Finite Group Databasebeta

← Group #13168377

Character table — Group #13168377

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size1111222222222222444444444444444444444666666668888888888888121212121212121212121212121212121212121212121212121218182424242424242424242424243636363636363636363636727272108108
order12223336666666663334666666666121212121212121244441212121236661212121212121212122444661212121212121212121212121212121212121212446661212121212121212124444412121212121212121244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111-11-11-1-11111111111111111111111-1-1-1-1-11-1-111111-1-1-1-1-1-11111-1-1-1-1-1
χ3111111111111111111111111111111111111111-1-111111111111111111111-11111-1-1-1-111-1-11111111111-1-111111-111-1-1-1-1-11-11-1-1-1-1-1-1-111-1-1-1
χ4111111111111111111111111111111111111111-1-111111111111111111-11-1-1-1-111-1-1-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1111-1-1-1-1-1-1111
χ51111111111111111111111111111111111111-1-111-1-1-1-111111111111111-11111-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-11-1111-1-1-1-1-1-11-1-1
χ61111111111111111111111111111111111111-1-111-1-1-1-11111111111111-1-1-11-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11111-11-11-1-1-1-1-1-1-111-111
χ71111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111-11-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-111-1-1-1-11-1-1-1-1-1-11111-1-1-111
χ81111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1
χ91111111111111111111-1111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-11-1-1-1111111-1-1-1-111-1-11111-1-1-1-111111-1-1-1-1-111-1-1-11-1-111111-1-1-11-11-1
χ101111111111111111111-1111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-11-1-1-11111-1-1-1-111-1-11111-1-1-1-111-1-1-111-11111-1-1-1-111-1-1-111-1-11-11-11
χ111111111111111111111-1111111111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-11-1-111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1111-1-11-1-1-1-111111-1-1-1-1-1-111-111-11
χ121111111111111111111-1111111111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111111-1-1111-1-11111-1-1111-1-11-1
χ131111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1111111-1-1-1-11111-1-1111-1-1-1-1-111-1-11-1-11111-1-1111-1-1-11
χ141111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-1-111-11111-1-1111-1-1-1-1-1-111-1111-1
χ151111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-1111-1-1-1-11111-1-111-1-1-1-1111111111-1-11-1-1-1-111-1-111-1-1-111-1-11-111-1
χ161111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-11111-1-111-1-1-1-1111111-1-1-111111-1-111-11-1-111111-1-1-11-1-11
χ17222222-122-12-12-1222-1-1222-1-1-1-1-1-1222-1-1-1-1-1-122002222-1-1-1-12-1-122-1-1-1-1222022-1-10000-1-10022-1-1-1-1-1-1-1-100-1-1-1-120-1-1000002020000000-1-1000
