Finite Group Databasebeta

← Group #13172112

Character table — Group #13172112

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117
size111122222222222222444444444444444444444466666688888888888812121212121212121212121212121212121212121212121818181818182424242424242424242424242424363636363636363636363654547272108
order1222223336666666663336666666666666666666441212121236666666666624444661212121212121212121212121212121222444466612121212121212121212122446666121212124412124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-11-11111111111111111111-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111-1111-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-11111-1-11111-111-1-1-1-1-1-1-1-1-1-111-1
χ41111111111111111111111111111111111111111111111111111111111-1-11-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11111-1-1-1-111-1-11
χ51111111111111111111111111111111111111111-1-1-1-1-1-111111111111111-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111111111-1-11111-1-1-1-1-1-1-1-1-1
χ61111111111111111111111111111111111111111-1-1-1-1-1-11111111111111-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-111-1-1-1-1-1-1-1-111111
χ71111111111111111111111111111111111111111-1-1-1-1-1-1111111111111-11-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-1-1-1-1-1-1111111-1-11
χ81111111111111111111111111111111111111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-111-1
χ91111-1-1111111111111111-1-1-1-1-1-1111-1-1-1-11111111111111-1-1-1-1111-1-1-1-111-1-1-111-1-1-1-111-1-11111-1-1-1-111-1-111111-11-11-1-1-111-1-1-1-1111-1-1-1-11111-11-1
χ101111-1-1111111111111111-1-1-1-1-1-1111-1-1-1-11111111111111-1-1-1-1111-1-1-1-11-1-11-111-1-1-1-111-1-11111-1-1-1-1-1-1-1-111111-1-11-11-1-1-1-11111-1-1-111-1-111-1-11-11
χ111111-1-1111111111111111-1-1-1-1-1-1111-1-1-1-11111111111111-1-1-1-1111-1-1-1-1-11-1-11-1-111-1-111-1-11111-1-1-1-1-1-111-1-1-1-1-111-11-11111-1-11-11-1-11111-1-1-1-1-111
χ121111-1-1111111111111111-1-1-1-1-1-1111-1-1-1-11111111111111-1-1-1-1111-1-1-1-1-1-1-111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1-11-11-1111-1-111-11-111-1-111-1-1111-1-1
χ131111-1-1111111111111111-1-1-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-11-1-1-1-1111-1-1-1-1111-1-111-1-111-1-111-1-1-1-111111111-1-1111-11-11-1-1-111-1-1-11-111-1-111-1-1-1-11-11
χ141111-1-1111111111111111-1-1-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-11-1-1-1-1111-1-1-1-11-111-111-1-111-1-111-1-1-1-11111-1-111-1-1111-1-11-11-1-1-1-1111-11-1-11111-1-111-11-1
χ151111-1-1111111111111111-1-1-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-11-1-1-1-1111-1-1-1-1-111-11-1-11111-1-111-1-1-1-11111-1-1-1-111-1-1-111-11-11111-1-111-1-1-111-1-111111-1-1
χ161111-1-1111111111111111-1-1-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-11-1-1-1-1111-1-1-1-1-1-1111-1-11111-1-111-1-1-1-1111111-1-111-1-1-11-11-1111-1-111-1-1111-1-1-1-111-1-1-111
χ1722222222-122-1-1-122222-1-12222-1-122-12222-1-1-1-1-12000000-1-1-1-1-1-1-1-1-1-1-1-122022222200000000000000220000-1-1-1-1-1-122-1-1-1-1-1-1200-1-1-1-1000000000
χ1822222222-122-1-1-122222-1-12222-1-122-12222-1-1-1-1-12000000-1-1-1-1-1-1-1-1-1-1-1-12-20-22222200000000000000-2-20000-1-1-1-111-2-2-1-11111-2001111000000000
χ1922222222-122-1-1-122222-1-12222-1-122-12222-1-1-1-1-12000000-1-1-1-1-1-1-1-1-1-1-1-1-2202-2-2-2-2-200000000000000-2-200001111-1-12211-1-1-1-1-2001111000000000
