Finite Group Databasebeta

← Group #13178344

Character table — Group #13178344

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120
size111122222222222222444444444444444444444444444444448888888888888888888888888888888888181818181818181836363636363636363636363636363636363636363636363672727272
order1222333446666666663333344666666666666666121212121212121212121212121212121212121212121212121212121212121212121212121212121212121222441212121244444444446612121212121212121212121212121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11-1111-1-1-1-1-111-1-1-1-1-1-111-1-111-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-11-1-1-1111-1-1-1-111-1-1-1-1-1-111-1-111
χ511111111111111111111111-1-11111111111111111111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1111-1-11-1-1111111-1-1-1-11111-1-1-1-1
χ611111111111111111111111-1-11111111111111111111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-111-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ711111111111111111111111-1-11111111111111111111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-11-1-1-111-1-111-1-1111111-1-1-1-111
χ811111111111111111111111-1-11111111111111111111-1-1-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11-1111-1-1-1-1-1-1111111-1-11111-1-1
χ91111111-1-1111111111111111-1111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11-11-1-11-111-11111-1-111-1-1-1-1111-11-1
χ101111111-1-1111111111111111-1111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11-1-111-11-1-1111-1-11111-1-111-1-1-11-11
χ111111111-1-1111111111111111-1111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1111-11-1-1-11-1-11111-1-111-1-1-1-11-1-11
χ121111111-1-1111111111111111-1111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-11-1-11-1111-1-1-1-1-1-1-1-1-1111111-111-1
χ131111111-1-111111111111111-11111111111111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-111-1-1-111-111111-1-1-1-111-1-111-11-11
χ141111111-1-111111111111111-11111111111111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-11-1111-1-11-111-1-111-1-11111-1-11-11-1
χ151111111-1-111111111111111-11111111111111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111111-111-1-11-11-1-1-1111111-1-1-1-1-1-1-111-1
χ161111111-1-111111111111111-11111111111111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-11111111-1-1-111-11-11-1-1-1-1-1-111-1-111111-1-11
χ17222222-12222-122-1-1222-1-1-1-1222-1-1-1-12-1-1-1-12-1-1-1-12222-1-1-1-1-1-1222222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-12222-1-1-1-12200000000-1-10000-1-1-1-100000000
χ18222222-12222-122-1-1222-1-1-1-1222-1-1-1-12-1-1-1-12-1-1-1-12222-1-1-1-1-1-1222222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-21111-2-200000000110000111100000000
χ19222222-12222-122-1-1222-1-1-1-1-2-22-1-1-1-12-1-1-1-12-1-1-1-122221111-1-1-2-2-2-222-1-1-1-1-1-1-1-1-2-211111111-2-2111111112222-1-1-1-1-2-200000000-1-10000111100000000
χ20222222-12222-122-1-1222-1-1-1-1-2-22-1-1-1-12-1-1-1-12-1-1-1-122221111-1-1-2-2-2-222-1-1-1-1-1-1-1-1-2-211111111-2-211111111-2-2-2-211112200000000110000-1-1-1-100000000
χ21222222-1-2-222-122-1-1222-1-1-1-12-22-1-1-1-12-1-1-1-12-1-1-1-1-2-2-2-2-1-1111122-2-2-2-21111111122-1-1-1-1-1-1-1-1-2-21111111122-2-211112-200000000-1-10000-1-11100000000
χ22222222-1-2-222-122-1-1222-1-1-1-12-22-1-1-1-12-1-1-1-12-1-1-1-1-2-2-2-2-1-1111122-2-2-2-21111111122-1-1-1-1-1-1-1-1-2-211111111-2-222-1-1-1-1-220000000011000011-1-100000000
χ23222222-1-2-222-122-1-1222-1-1-1-1-222-1-1-1-12-1-1-1-12-1-1-1-1-2-2-2-211-1-111-2-222-2-211111111-2-21111111122-1-1-1-1-1-1-1-122-2-21111-2200000000-1-1000011-1-100000000