χ18222222-122-12-12-1222-1-1222-1-1-1-1-1-1222-1-1-1-1-1-122002222-1-1-1-12-1-122-1-1-1-1-22-20-2-2-1-10000-1-10022-1-1-1-1-1-1-1-1001111-201100000-20-2000000011000
χ19222222-122-12-12-1222-1-1222-1-1-1-1-1-1222-1-1-1-1-1-1-2-200-2-2-2-2-1-1-1-12-1-122-1-1-1-12-220221100001100-2-21111111100-1-1-1-120-1-100000-20-2000000011000
χ20222222-122-12-12-1222-1-1222-1-1-1-1-1-1222-1-1-1-1-1-1-2-200-2-2-2-2-1-1-1-12-1-122-1-1-1-1-2-2-20-2-21100001100-2-211111111001111-2011000002020000000-1-1000
χ21222222-122-12-12-1222-1-1-222-1-1-1-1-1-12-2-211111122002222-1-1-1-1-211-2-211112-2-2022-1-100001100-2-2-1-1-1-1111100-1-1-11-20110000020-200000001-1000
χ22222222-122-12-12-1222-1-1-222-1-1-1-1-1-12-2-211111122002222-1-1-1-1-211-2-21111-2-220-2-2-1-100001100-2-2-1-1-1-1111100111-120-1-100000-2020000000-11000
χ23222222-122-12-12-1222-1-1-222-1-1-1-1-1-12-2-2111111-2-200-2-2-2-2-1-1-1-1-211-2-2111122-2022110000-1-100221111-1-1-1-100-1-1-11-201100000-2020000000-11000
χ24222222-122-12-12-1222-1-1-222-1-1-1-1-1-12-2-2111111-2-200-2-2-2-2-1-1-1-1-211-2-21111-2220-2-2110000-1-100221111-1-1-1-100111-120-1-10000020-200000001-1000
χ2522222-12-12222-12-12-12-12-1-1-12-122-1-12222222200220000-1-1-1-1-1-1-1-1-1-1-1-1-12022-1-100222200-1-10000000000002-1-12-1-1-1-1-1-1-1-100202-1-1000000-100
χ2622222-12-12222-12-12-12-12-1-1-12-122-1-12222222200220000-1-1-1-1-1-1-1-1-1-1-1-1-1-20-221100222200-1-1000000000000-211-21-111-1-1-1-100-20-211000000100
χ2722222-12-12222-12-12-12-12-1-1-12-122-1-12222222200-2-20000-1-1-1-1-1-1-1-1-1-1-1-1-1202-2-1-100-2-2-2-200110000000000002-1-12-11-1-1111100-20-211000000100
χ2822222-12-12222-12-12-12-12-1-1-12-122-1-12222222200-2-20000-1-1-1-1-1-1-1-1-1-1-1-1-1-20-2-21100-2-2-2-20011000000000000-211-21111111100202-1-1000000-100
χ2922222-12-12222-12-12-12-1-2-1-1-12-122-1-1-2-2-2-2-2-2-2-200220000-1-1-1-111111111120-2-2-1-10022-2-200-1-10000000000002-1-1-21111-1-11100-202-1-1000000100
χ3022222-12-12222-12-12-12-1-2-1-1-12-122-1-1-2-2-2-2-2-2-2-200220000-1-1-1-1111111111-202-2110022-2-200-1-1000000000000-2112-11-1-1-1-1110020-211000000-100
χ3122222-12-12222-12-12-12-1-2-1-1-12-122-1-1-2-2-2-2-2-2-2-200-2-20000-1-1-1-111111111120-22-1-100-2-22200110000000000002-1-1-21-11111-1-10020-211000000-100
χ3222222-12-12222-12-12-12-1-2-1-1-12-122-1-1-2-2-2-2-2-2-2-200-2-20000-1-1-1-1111111111-20221100-2-2220011000000000000-2112-1-1-1-111-1-100-202-1-1000000100
χ332222-1222-12-12222-1-1-122-1-12-12-1-12-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-1222-1-1-1-1-1-102020022-1-1-1-12222-1-1-1-1-1-1-1-1-1-12200000200-1-1-1-12000000-1-1-1-100000
χ342222-1222-12-12222-1-1-122-1-12-12-1-12-1-1-122-1-1-1-122-2-2-1-1-1-1-1-1-1-1222-1-1-1-1-1-1020-20022111122-2-2-1-1-1-1-1-1-1-1-1-1-2-200000-2001111-2000000111100000