χ2022222222-122-1-1-122222-1-12222-1-122-12222-1-1-1-1-12000000-1-1-1-1-1-1-1-1-1-1-1-1-2-20-2-2-2-2-2-200000000000000220000111111-2-2111111200-1-1-1-1000000000
χ212222222-122-1222-12-12-12-122-1-122-1-12-1-1-1-1-1-122-1-122-1-1-1-1-122-1-1-1-1-1-1-1-1-120202-1-1-1-1-1-12222-1-1-1-1-1-1-1-10022222-1-120000-1-100000000000-1-1-1-100000
χ222222222-122-1222-12-12-12-122-1-122-1-12-1-1-1-1-1-122-1-122-1-1-1-1-122-1-1-1-1-1-1-1-1-1-2020-21111-1-12222-1-1-1-1-1-1-1-100-2-2-2-2-211-200001100000000000111100000
χ232222222-122-1222-12-12-12-122-1-122-1-12-1-1-1-1-1-122-1-1-2-21111-122-1-1-1-1-1-1-1-1-120-202-1-1-1-111-2-2-2-21111111100-2-2-2-22-1-120000-1-100000000000111100000
χ242222222-122-1222-12-12-12-122-1-122-1-12-1-1-1-1-1-122-1-1-2-21111-122-1-1-1-1-1-1-1-1-1-20-20-2111111-2-2-2-211111111002222-211-200001100000000000-1-1-1-100000
χ25222222-122-122222-12-1-1-12-1-12222-1-1-1-1-1-1-122-1-12-1222222-1-1-122-1-1-1-1-1-1-102220000022-1-1-1-1-1-1-1-1-1-1-1-1000000000022-1-100-1-1-1-10220000000000-1-10
χ26222222-122-122222-12-1-1-12-1-12222-1-1-1-1-1-1-122-1-12-1222222-1-1-122-1-1-1-1-1-1-10-22-20000022-1-1-1-1-1-1-1-1-1-1-1-10000000000-2-2110011110-2-20000000000110
χ27222222-122-122222-12-1-1-12-1-12222-1-1-1-1-1-1-122-1-12-1-2-2-2-2-2-2-1-1-122-1-1-1-1-1-1-102-2200000-2-2111111111111000000000022-1-100-1-1-1-10-2-20000000000110
χ28222222-122-122222-12-1-1-12-1-12222-1-1-1-1-1-1-122-1-12-1-2-2-2-2-2-2-1-1-122-1-1-1-1-1-1-10-2-2-200000-2-21111111111110000000000-2-2110011110220000000000-1-10
χ292222-2-222-122-1-1-122222-1-1-2-2-2-21122-1-2-2-2-2-1-1-1-1-12000000-11111-1-1-11111220-2-222-2-200000000000000220000-1-1-11-112-211-1-111-200-1-111000000000
χ302222-2-222-122-1-1-122222-1-1-2-2-2-21122-1-2-2-2-2-1-1-1-1-12000000-11111-1-1-111112-202-222-2-200000000000000-2-20000-1-1-111-1-221111-1-120011-1-1000000000
χ312222-2-222-122-1-1-122222-1-1-2-2-2-21122-1-2-2-2-2-1-1-1-1-12000000-11111-1-1-11111-220-22-2-22200000000000000-2-20000111-1-112-2-1-1-1-11120011-1-1000000000
χ322222-2-222-122-1-1-122222-1-1-2-2-2-21122-1-2-2-2-2-1-1-1-1-12000000-11111-1-1-11111-2-2022-2-22200000000000000220000111-11-1-22-1-111-1-1-200-1-111000000000
χ332222-2-22-122-1222-12-12-12-1-2-211-2-2-1-121111-1-122-1-122-1-1-1-1-1-2-211-1-1-1111120-20-2-1-1111122-2-2-1-1-1-1111100-2-2222-1-1-20000110000000000011-1-100000
χ342222-2-22-122-1222-12-12-12-1-2-211-2-2-1-121111-1-122-1-122-1-1-1-1-1-2-211-1-1-11111-20-20211-1-11122-2-2-1-1-1-111110022-2-2-21120000-1-100000000000-1-11100000
χ352222-2-22-122-1222-12-12-12-1-2-211-2-2-1-121111-1-122-1-1-2-21111-1-2-211-1-1-111112020-2-1-111-1-1-2-2221111-1-1-1-10022-2-22-1-1-200001100000000000-1-11100000
χ362222-2-22-122-1222-12-12-12-1-2-211-2-2-1-121111-1-122-1-1-2-21111-1-2-211-1-1-11111-2020211-1-1-1-1-2-2221111-1-1-1-100-2-222-21120000-1-10000000000011-1-100000
χ372222-2-2-122-122222-12-1-1-1211-2-2-2-2-1-1-1111122-1-12-1222222-111-2-2-1-1-1111102-2-200000-2-2-1-111-1-1-1-1111100000000002-2-1100-1-1110-2200000000001-10
χ382222-2-2-122-122222-12-1-1-1211-2-2-2-2-1-1-1111122-1-12-1222222-111-2-2-1-1-111110-2-2200000-2-2-1-111-1-1-1-111110000000000-221-10011-1-102-20000000000-110
χ392222-2-2-122-122222-12-1-1-1211-2-2-2-2-1-1-1111122-1-12-1-2-2-2-2-2-2-111-2-2-1-1-11111022-2000002211-1-11111-1-1-1-100000000002-2-1100-1-11102-20000000000-110
