-42-22-4-2-22200000000006−66−66−6006−66−66−6000000000000000000000000000000
χ4544-4-4400-44-400000000004-24-42-22-4-2-2220000000000−66−66−6600−66−66−66000000000000000000000000000000
χ4644-4-4400-44-40000000000-24-22-44-42-2-22200000000i6−i600i6−i6−i6i6i6−i600i6−i6−i6i6000000000000000000000000000000
χ4744-4-4400-44-40000000000-24-22-44-42-2-22200000000−i6i600−i6i6i6−i6−i6i600−i6i6i6−i6000000000000000000000000000000
χ4844-4-4400-44-40000000000-2-2-222-22211-1-1003i−3i003i−3ii6−i66−6−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23i6−i66−6−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23000000000000000000000000000000
χ4944-4-4400-44-40000000000-2-2-222-22211-1-1003i−3i003i−3i−i6i6−66ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23−i6i6−66ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23000000000000000000000000000000
χ5044-4-4400-44-40000000000-2-2-222-22211-1-100−3i3i00−3i3ii6−i6−66−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13i6−i6−66−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13000000000000000000000000000000
χ5144-4-4400-44-40000000000-2-2-222-22211-1-100−3i3i00−3i3i−i6i66−6ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13−i6i66−6ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13000000000000000000000000000000
χ524-44-4400-4-44000000000044-44-4-44-44-44-4000000000000000000000000000000000000000000000000000000
χ534-44-4400-4-4400000000004-2-4422-2-4-22-2200000000006−66−66−600−66−66−66000000000000000000000000000000
χ544-44-4400-4-4400000000004-2-4422-2-4-22-220000000000−66−66−66006−66−66−6000000000000000000000000000000
χ554-44-4400-4-440000000000-242-2-4-442-22-2200000000i6−i600i6−i6−i6i6−i6i600−i6i6i6−i6000000000000000000000000000000
χ564-44-4400-4-440000000000-242-2-4-442-22-2200000000−i6i600−i6i6i6−i6i6−i600i6−i6−i6i6000000000000000000000000000000
χ574-44-4400-4-440000000000-2-22-222-221-11-1003i−3i00−3i3ii6−i6−66−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−i6i66−6ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13000000000000000000000000000000
χ584-44-4400-4-440000000000-2-22-222-221-11-1003i−3i00−3i3i−i6i66−6ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13i6−i6−66−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13000000000000000000000000000000
χ594-44-4400-4-440000000000-2-22-222-221-11-100−3i3i003i−3ii6−i66−6−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−i6i6−66ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23000000000000000000000000000000
χ604-44-4400-4-440000000000-2-22-222-221-11-100−3i3i003i−3i−i6i6−66ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23i6−i66−6−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23000000000000000000000000000000
χ614-4-4444-44-4-444-4-44-444-4-4-2-222-222-21-1-1122-1-1-2-211-2-2-2-211112222-1-1-1-1000000000000000000000000000000
χ624-4-4444-44-4-444-4-4-44-4-444-2-222-222-21-1-1122-1-1-2-2112222-1-1-1-1-2-2-2-21111000000000000000000000000000000
χ634-4-444-444-4-4-4-4440000004-2-4-4-2224-222-2-24-2-22-4220000000000000000000000000000000000000000000000
χ644-4-444-444-4-4-4-444000000-24224-4-4-2-222-24-2-2-2-42220000000000000000000000000000000000000000000000
χ654-4-444-444-4-4-4-444000000-2-222-222-21-1-11-2-21122-1-100003i3i−3i−3i0000−3i−3i3i3i000000000000000000000000000000
χ664-4-444-444-4-4-4-444000000-2-222-222-21-1-11-2-21122-1-10000−3i−3i3i3i00003i3i−3i−3i000000000000000000000000000000
χ676666-366-3-3-3-3-3-3-366-3-3-3-300000000000000000000000000000000000022220000000022-1-1-1-1-1-1-1-100000000
χ686666-366-3-3-3-3-3-3-366-3-3-3-3000000000000000000000000000000000000-2-2-2-200000000-2-21111111100000000
χ696666-366-3-3-3-3-3-3-3-6-63333000000000000000000000000000000000000222200000000-2-2-1-1-1-1111100000000
χ706666-366-3-3-3-3-3-3-3-6-63333000000000000000000000000000000000000-2-2-2-200000000221111-1-1-1-100000000
χ716666-3-6-6-3-3-333330033−3333−330000000000000000000000000000000000002-22-20000000000-11-113−33−300000000
χ726666-3-6-6-3-3-333330033−3333−33000000000000000000000000000000000000-22-2200000000001-11-1−33−3300000000
χ736666-3-6-6-3-3-3333300−3333−33330000000000000000000000000000000000002-22-20000000000-11-11−33−3300000000
χ746666-3-6-6-3-3-3333300−3333−3333000000000000000000000000000000000000-22-2200000000001-11-13−33−300000000
χ756-6-66-36-6-333-3-3336-6-3-3330000000000000000000000000000000000002i2i−2i−2i000000002i−2i−i−iii−i−iii00000000
χ766-6-66-36-6-333-3-3336-6-3-333000000000000000000000000000000000000−2i−2i2i2i00000000−2i2iii−i−iii−i−i00000000
χ776-6-66-36-6-333-3-333-6633-3-30000000000000000000000000000000000002i2i−2i−2i00000000−2i2i−i−iiiii−i−i00000000
χ786-6-66-36-6-333-3-333-6633-3-3000000000000000000000000000000000000−2i−2i2i2i000000002i−2iii−i−i−i−iii00000000
χ796-6-66-3-66-33333-3-30033−33−33330000000000000000000000000000000000002i−2i−2i2i0000000000−iii−ii3−i3−i3i300000000
χ806-6-66-3-66-33333-3-30033−33−3333000000000000000000000000000000000000−2i2i2i−2i0000000000i−i−ii−i3i3i3−i300000000
χ816-6-66-3-66-33333-3-300−333333−330000000000000000000000000000000000002i−2i−2i2i0000000000−iii−i−i3i3i3−i300000000
χ826-6-66-3-66-33333-3-300−333333−33000000000000000000000000000000000000−2i2i2i−2i0000000000i−i−iii3−i3−i3i300000000
χ831212-12-12-6006-6663−6363−63000000000000000000000000000000000000000000000000000000000000000000000000
χ841212-12-12-6006-66−6363−6363000000000000000000000000000000000000000000000000000000000000000000000000
χ8512-1212-12-60066-663−63−6363000000000000000000000000000000000000000000000000000000000000000000000000
χ8612-1212-12-60066-6−636363−63000000000000000000000000000000000000000000000000000000000000000000000000

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