Finite Group Databasebeta

← Group #13178319

Character table — Group #13178319

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120
size111122222222222222444444444444444444444444444444448888888888888888888888888888888888181818181818181836363636363636363636363636363636363636363636363672727272
order122233344666666666333334466666666666666612121212121212121212121212121212121212121212121212121212121212121212121212121212121212122244121212122244444444666666121212121212121212121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-11-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-11-1-11-1-111-111-1-1-1-1-1-1-1-1-1-1111-1-11
χ4111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-11-111-1-11-1-1-1-1-1-1-1-11111-1-1-111-1
χ511111111111111111111111-1-1111111111111111-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111111111-11-11-11-11-1-11111-1-1-1-1111111-1-1-1-1
χ611111111111111111111111-1-1111111111111111-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11-11-111-1-111-1-1-1-1-1-1-1-1-1-11111
χ711111111111111111111111-1-1111111111111111-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-111-1111-1-11111-1-1-1-111-111-1
χ811111111111111111111111-1-1111111111111111-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11111-1-11-1-1-1-1-111111111-1-11-1-11
χ91111111-1-1111111111111111-111111111111111111-1-1-1-1-1-1-1-11-11-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-11-1-111111111-1-1-1-111-1-1-11-11
χ101111111-1-1111111111111111-111111111111111111-1-1-1-1-1-1-1-11-11-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11-1-111-111-1-1-1-11111-1-111-1-1111-11-1
χ111111111-1-1111111111111111-111111111111111111-1-1-1-1-1-1-1-11-11-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1111-1-11-11-111-1-1-1-11111-1-1-1-1-1-111
χ121111111-1-1111111111111111-111111111111111111-1-1-1-1-1-1-1-11-11-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11-111-11-11-1-1-1-1-1-111-1-1111111-1-1
χ131111111-1-111111111111111-11111111111111111-1-1-1-1-1-111-1-1-11-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-111-1111-1-1-11111-1-111-1-111-1-11-11-1
χ141111111-1-111111111111111-11111111111111111-1-1-1-1-1-111-1-1-11-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1111-1-111-1-11111-1-111-11-11
χ151111111-1-111111111111111-11111111111111111-1-1-1-1-1-111-1-1-11-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111111111-111-1-1-1-1111-1-111-1-111-1-1-1-111-1-1
χ161111111-1-111111111111111-11111111111111111-1-1-1-1-1-111-1-1-11-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111111-1-1-1-11111-1-1-1-1-111-1-1-1-11111-1-111
χ17222222-1222-12-122-1222-1-1-1-1222-1-1-1-12-1-1-1-12-1-1-1-1-1-122-1-1-1-122222222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12222-1-1-1-1202000000000-1-1-1-1-1-10000000000
χ18222222-1222-12-122-1222-1-1-1-1222-1-1-1-12-1-1-1-12-1-1-1-1-1-122-1-1-1-122222222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-21111-20-20000000001111110000000000
