Finite Group Databasebeta

← Group #13168556

Character table — Group #13168556

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117
size1111222222222222444444444444444444444666666666688888888888881212121212121212121212121212121212121212121212121218181818242424242424242424242424363636363636363636365454727272108
order122233366666666633346666666661212121212121212444444121212123666121212121212121212444121212121212121212121212121212121212121212122244121212121212121212121212244466661212441212124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-11-11111-1-1111111111111111111-1-1-1-11-1-1-1-1-111111-1-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111-1-1111111111111111111-11111111-1-1-1-111-1-111111111-1-1-1-111-111111-1-1-1-1-11-11-1-1-1-1-1-1-1-111-1-1
χ411111111111111111111111111111111111111111-1-111111111111111111-1-1-11111-1-1-1-1-1-111-1-111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-11111-1-111
χ51111111111111111111111111111111111111-1-1-1-111-1-1-1-11111111111111111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-111111111111111-1-11-1-1-1-1-111-1-1-1-11-1
χ61111111111111111111111111111111111111-1-1-1-111-1-1-1-11111111111111-11-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-11111-11-11-1-1-1-1-1-11111-11
χ71111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111111111111111-11-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-111111-1-1-1-11-1-1-11111-1-111-1-1-11
χ81111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1111-1
χ91111111111111111111-1111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-11-1-111-1-11111-1-111111111-1-1-1-11111-1-1-1111-1-111-1-1-1-1-1111-1-111-1-11-1-11
χ101111111111111111111-1111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-111-1-111111111-1-1-1-111-1-111-1-1-1-11111-1-1-111-111-1-1-1-111-111-1
χ111111111111111111111-1111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-111-1-111-1-11111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111-111-1-111-1-1111-11-1
χ121111111111111111111-1111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-111111-1-1-111-1-11111-1-1-1-11111-1-1-11-11
χ131111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-11-1-1-1-1111111-1-1-1-111-1-1-1-11111-1-111-1-1-1111-1-111-1-111-1-1-1-1111111-11-1-1
χ141111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-11-1-111-1-111-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-11111-1-11-111-1-111-1-1-1-11-111
χ151111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-111-1-1-11111-1-111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-111-111-111-1-1-1-1-1-1-1111
χ161111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111111-1-1-111-1-111-1-1-1111-1-111111-1-1-1
χ17222222-1-122-1-122222-1-122-1-1-12-1-12-1-1-122-1-1-1-1222222-1-1-1-1-1-1-1-12-1-122-1-1-1-1020-1-12200-1-1-1-12222-1-1-1-1-1-1-1-1220000200000-1-1-1-12000-1-1-1-100000000
χ18222222-1-122-1-122222-1-122-1-1-12-1-12-1-1-122-1-1-1-12222-2-2-1-1-1-1-1-1-1-12-1-122-1-1-1-10-20-1-12200111122-2-2-1-1-1-1-1-1-1-1-2-20000-2000001111-2000111100000000