χ24222222-1-2-222-122-1-1222-1-1-1-1-222-1-1-1-12-1-1-1-12-1-1-1-1-2-2-2-211-1-111-2-222-2-211111111-2-21111111122-1-1-1-1-1-1-1-1-2-222-1-1-1-12-200000000110000-1-11100000000
χ2522222-12222-122-1222-1-12-1-1-122-12-1-1-1-12-1-1-1-12-1-1-122-1-12222222-12-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-10000000000020002220000-1-1000000-1-100-1-1
χ2622222-12222-122-1222-1-12-1-1-122-12-1-1-1-12-1-1-1-12-1-1-122-1-12222222-12-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-100000000000-2000-2-2-2000011000000110011
χ2722222-12222-122-1222-1-12-1-1-1-2-2-12-1-1-1-12-1-1-1-12-1-1-122-1-1-2-2-2-222-21-21-1-122-1-1-1-1-1-111-2-211111111-2-21111110000000000020002-2-20000-1-1000000-1-10011
χ2822222-12222-122-1222-1-12-1-1-1-2-2-12-1-1-1-12-1-1-1-12-1-1-122-1-1-2-2-2-222-21-21-1-122-1-1-1-1-1-111-2-211111111-2-211111100000000000-2000-2220000110000001100-1-1
χ2922222-12-2-22-122-1222-1-12-1-1-12-2-12-1-1-1-12-1-1-1-12-1-1-1-2-21122-2-2-2-22-1-2111-2-2111111-1-122-1-1-1-1-1-111-2-2111111000000000002000-2-220000-1-100000011001-1
χ3022222-12-2-22-122-1222-1-12-1-1-12-2-12-1-1-1-12-1-1-1-12-1-1-1-2-21122-2-2-2-22-1-2111-2-2111111-1-122-1-1-1-1-1-111-2-211111100000000000-200022-2000011000000-1-100-11
χ3122222-12-2-22-122-1222-1-12-1-1-1-22-12-1-1-1-12-1-1-1-12-1-1-1-2-211-2-222-2-2-212-111-2-211111111-2-2111111-1-122-1-1-1-1-1-1000000000002000-22-20000-1-10000001100-11
χ3222222-12-2-22-122-1222-1-12-1-1-1-22-12-1-1-1-12-1-1-1-12-1-1-1-2-211-2-222-2-2-212-111-2-211111111-2-2111111-1-122-1-1-1-1-1-100000000000-20002-22000011000000-1-1001-1
χ332222-12222-122-1222-12-1-12-1-122-1-12-1-1-1-12-1-1-1-12-1-1-1-122222222-12-12-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-100000000002022200000-1-1000000-1-100-1-100
χ342222-12222-122-1222-12-1-12-1-122-1-12-1-1-1-12-1-1-1-12-1-1-1-122222222-12-12-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-10000000000-20-2-2-2000001100000011001100
χ352222-12222-122-1222-12-1-12-1-1-2-2-1-12-1-1-1-12-1-1-1-12-1-1-1-122-2-2-2-2221-21-2-1-1-1-122-1-1-1-11111-2-211111111-2-211110000000000202-2-200000-1-1000000-1-1001100
χ362222-12222-122-1222-12-1-12-1-1-2-2-1-12-1-1-1-12-1-1-1-12-1-1-1-122-2-2-2-2221-21-2-1-1-1-122-1-1-1-11111-2-211111111-2-211110000000000-20-22200000110000001100-1-100
χ372222-122-2-2-122-1222-12-1-12-1-12-2-1-12-1-1-1-12-1-1-1-12-1-111-2-222-2-2-2-2-121-21111-2-21111-1-1-1-122-1-1-1-11111-2-21111000000000020-22-200000-1-10000001100-1100
χ382222-122-2-2-122-1222-12-1-12-1-12-2-1-12-1-1-1-12-1-1-1-12-1-111-2-222-2-2-2-2-121-21111-2-21111-1-1-1-122-1-1-1-11111-2-211110000000000-202-220000011000000-1-1001-100
χ392222-122-2-2-122-1222-12-1-12-1-1-22-1-12-1-1-1-12-1-1-1-12-1-111-2-2-2-222-2-21-2-121111-2-211111111-2-21111-1-1-1-122-1-1-1-1000000000020-2-2200000-1-100000011001-100
χ402222-122-2-2-122-1222-12-1-12-1-1-22-1-12-1-1-1-12-1-1-1-12-1-111-2-2-2-222-2-21-2-121111-2-211111111-2-21111-1-1-1-122-1-1-1-10000000000-2022-20000011000000-1-100-1100
χ4122-2-22222-222-2-2-22-2-2-22222200-2-2-2-2-222222-2-2-2-2-22-22-200002-200002-22-22-222-2-2000000000000000000002-22-222-2-200000000002-20000000000000000
χ4222-2-22222-222-2-2-22-2-2-22222200-2-2-2-2-222222-2-2-2-2-22-22-200002-200002-22-22-222-2-200000000000000000000-22-22-2-2220000000000-220000000000000000
χ4322-2-2222-2222-2-2-22-2-2-22222200-2-2-2-2-222222-2-2-2-2-2-22-220000-220000-22-22-22-2-222000000000000000000002-2-22-2-22200000000002-20000000000000000
χ4422-2-2222-2222-2-2-22-2-2-22222200-2-2-2-2-222222-2-2-2-2-2-22-220000-220000-22-22-22-2-22200000000000000000000-222-222-2-20000000000-220000000000000000
