Finite Group Databasebeta

← Group #13167374

Character table — Group #13167374

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84
size111122222244444444444444888888888888888888181818181818181836363636363636363636363636363636363636363636363636363636363672727272
order12443688121233661212121224242424242433661212121224242424242424242424246688121222444466888888121212121212242424242424242424246122424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111-11-1-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111-11-11-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111
χ411111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-1
χ5111111-1-11111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1
χ6111111-1-11111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1111-11-11111-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111
χ7111111-1-11111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-111-11-1111-1-111-1-1-1-1-1-11111-1-11111-1-1-1-111-1-1
χ8111111-1-11111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-111
χ911-1-111i−i-1-11111-1-1-1-1i−iii−i−i1111-1-1-1-1i−iiiii−i−i−i−i-11-1-1i−i1111-1-1i−i11i−ii−i1-1-1-1ii−i−ii−iii−i−i11-1-11-1i−i
χ1011-1-111i−i-1-11111-1-1-1-1i−iii−i−i1111-1-1-1-1i−iiiii−i−i−i−i-11-1-1i−i111-1-11−ii11i−i−ii-11-1-1−i−iiii−iii−i−i-1-111-11−ii
χ1111-1-111i−i-1-11111-1-1-1-1i−iii−i−i1111-1-1-1-1i−iiiii−i−i−i−i-11-1-1i−i11-111-1−ii-1-1−iii−i-1111−i−iiii−i−i−iii-1-1111-1i−i
χ1211-1-111i−i-1-11111-1-1-1-1i−iii−i−i1111-1-1-1-1i−iiiii−i−i−i−i-11-1-1i−i11-1-111i−i-1-1−ii−ii1-111ii−i−ii−i−i−iii11-1-1-11−ii
χ1311-1-111−ii-1-11111-1-1-1-1−ii−i−iii1111-1-1-1-1−ii−i−i−i−iiiii-11-1-1−ii1111-1-1−ii11−ii−ii1-1-1-1−i−iii−ii−i−iii11-1-11-1−ii
χ1411-1-111−ii-1-11111-1-1-1-1−ii−i−iii1111-1-1-1-1−ii−i−i−i−iiiii-11-1-1−ii111-1-11i−i11−iii−i-11-1-1ii−i−i−ii−i−iii-1-111-11i−i
χ1511-1-111−ii-1-11111-1-1-1-1−ii−i−iii1111-1-1-1-1−ii−i−i−i−iiiii-11-1-1−ii11-111-1i−i-1-1i−i−ii-1111ii−i−i−iiii−i−i-1-1111-1−ii
χ1611-1-111−ii-1-11111-1-1-1-1−ii−i−iii1111-1-1-1-1−ii−i−i−i−iiiii-11-1-1−ii11-1-111−ii-1-1i−ii−i1-111−i−iii−iiii−i−i11-1-1-11i−i
χ17222222222222222222222222222222222222222222-2-2-2-2-2-2-2-200000000000000000000-2-2000000000000
χ18222222-2-22222222222-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-222-2-20000000000000000000022000000000000
χ192222-1-122-1-122222222-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-122-1-10000220000002200-1-1-1-1-1-10000-1-1-1-10000
χ202222-1-122-1-122222222-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-122-1-10000-2-2000000-2-2001111-1-1000011110000
χ212222-1-122-1-122222222-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-211-2-21100000000000000003−33−31100003−33−30000
χ222222-1-122-1-122222222-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-211-2-2110000000000000000−33−33110000−33−330000
