Finite Group Databasebeta

← Group #13172245

Character table — Group #13172245

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117
size111122222222222222444444444444444444444466666688888888888812121212121212121212121212121212121212121212121818181818182424242424242424242424242424363636363636363636363654547272108
order122222333666666666333666666666666666666644121212123666666666664444412121212121212121212121212121212121244444412121212121212121212121212122441212121212121212446124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-11-111111111111111111111111-1-1-1-11-11-11111-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111-11-11111-1-1-1-1111111111111-1-1-1-1-1-111-11-11-1-1-1-111111-11-1-1-1-1-1-1-1-1-1-111-1
χ41111111111111111111111111111111111111111111111111111111111-1-1-1-1111-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1111111-1-11
χ51111111111111111111111111111111111111111-1-1-1-1-1-11111111111111111-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-11-1-1-1-1-11111-1-1-1-1-1
χ61111111111111111111111111111111111111111-1-1-1-1-1-11111111111111-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-11111-1-1-1-11-11-1-1-1-1-1-1-1-111111
χ71111111111111111111111111111111111111111-1-1-1-1-1-1111111111111-11-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-11-11-1-1-1-11111-1-1-11111-1-1-1-111-1-11
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
χ91111-1-1111111111111111-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1111-1-1-1-111-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-111111-111-1-111-1-111-1-11-1-111-1-111-1-1111-1-1
χ101111-1-1111111111111111-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1111-1-1-1-11-1-11-1-1-111-1-111-1-11111-1-1-1-1-1-111-1-1-111-1-1111-1-1-1-111-11111-1-1-1-111-1-1-111
χ111111-1-1111111111111111-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1111-1-1-1-1-111-1-1-1-1-1-11111-1-11111-1-1-1-111-1-1-1-11-1-111-1-1-11111-1-111-1-1-111-1-111-1-11-11
χ121111-1-1111111111111111-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1111-1-1-1-1-1-111-1-1-1-1-11111-1-11111-1-1-1-111-1-111-11-1-111-1-111-1-111-1-11-1-11111-1-111-11-1
χ131111-1-1111111111111111-1-1-1-1-1-11111-1-1-1-111111-1-1-1-1-1-11-1-1-1-1111-1-1-1-111-1-111111-1-1-1-111-1-1-1-1111111-1-1111-111-1-111-1-111-1-1-1-11-1-11111-1-1-1-1-111
χ141111-1-1111111111111111-1-1-1-1-1-11111-1-1-1-111111-1-1-1-1-1-11-1-1-1-1111-1-1-1-11-1-1111111-1-1-1-111-1-1-1-1111111-1-1-1-1-111-1-1111-1-1-1-11111-1-1-111-1-111111-1-1
χ151111-1-1111111111111111-1-1-1-1-1-11111-1-1-1-111111-1-1-1-1-1-11-1-1-1-1111-1-1-1-1-111-1111-1-111-1-111-1-1-1-11111-1-111-1-11-1-111-1-1-11111-1-1-11111-1-1-1-11111-11-1
χ161111-1-1111111111111111-1-1-1-1-1-11111-1-1-1-111111-1-1-1-1-1-11-1-1-1-1111-1-1-1-1-1-111111-1-111-1-111-1-1-1-11111-1-11111-11-1-111-1-111-1-1111-1-111-1-111-1-1-1-11-11
χ1722222222-12-1-12222-122-1-12222-1-12-1-1-1-1-1-1-122-1-1-1222222-122-1-1-1-1-1-1-1-1-102022220000-1-1-1-1-1-1-1-1-1-1-1-1000000-1-102020000-1-1-1-12020000000000-1-10
χ1822222222-12-1-12222-122-1-12222-1-12-1-1-1-1-1-1-122-1-1-1222222-122-1-1-1-1-1-1-1-1-10-20-22220000-1-1-1-1-1-1-1-1-1-1-1-1000000110-20-200001111-20-20000000000110
χ1922222222-12-1-12222-122-1-12222-1-12-1-1-1-1-1-1-122-1-1-1-2-2-2-2-2-2-122-1-1-1-1-1-1-1-1-10202-2-2-20000111111111111000000-1-102020000-1-1-1-1-20-20000000000110