χ402222-2-2-122-122222-12-1-1-1211-2-2-2-2-1-1-1111122-1-12-1-2-2-2-2-2-2-111-2-2-1-1-111110-222000002211-1-11111-1-1-1-10000000000-221-10011-1-10-2200000000001-10
χ4122-2-200222-2-22-2-222-2-22220000002-2-200002-22-2-2-22i−2i2i2i−2i−2i200002-2-20000000000000002i−2i002i2i−2i−2i00002-20000000000000000000002-20000002i−2i000
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χ4322-2-200222-2-22-2-222-2-22220000002-2-200002-22-2-2-2−2i2i−2i−2i2i2i200002-2-2000000000000000−2i2i00−2i−2i2i2i00002-20000000000000000000002-2000000−2i2i000
χ4422-2-200222-2-22-2-222-2-22220000002-2-200002-22-2-2-2−2i2i−2i−2i2i2i200002-2-2000000000000000−2i2i00−2i−2i2i2i0000-22000000000000000000000-220000002i−2i000
χ452-2-222-222222-22-2-2-2-2-22222-22-22-2-22222-2-2-2-2-2-22-200000022-22-2-22-222-2-200000000000000000000000002i−2i2i−2i0000000000000000000002i−2i2i−2i00000
χ462-2-222-222222-22-2-2-2-2-22222-22-22-2-22222-2-2-2-2-2-22-200000022-22-2-22-222-2-20000000000000000000000000−2i2i−2i2i000000000000000000000−2i2i−2i2i00000
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χ482-2-222-22-122-1-22-21-21-2-12-12-2-112-21-12-1-11111-2-2-11003−33−3-12-2-111-11-1-11100000i3−i3i3−i33−300003−33−333−3−300−2i2i−2i2i0i3−i300000i3−i300000000000i−ii−i00000
χ492-2-222-22-122-1-22-21-21-2-12-12-2-112-21-12-1-11111-2-2-1100−33−33-12-2-111-11-1-11100000−i3i3−i3i3−330000−33−33−3−33300−2i2i−2i2i0−i3i300000−i3i300000000000i−ii−i00000
χ502-2-222-22-122-1-22-21-21-2-12-12-2-112-21-12-1-11111-2-2-1100−33−33-12-2-111-11-1-11100000i3−i3i3−i3−330000−33−33−3−333002i−2i2i−2i0i3−i300000i3−i300000000000−ii−ii00000
χ512-2-22-2222222-22-2-2-2-2-2222-22-22-22-222-2-222-2-2-2-22-20000002-22-22-22-2-2-22200000000000000000000000002i−2i−2i2i0000000000000000000002i−2i−2i2i00000
χ522-2-22-2222222-22-2-2-2-2-2222-22-22-22-222-2-222-2-2-2-22-20000002-22-22-22-2-2-2220000000000000000000000000−2i2i2i−2i000000000000000000000−2i2i2i−2i00000
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χ562-2-22-222-122-1-22-21-21-2-12-1-221-1-221-1211-1-111-2-2-1100−33−33-1-221-11-1111-1-100000i3−i3−i3i33−30000−33−3333−3−300−2i2i2i−2i0i3−i300000−i3i300000000000i−i−ii00000
χ574444444-2-24-2-2-2-2-24-24-2-2144-2-2-2-2-2-2-2-2-2-2-211-2-21-20000001-2-211111111140004-2-2-2-200000000000000000000-211-200001100000000000000000000
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χ59444444-24-2-24-2-2-24-24-2-21-2-2-244-2-2-2-21-2-2-2-2-2-211-2-2000000111-2-21111111040400000000000000000000000000000-2-2-2-20011110000000000000000
χ60444444-24-2-24-2-2-24-24-2-21-2-2-244-2-2-2-21-2-2-2-2-2-211-2-2000000111-2-211111110-40-400000000000000000000000000000222200-1-1-1-10000000000000000
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χ894-44-400-2-2422-4-4422-2-21-2-2000000-1-12-333-32-22-221002i3−2i3−2i32i310000-1-11-333-300000000000002i3−2i3−i3i3i3−i3−i3i3i3−i3000000000000000000000000000000000000
χ904-4-444-444-2442-22-4-4-4-44-2-24-44-4-22-44-244-4-42222-2-4000000-2-22-222-22-2-22200000000000000000000000000000000000000000000000000000000000
χ914-4-444-44-2-24-22-222-42-4-2-214-4-22-222-2-2-2-222-1-122120000001-221-1-11-111-1-100000−2i32i3−2i32i3000000000000000000000i3−i300000i3−i300000000000000000000
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χ944-4-444-4-24-2-242-22-42-42-21-2-224-4-222-21-2-22222-1-1-2200000011-1-22-11-111-1-10000000000000000000000000000000000000003i−3i3i−3i0000000000000000