χ352222-1222-12-12222-1-1-122-1-12-12-1-12-1-1-122-1-1-1-1-2-2221111-1-1-1-1222-1-1-1-1-1-10-20200-2-2-1-1-1-1-2-2221111111111-2-200000200-1-1-1-1-2000000111100000
χ362222-1222-12-12222-1-1-122-1-12-12-1-12-1-1-122-1-1-1-1-2-2-2-21111-1-1-1-1222-1-1-1-1-1-10-20-200-2-21111-2-2-2-211111111112200000-20011112000000-1-1-1-100000
χ372222-1222-12-12222-1-1-12-2-1-12-12-1-12-111-2-211112222-1-1-1-1-1-1-1-1-2-2-21111110-20-20022-1-111-2-22211-1-1-1-111112200000-200-1-111-2000000-1-11100000
χ382222-1222-12-12222-1-1-12-2-1-12-12-1-12-111-2-2111122-2-2-1-1-1-1-1-1-1-1-2-2-21111110-202002211-1-1-2-2-2-211-1-1-1-11111-2-20000020011-1-1200000011-1-100000
χ392222-1222-12-12222-1-1-12-2-1-12-12-1-12-111-2-21111-2-2221111-1-1-1-1-2-2-2111111020-200-2-2-1-1112222-1-11111-1-1-1-1-2-200000-200-1-111200000011-1-100000
χ402222-1222-12-12222-1-1-12-2-1-12-12-1-12-111-2-21111-2-2-2-21111-1-1-1-1-2-2-2111111020200-2-211-1-122-2-2-1-11111-1-1-1-1220000020011-1-1-2000000-1-11100000
χ412-2-22222-2-2-222-2-22-22220-2-2-222-2-2-22000000002i−2i2-22i2i−2i−2i2-2-220000000000000002i−2i2-200002-2002i2i−2i−2i00002i−2i000000002-20000000002i−2i0000000
χ422-2-22222-2-2-222-2-22-22220-2-2-222-2-2-22000000002i−2i-222i2i−2i−2i2-2-220000000000000002i−2i-220000-22002i2i−2i−2i0000−2i2i00000000-22000000000−2i2i0000000
χ432-2-22222-2-2-222-2-22-22220-2-2-222-2-2-2200000000−2i2i2-2−2i−2i2i2i2-2-22000000000000000−2i2i2-200002-200−2i−2i2i2i0000−2i2i000000002-2000000000−2i2i0000000
χ442-2-22222-2-2-222-2-22-22220-2-2-222-2-2-2200000000−2i2i-22−2i−2i2i2i2-2-22000000000000000−2i2i-220000-2200−2i−2i2i2i00002i−2i00000000-220000000002i−2i0000000
χ452-2-22-122-21-2-12-2-221-1-12011-2-1211-2-1−i3i300−i3−i3i3i32i−2i2-2−i−iii-111-1000−i3i3−i3−i3i3i30000002i−2i-11−i3i3002-23−3−i−iii33−3−32i−2i00000000-11−i3i30000000−ii3−300000
χ462-2-22-122-21-2-12-2-221-1-12011-2-1211-2-1−i3i300−i3−i3i3i32i−2i-22−i−iii-111-1000−i3i3−i3−i3i3i30000002i−2i1-1i3−i300-223−3−i−iii33−3−3−2i2i000000001-1i3−i30000000i−i−3300000
χ472-2-22-122-21-2-12-2-221-1-12011-2-1211-2-1−i3i300−i3−i3i3i3−2i2i2-2ii−i−i-111-1000−i3i3−i3−i3i3i3000000−2i2i-11−i3i3002-2−33ii−i−i−3−333−2i2i00000000-11−i3i30000000i−i−3300000
χ482-2-22-122-21-2-12-2-221-1-12011-2-1211-2-1−i3i300−i3−i3i3i3−2i2i-22ii−i−i-111-1000−i3i3−i3−i3i3i3000000−2i2i1-1i3−i300-22−33ii−i−i−3−3332i−2i000000001-1i3−i30000000−ii3−300000
χ492-2-22-122-21-2-12-2-221-1-12011-2-1211-2-1i3−i300i3i3−i3−i32i−2i2-2−i−iii-111-1000i3−i3i3i3−i3−i30000002i−2i-11i3−i3002-2−33−i−iii−3−3332i−2i00000000-11i3−i30000000−ii−3300000
χ502-2-22-122-21-2-12-2-221-1-12011-2-1211-2-1i3−i300i3i3−i3−i32i−2i-22−i−iii-111-1000i3−i3i3i3−i3−i30000002i−2i1-1−i3i300-22−33−i−iii−3−333−2i2i000000001-1−i3i30000000i−i3−300000