χ2022222222-12-1-12222-122-1-12222-1-12-1-1-1-1-1-1-122-1-1-1-2-2-2-2-2-2-122-1-1-1-1-1-1-1-1-10-20-2-2-2-20000111111111111000000110-20-2000011112020000000000-1-10
χ212222222-122222-1-1-122-12-122-1-122-12-1-1-1-1-1-1-1-122-122-1-1-1-1-1-1-122-1-1-1-1-1-1-120202-1-1-1-1-1-12222-1-1-1-1-1-1-1-1222200002020-1-1-1-10000000-1-1-1-1000000000
χ222222222-122222-1-1-122-12-122-1-122-12-1-1-1-1-1-1-1-122-122-1-1-1-1-1-1-122-1-1-1-1-1-1-1-20-202-1-111112222-1-1-1-1-1-1-1-1-2-2-2-20000-20-20111100000001111000000000
χ232222222-122222-1-1-122-12-122-1-122-12-1-1-1-1-1-1-1-122-1-2-21111-1-1-122-1-1-1-1-1-1-12020-211-1-1-1-1-2-2-2-211111111-2-2-2-200002020-1-1-1-100000001111000000000
χ242222222-122222-1-1-122-12-122-1-122-12-1-1-1-1-1-1-1-122-1-2-21111-1-1-122-1-1-1-1-1-1-1-20-20-2111111-2-2-2-21111111122220000-20-2011110000000-1-1-1-1000000000
χ25222222-122-122-12222-1-1-12-1-12222-1-1222222-1-1-1-12000000-1-1-1-1-1-1-1-1-1-1-1-12222000222200000000000000002222-1-1-1-1-1-1-1-1-1-1-1-10200000-1-1-1-100000
χ26222222-122-122-12222-1-1-12-1-12222-1-1222222-1-1-1-12000000-1-1-1-1-1-1-1-1-1-1-1-12-22-200022220000000000000000-2-2-2-2-11-11-1-1-1-111110-200000111100000
χ27222222-122-122-12222-1-1-12-1-12222-1-1222222-1-1-1-12000000-1-1-1-1-1-1-1-1-1-1-1-1-22-22000-2-2-2-20000000000000000-2-2221-11-11111-1-1-1-10-200000111100000
χ28222222-122-122-12222-1-1-12-1-12222-1-1222222-1-1-1-12000000-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2000-2-2-2-2000000000000000022-2-21111111111110200000-1-1-1-100000
χ292222-2-222-12-1-12222-122-1-1-2-2-2-2112-1-1-1111122-1-1-1222222-1-2-211-1-1-11111020-2-2-2-20000-1-111-1-1-1-11111000000-11020-20000-1-11120-20000000000-110
χ302222-2-222-12-1-12222-122-1-1-2-2-2-2112-1-1-1111122-1-1-1222222-1-2-211-1-1-111110-202-2-2-20000-1-111-1-1-1-111110000001-10-202000011-1-1-20200000000001-10
χ312222-2-222-12-1-12222-122-1-1-2-2-2-2112-1-1-1111122-1-1-1-2-2-2-2-2-2-1-2-211-1-1-11111020-2222000011-1-11111-1-1-1-1000000-11020-20000-1-111-20200000000001-10
χ322222-2-222-12-1-12222-122-1-1-2-2-2-2112-1-1-1111122-1-1-1-2-2-2-2-2-2-1-2-211-1-1-111110-202222000011-1-11111-1-1-1-10000001-10-202000011-1-120-20000000000-110
χ332222-2-22-122222-1-1-122-12-1-2-211-2-2-12-1-11111-1-122-122-1-1-1-1-111-2-2-1-1-1111120-20-211-1-11122-2-2-1-1-1-11111-2-222000020-20-1-1110000000-1-111000000000
χ342222-2-22-122222-1-1-122-12-1-2-211-2-2-12-1-11111-1-122-122-1-1-1-1-111-2-2-1-1-11111-2020-21111-1-122-2-2-1-1-1-1111122-2-20000-202011-1-1000000011-1-1000000000
χ352222-2-22-122222-1-1-122-12-1-2-211-2-2-12-1-11111-1-122-1-2-21111-111-2-2-1-1-1111120-202-1-1-1-111-2-2221111-1-1-1-122-2-2000020-20-1-111000000011-1-1000000000
χ362222-2-22-122222-1-1-122-12-1-2-211-2-2-12-1-11111-1-122-1-2-21111-111-2-2-1-1-11111-20202-1-111-1-1-2-2221111-1-1-1-1-2-2220000-202011-1-10000000-1-111000000000
χ372222-2-2-122-122-12222-1-1-1211-2-2-2-2-1-122-2-2-2-2-1-1-1-12000000-11111-1-1-1111122-2-200022-2-20000000000000000222-2-1-111-1-111-1-1110-200000-1-11100000
χ382222-2-2-122-122-12222-1-1-1211-2-2-2-2-1-122-2-2-2-2-1-1-1-12000000-11111-1-1-111112-2-2200022-2-20000000000000000-2-2-22-111-1-1-11111-1-1020000011-1-100000