χ19222222-1-122-1-122222-1-122-1-1-12-1-12-1-1-122-1-1-1-1-2-2-2-2221111-1-1-1-12-1-122-1-1-1-102011-2-200-1-1-1-1-2-22211111111-2-20000200000-1-1-1-1-2000111100000000
χ20222222-1-122-1-122222-1-122-1-1-12-1-12-1-1-122-1-1-1-1-2-2-2-2-2-21111-1-1-1-12-1-122-1-1-1-10-2011-2-2001111-2-2-2-211111111220000-20000011112000-1-1-1-100000000
χ21222222-1-122-1-122222-1-1-22-1-1-12-1-12-111-2-2111122-2-2221111-1-1-1-1-211-2-211110-20-1-1-2-200-1-1112222-1-1-1-11111220000-200000-1-111-2000-1-11100000000
χ22222222-1-122-1-122222-1-1-22-1-1-12-1-12-111-2-2111122-2-2-2-21111-1-1-1-1-211-2-21111020-1-1-2-20011-1-122-2-2-1-1-1-11111-2-2000020000011-1-1200011-1-100000000
χ23222222-1-122-1-122222-1-1-22-1-1-12-1-12-111-2-21111-2-22222-1-1-1-1-1-1-1-1-211-2-211110-20112200-1-111-2-2221111-1-1-1-1-2-20000-200000-1-111200011-1-100000000
χ24222222-1-122-1-122222-1-1-22-1-1-12-1-12-111-2-21111-2-222-2-2-1-1-1-1-1-1-1-1-211-2-2111102011220011-1-1-2-2-2-21111-1-1-1-122000020000011-1-1-2000-1-11100000000
χ2522222-1222-1222-12-1-12-12-122-1-1-1-1-1222-1-1-1-1-1-12222002222-1-1-1-1222-1-1-1-1-1-120222-1-1220000-1-100-1-1-1-1-1-1-1-100002-10-1-1-1-1-10000020200000000-1-100
χ2622222-1222-1222-12-1-12-12-122-1-1-1-1-1222-1-1-1-1-1-12222002222-1-1-1-1222-1-1-1-1-1-1-20-222-1-1-2-20000-1-100-1-1-1-1-1-1-1-10000-2101111100000-20-2000000001100
χ2722222-1222-1222-12-1-12-12-122-1-1-1-1-1222-1-1-1-1-1-1-2-2-2-200-2-2-2-2-1-1-1-1222-1-1-1-1-1-1202-2-21122000011001111111100002-10-1-1-1-1-100000-20-2000000001100
χ2822222-1222-1222-12-1-12-12-122-1-1-1-1-1222-1-1-1-1-1-1-2-2-2-200-2-2-2-2-1-1-1-1222-1-1-1-1-1-1-20-2-2-211-2-200001100111111110000-210111110000020200000000-1-100
χ2922222-1222-1222-12-1-12-1-2-122-1-1-1-1-12-2-211111122-2-200-2-2-2-2-1-1-1-1-2-2-211111120-22211220000-1-100-1-1-1-111110000-210-1-1-11100000-20200000000-1100
χ3022222-1222-1222-12-1-12-1-2-122-1-1-1-1-12-2-211111122-2-200-2-2-2-2-1-1-1-1-2-2-2111111-2022211-2-20000-1-100-1-1-1-1111100002-10111-1-10000020-2000000001-100
χ3122222-1222-1222-12-1-12-1-2-122-1-1-1-1-12-2-2111111-2-222002222-1-1-1-1-2-2-211111120-2-2-2-1-122000011001111-1-1-1-10000-210-1-1-1110000020-2000000001-100
χ3222222-1222-1222-12-1-12-1-2-122-1-1-1-1-12-2-2111111-2-222002222-1-1-1-1-2-2-2111111-202-2-2-1-1-2-2000011001111-1-1-1-100002-10111-1-100000-20200000000-1100
χ332222-1222-1222-12-12-1-122-1-1-12-122-1-1222222220000220000-1-1-1-1-1-1-1-1-1-1-1-1-12220000-1-1222200-1-1000000000022-12-12-1-1-1-1-1-1-1-100200000-1-10000-10
χ342222-1222-1222-12-12-1-122-1-1-12-122-1-1222222220000220000-1-1-1-1-1-1-1-1-1-1-1-1-1-22-2000011222200-1-10000000000-2-21-2-1-21111-1-1-1-100-20000011000010
χ352222-1222-1222-12-12-1-122-1-1-12-122-1-1222222220000-2-20000-1-1-1-1-1-1-1-1-1-1-1-1-12-220000-1-1-2-2-2-200110000000000-2-2-1212-1-1-1-1111100-20000011000010
χ362222-1222-1222-12-12-1-122-1-1-12-122-1-1222222220000-2-20000-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2000011-2-2-2-200110000000000221-21-21111111100200000-1-10000-10
