Finite Group Databasebeta

← Group #13138873

Character table — Group #13138873

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size111122222222224444446666666612121212121212121212121212121212121212121212121212121212181818183636363636363636363636363636363636367272727272727272
order1222344666121212128824242424336666663666121212121212121224242424242424242424242424242424444422224444881212121224242424666612121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1
χ411111111111111111111111111111111111111111111111111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-111
χ511111111111111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-11111-1-1-1-111-1-1-1-111
χ611111111111111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-1-1-11111-1-1
χ711111111111111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111111111-1-1-1-1
χ811111111111111-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-11111
χ911-1-11-111-1-1-1-111i−iii−i−i11-1-111-1-11-1-111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−iii−i−i1-11-1i−ii−i1-1ii−i−i11-1-11-11-1i−ii−i
χ1011-1-11-111-1-1-1-111i−iii−i−i11-1-111-1-11-1-111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−iii−i−i-11-11−ii−ii1-1ii−i−i11-1-1-11-11−ii−ii
χ1111-1-11-111-1-1-1-111i−iii−i−i11-1-111-1-11-1-111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−iii1-1-11i−i−ii-11−i−iii-1-1111-1-11i−i−ii
χ1211-1-11-111-1-1-1-111i−iii−i−i11-1-111-1-11-1-111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−iii-111-1−iii−i-11−i−iii-1-111-111-1−iii−i
χ1311-1-11-111-1-1-1-111−ii−i−iii11-1-111-1-11-1-111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiiiii−i−i1-1-11−iii−i-11ii−i−i-1-1111-1-11−iii−i
χ1411-1-11-111-1-1-1-111−ii−i−iii11-1-111-1-11-1-111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiiiii−i−i-111-1i−i−ii-11ii−i−i-1-111-111-1i−i−ii
χ1511-1-11-111-1-1-1-111−ii−i−iii11-1-111-1-11-1-111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−iii1-11-1−ii−ii1-1−i−iii11-1-11-11-1−ii−ii
χ1611-1-11-111-1-1-1-111−ii−i−iii11-1-111-1-11-1-111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−iii-11-11i−ii−i1-1−i−iii11-1-1-11-11i−ii−i
χ17222222222222222222222-12-12-12-1-1-1-1-12-1-1-12-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1000000220022000000000000-1-100-1-1
χ18222222222222222222222-12-12-12-1-1-1-1-12-1-1-12-1-1-122-1-1-1-1-1-122-1-1-1-1-1-1000000-2-200-2-2000000000000110011
χ1922222222222222222222-12-12-12-12-1-1-1-1-12-1-1-12-1-1-1-122-1-1-1-1-1-122-1-1-1-10000220022000000000000-1-100-1-100
χ2022222222222222222222-12-12-12-12-1-1-1-1-12-1-1-12-1-1-1-122-1-1-1-1-1-122-1-1-1-10000-2-200-2-200000000000011001100
χ2122222222222222-2-2-2-2-2-22-12-12-12-1-1-1-1-12-1-1-12-1-1-1-2-2111111-2-21111110000002200-2-2000000000000-1-10011
χ2222222222222222-2-2-2-2-2-22-12-12-12-1-1-1-1-12-1-1-12-1-1-1-2-2111111-2-2111111000000-2-200220000000000001100-1-1
χ2322222222222222-2-2-2-2-2-2-12-12-12-12-1-1-1-1-12-1-1-12-1-111-2-2111111-2-2111100002200-2-2000000000000-1-1001100
χ2422222222222222-2-2-2-2-2-2-12-12-12-12-1-1-1-1-12-1-1-12-1-111-2-2111111-2-211110000-2-200220000000000001100-1-100
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
χ2722-2-222-22-2-222-2-200000022-2-222-2-22-2-22-2-2-2-2222200000000000000002i−2i−2i2i00000000002i−2i−2i2i000000000000