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χ964-4-444-4-2-24-2-2-44-422221-2-2-22-224-4-11-211-1-12222-2-10023−2323−231-22-22-11-111-1-100000000023−230000−33−33−3−333000000000000000000000000000000000000
χ974-4-444-4-2-24-2-2-44-422221-2-2-22-224-4-11-211-1-12222-2-100−2323−23231-22-22-11-111-1-1000000000−232300003−33−333−3−3000000000000000000000000000000000000
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χ994-4-44-444-2-24-22-222-42-4-2-21-442-22-22-2-222-2-2-1-1221200000012-2-11-11-1-1-11100000−2i32i32i3−2i3000000000000000000000i3−i300000−i3i300000000000000000000
χ1004-4-44-444-2-24-22-222-42-4-2-21-442-22-22-2-222-2-2-1-1221200000012-2-11-11-1-1-111000002i3−2i3−2i32i3000000000000000000000−i3i300000i3−i300000000000000000000
χ1014-4-44-44-244-24-44-4-42-42-2-242-2-44-442-2-222-2-2-4-42242000000-22-2-442-2222-2-200000000000000000000000000000000000000000000000000000000000
χ1024-4-44-44-24-2-242-22-42-42-21-22-2-442-22-2122-2-222-1-1-220000001-112-2-11-1-1-1110000000000000000000000000000000000000003i−3i−3i3i0000000000000000
χ1034-4-44-44-24-2-242-22-42-42-21-22-2-442-22-2122-2-222-1-1-220000001-112-2-11-1-1-111000000000000000000000000000000000000000−3i3i3i−3i0000000000000000
χ1044-4-44-44-2-24-2-2-44-422221-2-22-22-2-44-11-2-1-1112222-2-10023−2323−2312-22-2-11-1-1-111000000000−23230000−33−3333−3−3000000000000000000000000000000000000
χ1054-4-44-44-2-24-2-2-44-422221-2-22-22-2-44-11-2-1-1112222-2-100−2323−232312-22-2-11-1-1-11100000000023−2300003−33−3−3−333000000000000000000000000000000000000
χ106888888-4-4-4-4-4-4-4-4-4-4-4-4222-4-4-4-4-4-42222222222222000000-12222-1-1-1-1-1-1-100000000000000000000000000000000000000000000000000000000000
χ1078888-8-8-4-4-4-4-4-4-4-4-4-4-4-4222444444222-2-2-2-2222222000000-1-2-2-2-2-1-1-1111100000000000000000000000000000000000000000000000000000000000
χ10888-8-8008-4-4-84-444-484-8-4-42000000-44400002-2-44-24000000200002-2-2000000000000000000000000000000000000000000000000000000000000000
χ10988-8-800-48-44-8-4448-4-84-42-4000000-44-20000-442-244000000200002-2-2000000000000000000000000000000000000000000000000000000000000000
χ11088-8-800-4-4-444-444-4-4442220000002-2-26-66-62-22-2-2-2000000-10000-111-33-3300000000000000000000000000000000000000000000000000000000000
χ11188-8-800-4-4-444-444-4-4442220000002-2-2-66-662-22-2-2-2000000-10000-1113-33-300000000000000000000000000000000000000000000000000000000000
χ1128-88-8008-4-4-8444-44-8-48-4-420000004440000-224-4-2-400000020000-2-22000000000000000000000000000000000000000000000000000000000000000
χ1138-88-800-48-44-844-4-848-4-42-400000044-200004-4-224-400000020000-2-22000000000000000000000000000000000000000000000000000000000000000
χ1148-88-800-4-4-44444-444-4-4222000000-2-2-26-6-66-22-22-22000000-1000011-1-333-300000000000000000000000000000000000000000000000000000000000
χ1158-88-800-4-4-44444-444-4-4222000000-2-2-2-666-6-22-22-22000000-1000011-13-3-3300000000000000000000000000000000000000000000000000000000000
χ1168-8-888-8-4-4-4-4-44-444444222-44-44-44-22222-2-2-2-2-2-22-2000000-12-22-21-11-1-11100000000000000000000000000000000000000000000000000000000000
χ1178-8-88-88-4-4-4-4-44-4444442224-44-44-4-222-2-222-2-2-2-22-2000000-1-22-221-1111-1-100000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).