χ232222-1-1-2-2-1-12222222211-2-2-2-2-1-1-1-1-1-1-1-1-2-21111111122-1-1-2-2-1-1000022000000-2-200-1-1-1-111000011110000
χ242222-1-1-2-2-1-12222222211-2-2-2-2-1-1-1-1-1-1-1-1-2-21111111122-1-1-2-2-1-10000-2-200000022001111110000-1-1-1-10000
χ252222-1-1-2-2-1-12222222211-2-2-2-2-1-1-1-1-1-1-1-1-2-211111111-2-211221100000000000000003−33−3-1-10000−33−330000
χ262222-1-1-2-2-1-12222222211-2-2-2-2-1-1-1-1-1-1-1-1-2-211111111-2-21122110000000000000000−33−33-1-100003−33−30000
χ2722-2-2222i−2i-2-22222-2-2-2-22i−2i2i2i−2i−2i2222-2-2-2-22i−2i2i2i2i2i−2i−2i−2i−2i2-222−2i2i-2-200000000000000000000−2i2i000000000000
χ2822-2-222−2i2i-2-22222-2-2-2-2−2i2i−2i−2i2i2i2222-2-2-2-2−2i2i−2i−2i−2i−2i2i2i2i2i2-2222i−2i-2-2000000000000000000002i−2i000000000000
χ2922-2-2-1-12i−2i112222-2-2-2-2−ii2i2i−2i−2i-1-1-1-111112i−2i−i−i−i−iiiii2-2-1-1−2i2i110000000000000000−i3i3i3−i3i−i0000−333−30000
χ3022-2-2-1-12i−2i112222-2-2-2-2−ii2i2i−2i−2i-1-1-1-111112i−2i−i−i−i−iiiii2-2-1-1−2i2i110000000000000000i3−i3−i3i3i−i00003−3−330000
χ3122-2-2-1-12i−2i112222-2-2-2-2−ii2i2i−2i−2i-1-1-1-111112i−2i−i−i−i−iiiii-22112i−2i-1-100002i−2i0000002-200−i−iii−ii0000-1-1110000
χ3222-2-2-1-12i−2i112222-2-2-2-2−ii2i2i−2i−2i-1-1-1-111112i−2i−i−i−i−iiiii-22112i−2i-1-10000−2i2i000000-2200ii−i−i−ii000011-1-10000
χ3322-2-2-1-1−2i2i112222-2-2-2-2i−i−2i−2i2i2i-1-1-1-11111−2i2iiiii−i−i−i−i2-2-1-12i−2i110000000000000000−i3i3i3−i3−ii00003−3−330000
χ3422-2-2-1-1−2i2i112222-2-2-2-2i−i−2i−2i2i2i-1-1-1-11111−2i2iiiii−i−i−i−i2-2-1-12i−2i110000000000000000i3−i3−i3i3−ii0000−333−30000
χ3522-2-2-1-1−2i2i112222-2-2-2-2i−i−2i−2i2i2i-1-1-1-11111−2i2iiiii−i−i−i−i-2211−2i2i-1-100002i−2i000000-2200−i−iiii−i000011-1-10000
χ3622-2-2-1-1−2i2i112222-2-2-2-2i−i−2i−2i2i2i-1-1-1-11111−2i2iiiii−i−i−i−i-2211−2i2i-1-10000−2i2i0000002-200ii−i−ii−i0000-1-1110000
χ3744444444441-21-211-2-24411111-21-211-2-2-2-211-2-211-2-200000000202000-1-1220000-1-1000000-1-1-1-100000000
χ3844444444441-21-211-2-24411111-21-211-2-2-2-211-2-211-2-200000000-20-200011-2-2000011000000111100000000
χ394444444444-21-21-2-21144-2-2-2-2-21-21-2-21111-2-211-2-21100000000020200000022000000000000000000-1-1-1-1
χ404444444444-21-21-2-21144-2-2-2-2-21-21-2-21111-2-211-2-211000000000-20-2000000-2-20000000000000000001111
χ41444444-4-4441-21-211-2-2-4-4-1-1-1-11-21-211-2-222-1-122-1-12200000000202000-1-1-2-20000-1-1000000111100000000
χ42444444-4-4441-21-211-2-2-4-4-1-1-1-11-21-211-2-222-1-122-1-12200000000-20-20001122000011000000-1-1-1-100000000
χ43444444-4-444-21-21-2-211-4-42222-21-21-2-211-1-122-1-122-1-1000000000202000000-2-2000000000000000000-1-111
χ44444444-4-444-21-21-2-211-4-42222-21-21-2-211-1-122-1-122-1-1000000000-20-20000002200000000000000000011-1-1
χ4544-4-4444i−4i-4-41-21-2-1-1224i−4iii−i−i1-21-2-1-122−2i2iii−2i−2i−i−i2i2i0000000020-2000-1-12i−2i000011000000−i−iii00000000
χ4644-4-4444i−4i-4-41-21-2-1-1224i−4iii−i−i1-21-2-1-122−2i2iii−2i−2i−i−i2i2i00000000-20200011−2i2i0000-1-1000000ii−i−i00000000