χ2822-2-222-22-2-222-2-200000022-2-222-2-22-2-22-2-2-2-222220000000000000000−2i2i2i−2i0000000000−2i2i2i−2i000000000000
χ2922-2-22-222-2-2-2-2222i−2i2i2i−2i−2i2-1-212-1-21-111-12-1-1-1-21112i2i−i−i−i−i−i−i−2i−2iiiiiii0000002-2002i−2i000000000000-1100−ii
χ3022-2-22-222-2-2-2-2222i−2i2i2i−2i−2i2-1-212-1-21-111-12-1-1-1-21112i2i−i−i−i−i−i−i−2i−2iiiiiii000000-2200−2i2i0000000000001-100i−i
χ3122-2-22-222-2-2-2-2222i−2i2i2i−2i−2i-121-2-121-2-111-1-12-1-11-211−i−i2i2i−i−i−i−iii−2i−2iiiii00002-2002i−2i000000000000-1100−ii00
χ3222-2-22-222-2-2-2-2222i−2i2i2i−2i−2i-121-2-121-2-111-1-12-1-11-211−i−i2i2i−i−i−i−iii−2i−2iiiii0000-2200−2i2i0000000000001-100i−i00
χ3322-2-22-222-2-2-2-222−2i2i−2i−2i2i2i2-1-212-1-21-111-12-1-1-1-2111−2i−2iiiiiii2i2i−i−i−i−i−i−i0000002-200−2i2i000000000000-1100i−i
χ3422-2-22-222-2-2-2-222−2i2i−2i−2i2i2i2-1-212-1-21-111-12-1-1-1-2111−2i−2iiiiiii2i2i−i−i−i−i−i−i000000-22002i−2i0000000000001-100−ii
χ3522-2-22-222-2-2-2-222−2i2i−2i−2i2i2i-121-2-121-2-111-1-12-1-11-211ii−2i−2iiiii−i−i2i2i−i−i−i−i00002-200−2i2i000000000000-1100i−i00
χ3622-2-22-222-2-2-2-222−2i2i−2i−2i2i2i-121-2-121-2-111-1-12-1-11-211ii−2i−2iiiii−i−i2i2i−i−i−i−i0000-22002i−2i0000000000001-100−ii00
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
χ3944444-4-4444-4-4-4-40000004-24-24-24-2-2-2-2-2-4222-42220000000000000000000000000000000000000000000000
χ4044444-4-4444-4-4-4-4000000-24-24-24-24-2-2-2-22-4222-4220000000000000000000000000000000000000000000000
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
χ4344-4-444-44-4-444-4-40000004-2-424-2-42-222-2-42224-2-2-20000000000000000000000000000000000000000000000
χ4444-4-444-44-4-444-4-4000000-242-4-242-4-222-22-422-24-2-20000000000000000000000000000000000000000000000
χ4544-4-444-44-4-444-4-4000000-2-222-2-2221-1-1122-1-1-2-211000033-3-30000-3-333000000000000000000000000000000
χ4644-4-444-44-4-444-4-4000000-2-222-2-2221-1-1122-1-1-2-2110000-3-333000033-3-3000000000000000000000000000000
χ4744-4-44-444-4-4-4-4444i−4i4i4i−4i−4i-2-222-2-2221-1-11-2-21122-1-1−2i−2i−2i−2iiiii2i2i2i2i−i−i−i−i000000000000000000000000000000
χ4844-4-44-444-4-4-4-444−4i4i−4i−4i4i4i-2-222-2-2221-1-11-2-21122-1-12i2i2i2i−i−i−i−i−2i−2i−2i−2iiiii000000000000000000000000000000
χ494-44-4400-44-40000000000444-4-4-4-4444-4-4000000000000000000000000000000000000000000000000000000
χ504-44-4400-44-400000000004-242-42-4-2-2-2220000000000i6−i6i6−i6i6−i600i6−i6i6−i6i6−i6000000000000000000000000000000
χ514-44-4400-44-400000000004-242-42-4-2-2-2220000000000−i6i6−i6i6−i6i600−i6i6−i6i6−i6i6000000000000000000000000000000
χ524-44-4400-44-40000000000-24-2-42-424-2-222000000006−6006−6−666−6006−6−66000000000000000000000000000000
χ534-44-4400-44-40000000000-24-2-42-424-2-22200000000−6600−666−6−6600−666−6000000000000000000000000000000
χ544-44-4400-44-40000000000-2-2-22222-211-1-1003i−3i003i−3i6−6i6−i6−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ236−6i6−i6−ζ5+ζ13ζ5−ζ13−ζ7+ζ23ζ7−ζ23000000000000000000000000000000
χ554-44-4400-44-40000000000-2-2-22222-211-1-1003i−3i003i−3i−66−i6i6ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23−66−i6i6ζ5−ζ13−ζ5+ζ13ζ7−ζ23−ζ7+ζ23000000000000000000000000000000