χ392222-2-2-122-122-12222-1-1-1211-2-2-2-2-1-122-2-2-2-2-1-1-1-12000000-11111-1-1-11111-222-2000-2-2220000000000000000-2-22-21-1-1111-1-1-1-111020000011-1-100000
χ402222-2-2-122-122-12222-1-1-1211-2-2-2-2-1-122-2-2-2-2-1-1-1-12000000-11111-1-1-11111-2-222000-2-222000000000000000022-2211-1-111-1-111-1-10-200000-1-11100000
χ412-22-200222-22-2-2-22-2-22222000000-2-22-200002-22-2-22i−2i2i2i−2i−2i200002-2-20000000000000002i−2i002i2i−2i−2i000000002-20000000000000000000002-2002i−2i000
χ422-22-200222-22-2-2-22-2-22222000000-2-22-200002-22-2-22i−2i2i2i−2i−2i200002-2-20000000000000002i−2i002i2i−2i−2i00000000-22000000000000000000000-2200−2i2i000
χ432-22-200222-22-2-2-22-2-22222000000-2-22-200002-22-2-2−2i2i−2i−2i2i2i200002-2-2000000000000000−2i2i00−2i−2i2i2i000000002-20000000000000000000002-200−2i2i000
χ442-22-200222-22-2-2-22-2-22222000000-2-22-200002-22-2-2−2i2i−2i−2i2i2i200002-2-2000000000000000−2i2i00−2i−2i2i2i00000000-22000000000000000000000-22002i−2i000
χ452-2-222-22222-2-2-22-2-22-22222-22-22-222-2-222-2-2-2-2-2-2200000022-22-2-22-222-2-2000000000000000000000002i−2i2i−2i00000000000000000002i−2i2i−2i000000000
χ462-2-222-22222-2-2-22-2-22-22222-22-22-222-2-222-2-2-2-2-2-2200000022-22-2-22-222-2-200000000000000000000000−2i2i−2i2i0000000000000000000−2i2i−2i2i000000000
χ472-2-222-22-122-2-2-2-1112-2-12-12-2-112-2-1211-1-11111-2-2-100−i3i3−i3i3-1-112-21-11-1-11100000−i3i33−33−30000−i3i3−i3i3−i3−i3i3i32i−2i2i−2i000000003−33−30000000−ii−ii000000000
χ482-2-222-22-122-2-2-2-1112-2-12-12-2-112-2-1211-1-11111-2-2-100−i3i3−i3i3-1-112-21-11-1-11100000−i3i3−33−330000−i3i3−i3i3−i3−i3i3i3−2i2i−2i2i00000000−33−330000000i−ii−i000000000
χ492-2-222-22-122-2-2-2-1112-2-12-12-2-112-2-1211-1-11111-2-2-100i3−i3i3−i3-1-112-21-11-1-11100000i3−i33−33−30000i3−i3i3−i3i3i3−i3−i3−2i2i−2i2i000000003−33−30000000i−ii−i000000000
χ502-2-222-22-122-2-2-2-1112-2-12-12-2-112-2-1211-1-11111-2-2-100i3−i3i3−i3-1-112-21-11-1-11100000i3−i3−33−330000i3−i3i3−i3i3i3−i3−i32i−2i2i−2i00000000−33−330000000−ii−ii000000000
χ512-2-22-222222-2-2-22-2-22-2222-22-22-2222-2-2-2-222-2-2-2-220000002-22-22-22-2-2-222000000000000000000000002i−2i−2i2i0000000000000000000−2i2i2i−2i000000000
χ522-2-22-222222-2-2-22-2-22-2222-22-22-2222-2-2-2-222-2-2-2-220000002-22-22-22-2-2-22200000000000000000000000−2i2i2i−2i00000000000000000002i−2i−2i2i000000000
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χ552-2-22-222-122-2-2-2-1112-2-12-1-221-1-22-121111-1-111-2-2-100i3−i3i3−i3-11-1-221-1111-1-100000−i3i33−3−330000i3−i3i3−i3−i3−i3i3i32i−2i−2i2i000000003−3−330000000i−i−ii000000000
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χ574444444-2-24-2-24-2-2-2-24-2-2144-2-2-2-2-2-2111111-2-2-2-2144-2-2-2-21-2-2-2-2111111100004-2-20000-2-2-2-211111111000000000000000000000000000000000000
χ584444444-2-24-2-24-2-2-2-24-2-2144-2-2-2-2-2-2111111-2-2-2-21-4-422221-2-2-2-211111110000-42200002222-1-1-1-1-1-1-1-1000000000000000000000000000000000000
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χ7744-4-4004-2-2-42-2422-22-4-2-2100000022-11-33-332-22-2-100−232323−2310000-1-11-33-33000000000000023−233−3−33−33−33000000000000000000000000000000000000
χ7844-4-400-2442-44-2-4-44-42-2-2400000022-4400002-22-2-4000000-2000022-20000000000000000000000000000000000000000000000000000000023−2300000