χ4744-4-4444i−4i-4-4-21-2122-1-14i−4i−2i−2i2i2i-21-2122-1-1i−i−2i−2iii2i2i−i−i00000000020-20000002i−2i000000000000000000-11−ii
χ4844-4-4444i−4i-4-4-21-2122-1-14i−4i−2i−2i2i2i-21-2122-1-1i−i−2i−2iii2i2i−i−i000000000-202000000−2i2i0000000000000000001-1i−i
χ4944-4-444−4i4i-4-41-21-2-1-122−4i4i−i−iii1-21-2-1-1222i−2i−i−i2i2iii−2i−2i0000000020-2000-1-1−2i2i000011000000ii−i−i00000000
χ5044-4-444−4i4i-4-41-21-2-1-122−4i4i−i−iii1-21-2-1-1222i−2i−i−i2i2iii−2i−2i00000000-202000112i−2i0000-1-1000000−i−iii00000000
χ5144-4-444−4i4i-4-4-21-2122-1-1−4i4i2i2i−2i−2i-21-2122-1-1−ii2i2i−i−i−2i−2iii00000000020-2000000−2i2i000000000000000000-11i−i
χ5244-4-444−4i4i-4-4-21-2122-1-1−4i4i2i2i−2i−2i-21-2122-1-1−ii2i2i−i−i−2i−2iii000000000-2020000002i−2i0000000000000000001-1−ii
χ534-44i−4i4-4004i−4i1-2-12i−i2i−2i003ζ7+3ζ23−3ζ7−3ζ23−3ζ5−3ζ133ζ5+3ζ131-2-12i−i2i−2i003ζ7+3ζ23−3ζ7−3ζ2300−3ζ5−3ζ133ζ5+3ζ130000000000000000−i3i30000003−3000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ1300000000
χ544-44i−4i4-4004i−4i1-2-12i−i2i−2i003ζ7+3ζ23−3ζ7−3ζ23−3ζ5−3ζ133ζ5+3ζ131-2-12i−i2i−2i003ζ7+3ζ23−3ζ7−3ζ2300−3ζ5−3ζ133ζ5+3ζ130000000000000000i3−i3000000−33000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ1300000000
χ554-44i−4i4-4004i−4i1-2-12i−i2i−2i00−3ζ7−3ζ233ζ7+3ζ233ζ5+3ζ13−3ζ5−3ζ131-2-12i−i2i−2i00−3ζ7−3ζ233ζ7+3ζ23003ζ5+3ζ13−3ζ5−3ζ130000000000000000−i3i30000003−3000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ1300000000
χ564-44i−4i4-4004i−4i1-2-12i−i2i−2i00−3ζ7−3ζ233ζ7+3ζ233ζ5+3ζ13−3ζ5−3ζ131-2-12i−i2i−2i00−3ζ7−3ζ233ζ7+3ζ23003ζ5+3ζ13−3ζ5−3ζ130000000000000000i3−i3000000−33000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ1300000000
χ574-44i−4i4-4004i−4i44-4-44i−4i−4i4i00000044-4-44i−4i−4i4i0000000000000000000000000000000000000000000000000000
χ584-44i−4i-2200−2i2i44-4-44i−4i−4i4i000000-2-222−2i2i2i−2i000000000000−2i32i30023−230000000000000000000000000000000000
χ594-44i−4i-2200−2i2i44-4-44i−4i−4i4i000000-2-222−2i2i2i−2i0000000000002i3−2i300−23230000000000000000000000000000000000
χ604-4−4i4i4-400−4i4i1-2-12−ii−2i2i00−3ζ5−3ζ133ζ5+3ζ133ζ7+3ζ23−3ζ7−3ζ231-2-12−ii−2i2i00−3ζ5−3ζ133ζ5+3ζ13003ζ7+3ζ23−3ζ7−3ζ230000000000000000−i3i3000000−33000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ2300000000
χ614-4−4i4i4-400−4i4i1-2-12−ii−2i2i00−3ζ5−3ζ133ζ5+3ζ133ζ7+3ζ23−3ζ7−3ζ231-2-12−ii−2i2i00−3ζ5−3ζ133ζ5+3ζ13003ζ7+3ζ23−3ζ7−3ζ230000000000000000i3−i30000003−3000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ2300000000
χ624-4−4i4i4-400−4i4i1-2-12−ii−2i2i003ζ5+3ζ13−3ζ5−3ζ13−3ζ7−3ζ233ζ7+3ζ231-2-12−ii−2i2i003ζ5+3ζ13−3ζ5−3ζ1300−3ζ7−3ζ233ζ7+3ζ230000000000000000−i3i3000000−33000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ2300000000
χ634-4−4i4i4-400−4i4i1-2-12−ii−2i2i003ζ5+3ζ13−3ζ5−3ζ13−3ζ7−3ζ233ζ7+3ζ231-2-12−ii−2i2i003ζ5+3ζ13−3ζ5−3ζ1300−3ζ7−3ζ233ζ7+3ζ230000000000000000i3−i30000003−3000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ2300000000