χ19222222-1222-12-122-1222-1-1-1-1-2-22-1-1-1-12-1-1-1-12-1-1-1-11122-1-11122-2-2-2-2-2-21111111122-1-1-1-1-1-1-1-1-2-2111111112222-1-1-1-1-20-2000000000-1-111110000000000
χ20222222-1222-12-122-1222-1-1-1-1-2-22-1-1-1-12-1-1-1-12-1-1-1-11122-1-11122-2-2-2-2-2-21111111122-1-1-1-1-1-1-1-1-2-211111111-2-2-2-2111120200000000011-1-1-1-10000000000
χ21222222-1-2-22-12-122-1222-1-1-1-12-22-1-1-1-12-1-1-1-12-1-1-1-1-1-1-2-21111-2-22-22-222-1-1-1-1-1-1-1-1-2-211111111-2-21111111122-2-2111120-2000000000-1-1-1-1110000000000
χ22222222-1-2-22-12-122-1222-1-1-1-12-22-1-1-1-12-1-1-1-12-1-1-1-1-1-1-2-21111-2-22-22-222-1-1-1-1-1-1-1-1-2-211111111-2-211111111-2-222-1-1-1-1-2020000000001111-1-10000000000
χ23222222-1-2-22-12-122-1222-1-1-1-1-222-1-1-1-12-1-1-1-12-1-1-1-111-2-211-1-1-2-2-22-22-2-211111111-2-21111111122-1-1-1-1-1-1-1-122-2-21111-202000000000-1-111-1-10000000000
χ24222222-1-2-22-12-122-1222-1-1-1-1-222-1-1-1-12-1-1-1-12-1-1-1-111-2-211-1-1-2-2-22-22-2-211111111-2-21111111122-1-1-1-1-1-1-1-1-2-222-1-1-1-120-200000000011-1-1110000000000
χ2522222-1222-1222-1222-1-12-1-1-122-12-1-1-1-12-1-1-1-12-1-1-122222222-1-1-122-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1000000000200200220-1-10000000000-1-1-100-1
χ2622222-1222-1222-1222-1-12-1-1-122-12-1-1-1-12-1-1-1-12-1-1-122222222-1-1-122-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1000000000-200-200-2-20110000000000111001
χ2722222-1222-1222-1222-1-12-1-1-1-2-2-12-1-1-1-12-1-1-1-12-1-1-1-2-22222-2-2-1-11-2-2111-2-2111111-1-122-1-1-1-1-1-111-2-2111111000000000200-2002-20-1-10000000000-1-11001
χ2822222-1222-1222-1222-1-12-1-1-1-2-2-12-1-1-1-12-1-1-1-12-1-1-1-2-22222-2-2-1-11-2-2111-2-2111111-1-122-1-1-1-1-1-111-2-2111111000000000-200200-22011000000000011-100-1
χ2922222-12-2-2-1222-1222-1-12-1-1-12-2-12-1-1-1-12-1-1-1-12-1-1-122-2-2-2-2-2-211-1-221-1-122-1-1-1-1-1-111-2-211111111-2-2111111000000000200-200-220-1-1000000000011100-1
χ3022222-12-2-2-1222-1222-1-12-1-1-12-2-12-1-1-1-12-1-1-1-12-1-1-122-2-2-2-2-2-211-1-221-1-122-1-1-1-1-1-111-2-211111111-2-2111111000000000-2002002-20110000000000-1-1-1001
χ3122222-12-2-2-1222-1222-1-12-1-1-1-22-12-1-1-1-12-1-1-1-12-1-1-1-2-2-2-2-2-2221112-2-111-2-211111111-2-2111111-1-122-1-1-1-1-1-1000000000200200-2-20-1-1000000000011-1001
χ3222222-12-2-2-1222-1222-1-12-1-1-1-22-12-1-1-1-12-1-1-1-12-1-1-1-2-2-2-2-2-2221112-2-111-2-211111111-2-2111111-1-122-1-1-1-1-1-1000000000-200-200220110000000000-1-1100-1
χ332222-1222222-122-12-12-1-12-1-122-1-12-1-1-1-12-1-1-1-12-1-122-1-12222222-1-12-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-100000000000202200200000000-1-1-1-1000-1-10
χ342222-1222222-122-12-12-1-12-1-122-1-12-1-1-1-12-1-1-1-12-1-122-1-12222222-1-12-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-100000000000-20-2-200-2000000001111000110
χ352222-1222222-122-12-12-1-12-1-1-2-2-1-12-1-1-1-12-1-1-1-12-1-1-2-2-1-122-2-222-211-21111-2-21111-1-1-1-122-1-1-1-11111-2-2111100000000000202-200-200000000-1-1-1-1000110