χ512-2-22-122-21-2-12-2-221-1-12011-2-1211-2-1i3−i300i3i3−i3−i3−2i2i2-2ii−i−i-111-1000i3−i3i3i3−i3−i3000000−2i2i-11i3−i3002-23−3ii−i−i33−3−3−2i2i00000000-11i3−i30000000i−i3−300000
χ522-2-22-122-21-2-12-2-221-1-12011-2-1211-2-1i3−i300i3i3−i3−i3−2i2i-22ii−i−i-111-1000i3−i3i3i3−i3−i3000000−2i2i1-1−i3i300-223−3ii−i−i33−3−32i−2i000000001-1−i3i30000000−ii−3300000
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χ5544444-2-2-24-24-2-2-2-24-2-21-4-2-21-21-2-21-2-4-42222220000000011112-1-122-1-1-1-140-40-2-20000000000000000000000-211220-1-100000000000000000000
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χ584444-24-24-2-2-2-24-24-2-21-24-2-2-21-211-2-2-2-2-2-21111-4-400222211114-2-2-2-211110-40000220000220022-1-1-1-1-1-1-1-1000000000000000000000000000000
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χ7944-4-4-24-242222-4-2-4-2-21-20-22-2-121-12200−23233−33−30000−2323−232311-1-10−2323003−33−30000000000000000003−33−33-33-3000000000000000000000000000000
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χ864-44-4-244-4-242-44-4-42-2-2402-2-42-42-2420000000000002i3−2i3−2i32i3-22-220000000000000000000000000002i3−2i3−2i32i30000000000000000000000000000000000
χ874-44-4-24-2-4-2-22242-42-21-202-22-12-11-2200003i−3i−3i3i0000−2i32i32i3−2i31-11-1000003i−3i−3i3i000000000000−23230000i3−i3−i3i33−3−33000000000000000000000000000000
χ884-44-4-24-2-4-2-22242-42-21-202-22-12-11-2200003i−3i−3i3i00002i3−2i3−2i32i31-11-1000003i−3i−3i3i00000000000023−230000−i3i3i3−i3−333−3000000000000000000000000000000
χ894-44-4-24-2-4-2-22242-42-21-202-22-12-11-220000−3i3i3i−3i0000−2i32i32i3−2i31-11-100000−3i3i3i−3i00000000000023−230000i3−i3−i3i3−333−3000000000000000000000000000000
χ904-44-4-24-2-4-2-22242-42-21-202-22-12-11-220000−3i3i3i−3i00002i3−2i3−2i32i31-11-100000−3i3i3i−3i000000000000−23230000−i3i3i3−i33−3−33000000000000000000000000000000
χ914-4-4444-2-4-424-2-424-44-2-20-4-42-2-22224000000004i−4i004i4i−4i−4i-222-2000000000000000−2i2i0000000000−2i−2i2i2i0000000000000000000000000000000000
χ924-4-4444-2-4-424-2-424-44-2-20-4-42-2-2222400000000−4i4i00−4i−4i4i4i-222-20000000000000002i−2i00000000002i2i−2i−2i0000000000000000000000000000000000
χ934-4-444-242-4-4442-4-2-4-24-202224-2-4-42-200000000004-40000-222-2000000000000000004-40000-2200000000000000000000-22000000000000000000
χ944-4-444-242-4-4442-4-2-4-24-202224-2-4-42-20000000000-440000-222-200000000000000000-4400002-2000000000000000000002-2000000000000000000
χ954-4-44-24-2-422-2-2-4242-21-202221-2-1-12-2−2i32i300i3i3−i3−i34i−4i00−2i−2i2i2i1-1-11000−2i32i3i3i3−i3−i3000000−2i2i0000000023−23ii−i−i−3−333000000000000000000000000000000
χ964-4-44-24-2-422-2-2-4242-21-202221-2-1-12-2−2i32i300i3i3−i3−i3−4i4i002i2i−2i−2i1-1-11000−2i32i3i3i3−i3−i30000002i−2i00000000−2323−i−iii33−3−3000000000000000000000000000000