χ564-44-4400-44-40000000000-2-2-22222-211-1-100−3i3i00−3i3i6−6−i6i6ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ136−6−i6i6ζ7−ζ23−ζ7+ζ23ζ5−ζ13−ζ5+ζ13000000000000000000000000000000
χ574-44-4400-44-40000000000-2-2-22222-211-1-100−3i3i00−3i3i−66i6−i6−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13−66i6−i6−ζ7+ζ23ζ7−ζ23−ζ5+ζ13ζ5−ζ13000000000000000000000000000000
χ584-4-44400-4-44000000000044-44-4-44-44-44-4000000000000000000000000000000000000000000000000000000
χ594-4-44400-4-4400000000004-2-4-2-4242-22-2200000000006−66−66−600−66−66−66000000000000000000000000000000
χ604-4-44400-4-4400000000004-2-4-2-4242-22-220000000000−66−66−66006−66−66−6000000000000000000000000000000
χ614-4-44400-4-440000000000-24242-4-2-4-22-2200000000i6−i600i6−i6−i6i6−i6i600−i6i6i6−i6000000000000000000000000000000
χ624-4-44400-4-440000000000-24242-4-2-4-22-2200000000−i6i600−i6i6i6−i6i6−i600i6−i6−i6i6000000000000000000000000000000
χ634-4-44400-4-440000000000-2-22-222-221-11-1003i−3i00−3i3ii6−i6−66−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13−i6i66−6ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13000000000000000000000000000000
χ644-4-44400-4-440000000000-2-22-222-221-11-1003i−3i00−3i3i−i6i66−6ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ13i6−i6−66−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ13000000000000000000000000000000
χ654-4-44400-4-440000000000-2-22-222-221-11-100−3i3i003i−3ii6−i66−6−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23−i6i6−66ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23000000000000000000000000000000
χ664-4-44400-4-440000000000-2-22-222-221-11-100−3i3i003i−3i−i6i6−66ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23i6−i66−6−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23000000000000000000000000000000
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
χ7566-6-6-36-6-333-3-33300−3i33i33i3−3i30000000000000000000000000000000000002i−2i−2i2i0000000000−iii−i−333−300000000
χ7666-6-6-36-6-333-3-33300−3i33i33i3−3i3000000000000000000000000000000000000−2i2i2i−2i0000000000i−i−ii3−3−3300000000
χ7766-6-6-36-6-333-3-333003i3−3i3−3i33i30000000000000000000000000000000000002i−2i−2i2i0000000000−iii−i3−3−3300000000
χ7866-6-6-36-6-333-3-333003i3−3i3−3i33i3000000000000000000000000000000000000−2i2i2i−2i0000000000i−i−ii−333−300000000
χ7966-6-6-3-66-33333-3-36i−6i−3i−3i3i3i0000000000000000000000000000000000002i2i−2i−2i000000002-2−i−iii-1-11100000000
χ8066-6-6-3-66-33333-3-36i−6i−3i−3i3i3i000000000000000000000000000000000000−2i−2i2i2i00000000-22ii−i−i11-1-100000000
χ8166-6-6-3-66-33333-3-3−6i6i3i3i−3i−3i0000000000000000000000000000000000002i2i−2i−2i00000000-22−i−iii11-1-100000000
χ8266-6-6-3-66-33333-3-3−6i6i3i3i−3i−3i000000000000000000000000000000000000−2i−2i2i2i000000002-2ii−i−i-1-11100000000
χ8312-1212-12-6006-6663−6363−63000000000000000000000000000000000000000000000000000000000000000000000000
χ8412-1212-12-6006-66−6363−6363000000000000000000000000000000000000000000000000000000000000000000000000
χ8512-12-1212-60066-663−63−6363000000000000000000000000000000000000000000000000000000000000000000000000
χ8612-12-1212-60066-6−636363−63000000000000000000000000000000000000000000000000000000000000000000000000

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