χ362222-1222222-122-12-12-1-12-1-1-2-2-1-12-1-1-1-12-1-1-1-12-1-1-2-2-1-122-2-222-211-21111-2-21111-1-1-1-122-1-1-1-11111-2-2111100000000000-20-22002000000001111000-1-10
χ372222-122-2-222-122-12-12-1-12-1-12-2-1-12-1-1-1-12-1-1-1-12-1-12211-2-2-2-2-2-221-1-2-1-1-1-122-1-1-1-11111-2-211111111-2-211110000000000020-2200-200000000-1-1110001-10
χ382222-122-2-222-122-12-12-1-12-1-12-2-1-12-1-1-1-12-1-1-1-12-1-12211-2-2-2-2-2-221-1-2-1-1-1-122-1-1-1-11111-2-211111111-2-2111100000000000-202-20020000000011-1-1000-110
χ392222-122-2-222-122-12-12-1-12-1-1-22-1-12-1-1-1-12-1-1-1-12-1-1-2-211-2-222-2-2-2-1121111-2-211111111-2-21111-1-1-1-122-1-1-1-10000000000020-2-200200000000-1-111000-110
χ402222-122-2-222-122-12-12-1-12-1-1-22-1-12-1-1-1-12-1-1-1-12-1-1-2-211-2-222-2-2-2-1121111-2-211111111-2-21111-1-1-1-122-1-1-1-100000000000-202200-20000000011-1-10001-10
χ412-22-22222i−2i-22-2-22-2-22-22222200-2-2-2-2-222222-2-2-2-2-2002i−2i2i−2i002i−2i000000000000002i−2i2i−2i2i−2i2i2i−2i−2i00000000002-22i−2i2i2i−2i−2i0000000000002-200000000000000
χ422-22-22222i−2i-22-2-22-2-22-22222200-2-2-2-2-222222-2-2-2-2-2002i−2i2i−2i002i−2i000000000000002i−2i2i−2i2i−2i2i2i−2i−2i0000000000-22−2i2i−2i−2i2i2i000000000000-2200000000000000
χ432-22-2222−2i2i-22-2-22-2-22-22222200-2-2-2-2-222222-2-2-2-2-200−2i2i−2i2i00−2i2i00000000000000−2i2i−2i2i−2i2i−2i−2i2i2i00000000002-2−2i2i−2i−2i2i2i0000000000002-200000000000000
χ442-22-2222−2i2i-22-2-22-2-22-22222200-2-2-2-2-222222-2-2-2-2-200−2i2i−2i2i00−2i2i00000000000000−2i2i−2i2i−2i2i−2i−2i2i2i0000000000-222i−2i2i2i−2i−2i000000000000-2200000000000000
χ452-22-222-12i−2i-2-1-212-212-22-1-1-1-100-211112-1-1-1-1-21111−i3i32i−2i−ii3−32i−2i000000−i3i3−i3i3−i3−i3i3i32i−2i−ii−ii−i−iii003−33−333−3−32-22i−2i−i−iii000000000000-11−i3i33−30000000000
χ462-22-222-12i−2i-2-1-212-212-22-1-1-1-100-211112-1-1-1-1-21111−i3i32i−2i−ii3−32i−2i000000−i3i3−i3i3−i3−i3i3i32i−2i−ii−ii−i−iii003−33−333−3−3-22−2i2iii−i−i0000000000001-1i3−i3−330000000000
χ472-22-222-12i−2i-2-1-212-212-22-1-1-1-100-211112-1-1-1-1-21111i3−i32i−2i−ii−332i−2i000000i3−i3i3−i3i3i3−i3−i32i−2i−ii−ii−i−iii00−33−33−3−3332-22i−2i−i−iii000000000000-11i3−i3−330000000000
χ482-22-222-12i−2i-2-1-212-212-22-1-1-1-100-211112-1-1-1-1-21111i3−i32i−2i−ii−332i−2i000000i3−i3i3−i3i3i3−i3−i32i−2i−ii−ii−i−iii00−33−33−3−333-22−2i2iii−i−i0000000000001-1−i3i33−30000000000
χ492-22-222-1−2i2i-2-1-212-212-22-1-1-1-100-211112-1-1-1-1-21111−i3i3−2i2ii−i−33−2i2i000000−i3i3−i3i3−i3−i3i3i3−2i2ii−ii−iii−i−i00−33−33−3−3332-2−2i2iii−i−i000000000000-11−i3i3−330000000000
χ502-22-222-1−2i2i-2-1-212-212-22-1-1-1-100-211112-1-1-1-1-21111−i3i3−2i2ii−i−33−2i2i000000−i3i3−i3i3−i3−i3i3i3−2i2ii−ii−iii−i−i00−33−33−3−333-222i−2i−i−iii0000000000001-1i3−i33−30000000000
χ512-22-222-1−2i2i-2-1-212-212-22-1-1-1-100-211112-1-1-1-1-21111i3−i3−2i2ii−i3−3−2i2i000000i3−i3i3−i3i3i3−i3−i3−2i2ii−ii−iii−i−i003−33−333−3−32-2−2i2iii−i−i000000000000-11i3−i33−30000000000