χ4522-2-222-12-2221-2-2-11-2-22-1-1-1-100-211112-1-1-1-1-211112-22-23−33−3-1100002-2-11-11-1-111003−33−333−3−3003−33−333−3−32-22-2-1-1110000000000-1100003−33−300000000
χ4622-2-222-12-2221-2-2-11-2-22-1-1-1-100-211112-1-1-1-1-211112-22-23−33−3-1100002-2-11-11-1-111003−33−333−3−3003−33−333−3−3-22-2211-1-100000000001-10000−33−3300000000
χ4722-2-222-12-2221-2-2-11-2-22-1-1-1-100-211112-1-1-1-1-211112-22-2−33−33-1100002-2-11-11-1-11100−33−33−3−33300−33−33−3−3332-22-2-1-1110000000000-110000−33−3300000000
χ4822-2-222-12-2221-2-2-11-2-22-1-1-1-100-211112-1-1-1-1-211112-22-2−33−33-1100002-2-11-11-1-11100−33−33−3−33300−33−33−3−333-22-2211-1-100000000001-100003−33−300000000
χ4922-2-222-1-22221-2-2-11-2-22-1-1-1-100-211112-1-1-1-1-21111-22-223−3−331-10000-221-11-111-1-1003−33−333−3−300−33−33−3−3332-2-2211-1-10000000000-1100003−3−3300000000
χ5022-2-222-1-22221-2-2-11-2-22-1-1-1-100-211112-1-1-1-1-21111-22-223−3−331-10000-221-11-111-1-1003−33−333−3−300−33−33−3−333-222-2-1-11100000000001-10000−333−300000000
χ5122-2-222-1-22221-2-2-11-2-22-1-1-1-100-211112-1-1-1-1-21111-22-22−333−31-10000-221-11-111-1-100−33−33−3−333003−33−333−3−32-2-2211-1-10000000000-110000−333−300000000
χ5222-2-222-1-22221-2-2-11-2-22-1-1-1-100-211112-1-1-1-1-21111-22-22−333−31-10000-221-11-111-1-100−33−33−3−333003−33−333−3−3-222-2-1-11100000000001-100003−3−3300000000
χ5344444-2-2444-2-24-2-2-24-2-2-211144-2-2111-2-2111-2-211144-2-2-2-2-2-2-2-24-24-2-2-2-2-2111111-2-2-2-2111111-2-2-2-2111111000000000000000000000000000000000000
χ5444444-2-2444-2-24-2-2-24-2-2-2111-4-4-2-2111-2-2111-2-211144-2-22222-2-2-42-42-2-2-2-21111112222-1-1-1-1-1-12222-1-1-1-1-1-1000000000000000000000000000000000000
χ5544444-2-2-4-44-2-24-2-2-24-2-2-21114-4-2-2111-2-2111-2-2111-4-422-2-222224-2-422222-1-1-1-1-1-1-2-2-2-21111112222-1-1-1-1-1-1000000000000000000000000000000000000
χ5644444-2-2-4-44-2-24-2-2-24-2-2-2111-44-2-2111-2-2111-2-2111-4-42222-2-222-424-22222-1-1-1-1-1-12222-1-1-1-1-1-1-2-2-2-2111111000000000000000000000000000000000000
χ574444-24-244-24-2-24-2-2-24-21-21144-21-211-21-211-21-211-2-244-2-2-2-2-2-2-24-24-2-211-2-21111-2-211-2-21111-2-211-2-21111000000000000000000000000000000000000
χ584444-24-244-24-2-24-2-2-24-21-211-4-4-21-211-21-211-21-211-2-2442222-2-22-42-4-2-211-2-2111122-1-122-1-1-1-122-1-122-1-1-1-1000000000000000000000000000000000000
χ594444-24-2-4-4-24-2-24-2-2-24-21-2114-4-21-211-21-211-21-21122-4-4-2-22222-242-422-1-122-1-1-1-1-2-211-2-2111122-1-122-1-1-1-1000000000000000000000000000000000000
χ604444-24-2-4-4-24-2-24-2-2-24-21-211-44-21-211-21-211-21-21122-4-422-2-2222-4-2422-1-122-1-1-1-122-1-122-1-1-1-1-2-211-2-21111000000000000000000000000000000000000
χ614444-2-2444-2-24-2-244-2-21-2-211441-2-2111-2-2111-2-211-2-2-2-2444444-2-2-2-211-2-2-2-2111111-2-2-2-2111111-2-2-2-21111000000000000000000000000000000000000
χ624444-2-2444-2-24-2-244-2-21-2-211-4-41-2-2111-2-2111-2-211-2-2-2-2-4-4-4-444222211-2-2-2-21111-1-12222-1-1-1-1-1-12222-1-1-1-1000000000000000000000000000000000000
χ634444-2-24-4-4-2-24-2-244-2-21-2-2114-41-2-2111-2-2111-2-211222244-4-4-4-4-2-222-1-12222-1-1-1-111-2-2-2-21111-1-12222-1-1-1-1000000000000000000000000000000000000
χ644444-2-24-4-4-2-24-2-244-2-21-2-211-441-2-2111-2-2111-2-2112222-4-444-4-422-2-2-1-12222-1-1-1-1-1-12222-1-1-1-111-2-2-2-21111000000000000000000000000000000000000
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+3i32-2-2-2-22222-2-22222111111−1−3i32−1+3i32−1−3i32−1+3i32-1-1-1-1-1-11+3i321−3i321+3i321−3i32-1-1-1-1-1-11+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.