χ974-4-44-24-2-422-2-2-4242-21-202221-2-1-12-22i3−2i300−i3−i3i3i34i−4i00−2i−2i2i2i1-1-110002i3−2i3−i3−i3i3i3000000−2i2i00000000−2323ii−i−i33−3−3000000000000000000000000000000
χ984-4-44-24-2-422-2-2-4242-21-202221-2-1-12-22i3−2i300−i3−i3i3i3−4i4i002i2i−2i−2i1-1-110002i3−2i3−i3−i3i3i30000002i−2i0000000023−23−i−iii−3−333000000000000000000000000000000
χ994-4-44-2-2422-4-242-4-221-2-20-1-12-2-22221−2i32i300−2i3−2i32i32i3004-400001-1-11000i3−i3i3i3−i3−i300000000-22−2i32i300-22000000000000000000001-1i3−i30000000000000000
χ1004-4-44-2-2422-4-242-4-221-2-20-1-12-2-22221−2i32i300−2i3−2i32i32i300-4400001-1-11000i3−i3i3i3−i3−i3000000002-22i3−2i3002-200000000000000000000-11−i3i30000000000000000
χ1014-4-44-2-2422-4-242-4-221-2-20-1-12-2-222212i3−2i3002i32i3−2i3−2i3004-400001-1-11000−i3i3−i3−i3i3i300000000-222i3−2i300-22000000000000000000001-1−i3i30000000000000000
χ1024-4-44-2-2422-4-242-4-221-2-20-1-12-2-222212i3−2i3002i32i3−2i3−2i300-4400001-1-11000−i3i3−i3−i3i3i3000000002-2−2i32i3002-200000000000000000000-11i3−i30000000000000000
χ1038888-4-4-4-4-4-4-4-4-4-4-4-42228222222222-4-4-4-4222200000000-1-1-1-1-42222-1-1-1-100000000000000000000000000000000000000000000000000000000
χ1048888-4-4-4-4-4-4-4-4-4-4-4-4222-82222222224444-2-2-2-200000000-1-1-1-14-2-2-2-2111100000000000000000000000000000000000000000000000000000000
χ10588-8-8-4-48-44-84-8484-42-4-402-2-444-444-2000000000000000022-2-200000000000000000000000000000000000000000000000000000000000000000
χ10688-8-8-4-4-4-444444-44-422202-22-2-22-2-2-20043−43−2323−232300000000-1-1110−2323003−33−300000000000000000000000000000000000000000000000000000000
χ10788-8-8-4-4-4-444444-44-422202-22-2-22-2-2-200−434323−2323−2300000000-1-111023−2300−33−3300000000000000000000000000000000000000000000000000000000
χ1088-88-88-4-448-4-84-444-8-4-4204-4-24-24-42400000000000000002-22-200000000000000000000000000000000000000000000000000000000000000000
χ1098-88-8-4-484-484-8-4-8442-4-40-224444-4-4-200000000000000002-22-200000000000000000000000000000000000000000000000000000000000000000
χ1108-88-8-4-4-44-4-444-44442220-22-2-2-2-222-200006i−6i−6i6i00000000-11-1100000−3i3i3i−3i00000000000000000000000000000000000000000000000000000000
χ1118-88-8-4-4-44-4-444-44442220-22-2-2-2-222-20000−6i6i6i−6i00000000-11-11000003i−3i−3i3i00000000000000000000000000000000000000000000000000000000
χ1128-8-888-4-44-848-444-4-8-4-42044-2-4244-2-400000000000000002-2-2200000000000000000000000000000000000000000000000000000000000000000
χ1138-8-88-4-4-4444-4-444-442220-2-2-222-2-2-22−4i34i3002i32i3−2i3−2i300000000-111-10002i3−2i3−i3−i3i3i300000000000000000000000000000000000000000000000000000000
χ1148-8-88-4-4-4444-4-444-442220-2-2-222-2-2-224i3−4i300−2i3−2i32i32i300000000-111-1000−2i32i3i3i3−i3−i300000000000000000000000000000000000000000000000000000000

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