χ522-22-222-1−2i2i-2-1-212-212-22-1-1-1-100-211112-1-1-1-1-21111i3−i3−2i2ii−i3−3−2i2i000000i3−i3i3−i3i3i3−i3−i3−2i2ii−ii−iii−i−i003−33−333−3−3-222i−2i−i−iii0000000000001-1−i3i3−330000000000
χ5344444-2-244-2-24-2-24-24-2-2-211144-2-2111-2-2111-2-2111-2-244-2-2-2-2-2-2-244-2-2-2-2-2111111-2-2-2-2111111-2-2-2-2111111000000000000000000000000000000000000
χ5444444-2-244-2-24-2-24-24-2-2-2111-4-4-2-2111-2-2111-2-21112244-2-222-2-22-4-422222-1-1-1-1-1-1-2-2-2-21111112222-1-1-1-1-1-1000000000000000000000000000000000000
χ5544444-2-2-4-4-2-24-2-24-24-2-2-21114-4-2-2111-2-2111-2-2111-2-2-4-4222222-2-442-2-2-2-21111112222-1-1-1-1-1-12222-1-1-1-1-1-1000000000000000000000000000000000000
χ5644444-2-2-4-4-2-24-2-24-24-2-2-2111-44-2-2111-2-2111-2-211122-4-422-2-22224-4-22222-1-1-1-1-1-12222-1-1-1-1-1-1-2-2-2-2111111000000000000000000000000000000000000
χ574444-24-2444-2-2-24-2-2-24-21-21144-21-211-21-211-21-211-2-2-2-2-2-2-2-2444-2-24-2-211-2-21111-2-211-2-21111-2-211-2-21111000000000000000000000000000000000000
χ584444-24-2444-2-2-24-2-2-24-21-211-4-4-21-211-21-211-21-21122-2-2-2-22244-422-422-1-122-1-1-1-1-2-211-2-2111122-1-122-1-1-1-1000000000000000000000000000000000000
χ594444-24-2-4-44-2-2-24-2-2-24-21-2114-4-21-211-21-211-21-211-2-2222222-4-442-2-4-2-211-2-2111122-1-122-1-1-1-122-1-122-1-1-1-1000000000000000000000000000000000000
χ604444-24-2-4-44-2-2-24-2-2-24-21-211-44-21-211-21-211-21-211222222-2-2-4-4-4-22422-1-122-1-1-1-122-1-122-1-1-1-1-2-211-2-21111000000000000000000000000000000000000
χ614444-2-2444-24-24-2-24-2-21-2-211441-2-2111-2-2111-2-21144-2-24444-2-2-2-2-2-211-2-2-2-2111111-2-2-2-2111111-2-2-2-21111000000000000000000000000000000000000
χ624444-2-2444-24-24-2-24-2-21-2-211-4-41-2-2111-2-2111-2-211-4-4-2-244-4-4-2-22222-1-12222-1-1-1-111-2-2-2-21111-1-12222-1-1-1-1000000000000000000000000000000000000
χ634444-2-24-4-4-24-24-2-24-2-21-2-2114-41-2-2111-2-2111-2-2114422-4-4-4-422-22-2211-2-2-2-21111-1-12222-1-1-1-1-1-12222-1-1-1-1000000000000000000000000000000000000
χ644444-2-24-4-4-24-24-2-24-2-21-2-211-441-2-2111-2-2111-2-211-4-422-4-444222-22-2-1-12222-1-1-1-1-1-12222-1-1-1-111-2-2-2-21111000000000000000000000000000000000000
χ654444-2-2-244-2-2-2-2-2-2-2-2-2111−1−3i32−1+3i3244111−1−3i32−1+3i32111−1−3i32−1+3i32111−1−3i32−1+3i32-2-2-2-2-2-2-2-2-2-2-2-2-2-2111111−1−3i32−1+3i32−1−3i32−1+3i32111111−1−3i32−1+3i32−1−3i32−1+3i32111111−1−3i32−1+3i32−1−3i32−1+3i32000000000000000000000000000000000000
χ664444-2-2-244-2-2-2-2-2-2-2-2-2111−1−3i32−1+3i32-4-4111−1−3i32−1+3i32111−1−3i32−1+3i32111−1−3i32−1+3i3222-2-2-2-222-2-22222-1-1-1-1-1-11+3i321−3i321+3i321−3i32111111−1−3i32−1+3i32−1−3i32−1+3i32-1-1-1-1-1-11+3i321−3i321+3i321−3i32000000000000000000000000000000000000
χ674444-2-2-244-2-2-2-2-2-2-2-2-2111−1+3i32−1−3i3244111−1+3i32−1−3i32111−1+3i32−1−3i32111−1+3i32−1−3i32-2-2-2-2-2-2-2-2-2-2-2-2-2-2111111−1+3i32−1−3i32−1+3i32−1−3i32111111−1+3i32−1−3i32−1+3i32−1−3i32111111−1+3i32−1−3i32−1+3i32−1−3i32000000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.