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χ914-4-444-44-2-2422-4-222-2-4-2-214-4-22-22-2-2-1-111-1-12222100−2i32i3−2i32i31-22-22-11-111-1-100000−2i32i300000000i3−i3i3−i3i3i3−i3−i3000000000000000000000000000000000000
χ924-4-444-44-2-2422-4-222-2-4-2-214-4-22-22-2-2-1-111-1-122221002i3−2i32i3−2i31-22-22-11-111-1-1000002i3−2i300000000−i3i3−i3i3−i3−i3i3i3000000000000000000000000000000000000
χ934-4-444-4-244-2-4-424-4-442-2-24-224-44-4-2-2-4-444-4-422224000000-2-22-222-22-2-22200000000000000000000000000000000000000000000000000000000000
χ944-4-444-4-24-2-22224-4-4-22-21-2-224-4-22-2122-2-22222-1-1-20000001-221-1-11-111-1-10000000000000000000000000000000000000003i−3i3i−3i0000000000000000
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χ1004-4-44-444-2-2422-4-222-2-4-2-21-442-22-2-2-2-1-1-1-11122221002i3−2i32i3−2i312-22-2-11-1-1-11100000−2i32i300000000−i3i3−i3i3i3i3−i3−i3000000000000000000000000000000000000
χ1014-4-44-44-244-2-4-424-4-442-2-242-2-44-44-2-2-4-4-4-44422224000000-22-22-22-2222-2-200000000000000000000000000000000000000000000000000000000000
χ1024-4-44-44-24-2-22224-4-4-22-21-22-2-442-2-212222-2-222-1-1-200000012-2-11-11-1-1-1110000000000000000000000000000000000000003i−3i−3i3i0000000000000000
χ1034-4-44-44-24-2-22224-4-4-22-21-22-2-442-2-212222-2-222-1-1-200000012-2-11-11-1-1-111000000000000000000000000000000000000000−3i3i3i−3i0000000000000000
χ1044-4-44-44-2-24-2-4-42-222421-2-22-22-2-441-22222-2-2-1-122-20000001-112-2-11-1-1-111000000023−23−2323000000000000000000000000−333−300000000000000000000
χ1054-4-44-44-2-24-2-4-42-222421-2-22-22-2-441-22222-2-2-1-122-20000001-112-2-11-1-1-1110000000−232323−230000000000000000000000003−3−3300000000000000000000
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
χ1078888-8-8-4-4-4-4-4-4-4-4-4-4-4-42224444442222-2-2-2-222222000000-1-2-2-2-2-1-1-1111100000000000000000000000000000000000000000000000000000000000
χ10888-8-800-48-444-4-4-8-8844-42-40000004-24-400004-4-22400000020000-2-22000000000000000000000000000000000000000000000000000000000000000
χ10988-8-800-4-484-88-444-4-842-4-4000000-244-40000-224-4400000020000-2-22000000000000000000000000000000000000000000000000000000000000000
χ11088-8-800-4-4-444-4-444-444222000000-2-2-226-66-6-22-22-2000000-1000011-1-33-3300000000000000000000000000000000000000000000000000000000000
χ11188-8-800-4-4-444-4-444-444222000000-2-2-22-66-66-22-22-2000000-1000011-13-33-300000000000000000000000000000000000000000000000000000000000
χ1128-88-800-48-44-444-88-84-4-42-40000004-2-440000-442-24000000200002-2-2000000000000000000000000000000000000000000000000000000000000000
χ1138-88-800-4-4848-844-44-8-42-4-4000000-24-4400002-2-444000000200002-2-2000000000000000000000000000000000000000000000000000000000000000
χ1148-88-800-4-4-44-4444-444-4222000000-2-22-26-6-662-22-2-2000000-10000-111-333-300000000000000000000000000000000000000000000000000000000000
χ1158-88-800-4-4-44-4444-444-4222000000-2-22-2-666-62-22-2-2000000-10000-1113-3-3300000000000000000000000000000000000000000000000000000000000
χ1168-8-888-8-4-4-4-4444-444-44222-44-44-4422-2-222-2-2-2-2-2-22000000-12-22-21-11-1-11100000000000000000000000000000000000000000000000000000000000
χ1178-8-88-88-4-4-4-4444-444-442224-44-44-422-2-2-2-222-2-2-2-22000000-1-22-221-1111-1-100000000000000000000000000000000000000000000000000000000000

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