χ644-4−4i4i4-400−4i4i44-4-4−4i4i4i−4i00000044-4-4−4i4i4i−4i0000000000000000000000000000000000000000000000000000
χ654-4−4i4i-22002i−2i44-4-4−4i4i4i−4i000000-2-2222i−2i−2i2i000000000000−2i32i300−23230000000000000000000000000000000000
χ664-4−4i4i-22002i−2i44-4-4−4i4i4i−4i000000-2-2222i−2i−2i2i0000000000002i3−2i30023−230000000000000000000000000000000000
χ678888-4-488-4-42-42-422-4-4-4-42222-12-12-1-122-4-4-1-122-1-122000000000000000000000000000000000000000000
χ688888-4-488-4-4-42-42-4-422-4-4-4-4-4-42-12-122-1-12222-1-122-1-1000000000000000000000000000000000000000000
χ698888-4-4-8-8-4-42-42-422-4-444-2-2-2-2-12-12-1-1224411-2-211-2-2000000000000000000000000000000000000000000
χ708888-4-4-8-8-4-4-42-42-4-4224444442-12-122-1-1-2-2-2-211-2-211000000000000000000000000000000000000000000
χ7188-8-8-4-48i−8i442-42-4-2-244−4i4i2i2i−2i−2i-12-1211-2-2−4i4i−i−i2i2iii−2i−2i000000000000000000000000000000000000000000
χ7288-8-8-4-48i−8i44-42-4244-2-2−4i4i−4i−4i4i4i2-12-1-2-2112i−2i2i2i−i−i−2i−2iii000000000000000000000000000000000000000000
χ7388-8-8-4-4−8i8i442-42-4-2-2444i−4i−2i−2i2i2i-12-1211-2-24i−4iii−2i−2i−i−i2i2i000000000000000000000000000000000000000000
χ7488-8-8-4-4−8i8i44-42-4244-2-24i−4i4i4i−4i−4i2-12-1-2-211−2i2i−2i−2iii2i2i−i−i000000000000000000000000000000000000000000
χ758-88i−8i8-8008i−8i-424-2−4i4i−2i2i000000-424-2−4i4i−2i2i0000000000000000000000000000000000000000000000000000
χ768-88i−8i-4400−4i4i2-4-242i−2i4i−4i006ζ7+6ζ23−6ζ7−6ζ23−6ζ5−6ζ136ζ5+6ζ13-121-2−ii−2i2i00−3ζ7−3ζ233ζ7+3ζ23003ζ5+3ζ13−3ζ5−3ζ1300000000000000000000000000000000000000000000
χ778-88i−8i-4400−4i4i2-4-242i−2i4i−4i00−6ζ7−6ζ236ζ7+6ζ236ζ5+6ζ13−6ζ5−6ζ13-121-2−ii−2i2i003ζ7+3ζ23−3ζ7−3ζ2300−3ζ5−3ζ133ζ5+3ζ1300000000000000000000000000000000000000000000
χ788-88i−8i-4400−4i4i-424-2−4i4i−2i2i0000002-1-212i−2ii−i0000−3ζ7+3ζ233ζ7−3ζ23003ζ5−3ζ13−3ζ5+3ζ13000000000000000000000000000000000000000000
χ798-88i−8i-4400−4i4i-424-2−4i4i−2i2i0000002-1-212i−2ii−i00003ζ7−3ζ23−3ζ7+3ζ2300−3ζ5+3ζ133ζ5−3ζ13000000000000000000000000000000000000000000
χ808-8−8i8i8-800−8i8i-424-24i−4i2i−2i000000-424-24i−4i2i−2i0000000000000000000000000000000000000000000000000000
χ818-8−8i8i-44004i−4i2-4-24−2i2i−4i4i00−6ζ5−6ζ136ζ5+6ζ136ζ7+6ζ23−6ζ7−6ζ23-121-2i−i2i−2i003ζ5+3ζ13−3ζ5−3ζ1300−3ζ7−3ζ233ζ7+3ζ2300000000000000000000000000000000000000000000
χ828-8−8i8i-44004i−4i2-4-24−2i2i−4i4i006ζ5+6ζ13−6ζ5−6ζ13−6ζ7−6ζ236ζ7+6ζ23-121-2i−i2i−2i00−3ζ5−3ζ133ζ5+3ζ13003ζ7+3ζ23−3ζ7−3ζ2300000000000000000000000000000000000000000000
χ838-8−8i8i-44004i−4i-424-24i−4i2i−2i0000002-1-21−2i2i−ii00003ζ5−3ζ13−3ζ5+3ζ1300−3ζ7+3ζ233ζ7−3ζ23000000000000000000000000000000000000000000
χ848-8−8i8i-44004i−4i-424-24i−4i2i−2i0000002-1-21−2i2i−ii0000−3ζ5+3ζ133ζ5−3ζ13003ζ7−3ζ23−3ζ7+3ζ23000000000000000000000000000000000000000000

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