χ372222-1222-1222-12-12-1-12-2-1-1-12-122-1-1-2-2-2-2-2-2-2-20000220000-1-1-1-11111111112-2-20000-1-122-2-200-1-10000000000221-212-1-111-1-11100-200000-1-1000010
χ382222-1222-1222-12-12-1-12-2-1-1-12-122-1-1-2-2-2-2-2-2-2-20000220000-1-1-1-1111111111-2-2200001122-2-200-1-10000000000-2-2-121-211-1-1-1-11100200000110000-10
χ392222-1222-1222-12-12-1-12-2-1-1-12-122-1-1-2-2-2-2-2-2-2-20000-2-20000-1-1-1-111111111122-20000-1-1-2-22200110000000000-2-21-2-12-1-11111-1-100200000110000-10
χ402222-1222-1222-12-12-1-12-2-1-1-12-122-1-1-2-2-2-2-2-2-2-20000-2-20000-1-1-1-1111111111-222000011-2-2220011000000000022-12-1-211-1-111-1-100-200000-1-1000010
χ412-22-2222-2-22-22-2-22-222202-2-2-2-22-2-2200000000002-20022-2-222-2-2000000000000002-20000000000000022-2-2002i−2i000000000000000000002i−2i2i−2i0000
χ422-22-2222-2-22-22-2-22-222202-2-2-2-22-2-2200000000002-20022-2-222-2-2000000000000002-20000000000000022-2-200−2i2i00000000000000000000−2i2i−2i2i0000
χ432-22-2222-2-22-22-2-22-222202-2-2-2-22-2-220000000000-2200-2-22222-2-200000000000000-2200000000000000-2-222002i−2i000000000000000000002i−2i−2i2i0000
χ442-22-2222-2-22-22-2-22-222202-2-2-2-22-2-220000000000-2200-2-22222-2-200000000000000-2200000000000000-2-22200−2i2i00000000000000000000−2i2i2i−2i0000
χ452-2-222222-2-2-2-222-2-22220-2-222-2-2-22-2000000002i−2i002i−2i00002-2-220000000000002i−2i00002i−2i002i−2i2i−2i2i2i−2i−2i00002-200000000002i−2i0000002-20000000000
χ462-2-222222-2-2-2-222-2-22220-2-222-2-2-22-2000000002i−2i00−2i2i00002-2-220000000000002i−2i0000−2i2i002i−2i−2i2i2i2i−2i−2i0000-220000000000−2i2i000000-220000000000
χ472-2-222222-2-2-2-222-2-22220-2-222-2-2-22-200000000−2i2i002i−2i00002-2-22000000000000−2i2i00002i−2i00−2i2i2i−2i−2i−2i2i2i0000-2200000000002i−2i000000-220000000000
χ482-2-222222-2-2-2-222-2-22220-2-222-2-2-22-200000000−2i2i00−2i2i00002-2-22000000000000−2i2i0000−2i2i00−2i2i−2i2i−2i−2i2i2i00002-20000000000−2i2i0000002-20000000000
χ492-2-2222-1-1-2-21122-2-22-1-10-21-1-1-21121−i3i300−i3−i3i3i32i−2i002i−2i3−33−3-111-10−i3i300−i3−i3i3i3000−ii0000−ii3−32i−2i2i−2i−i−iii3−33−32-20000000000−ii3−30000-11−i3i300000000
χ502-2-2222-1-1-2-21122-2-22-1-10-21-1-1-21121−i3i300−i3−i3i3i32i−2i00−2i2i3−33−3-111-10−i3i300−i3−i3i3i3000−ii0000i−i−332i−2i−2i2i−i−iii3−33−3-220000000000i−i−3300001-1i3−i300000000
χ512-2-2222-1-1-2-21122-2-22-1-10-21-1-1-21121−i3i300−i3−i3i3i3−2i2i002i−2i−33−33-111-10−i3i300−i3−i3i3i3000i−i0000−ii3−3−2i2i2i−2iii−i−i−33−33-220000000000−ii3−300001-1i3−i300000000
χ522-2-2222-1-1-2-21122-2-22-1-10-21-1-1-21121−i3i300−i3−i3i3i3−2i2i00−2i2i−33−33-111-10−i3i300−i3−i3i3i3000i−i0000i−i−33−2i2i−2i2iii−i−i−33−332-20000000000i−i−330000-11−i3i300000000
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χ542-2-2222-1-1-2-21122-2-22-1-10-21-1-1-21121i3−i300i3i3−i3−i32i−2i00−2i2i−33−33-111-10i3−i300i3i3−i3−i3000−ii0000i−i3−32i−2i−2i2i−i−iii−33−33-220000000000i−i3−300001-1−i3i300000000
χ552-2-2222-1-1-2-21122-2-22-1-10-21-1-1-21121i3−i300i3i3−i3−i3−2i2i002i−2i3−33−3-111-10i3−i300i3i3−i3−i3000i−i0000−ii−33−2i2i2i−2iii−i−i3−33−3-220000000000−ii−3300001-1−i3i300000000
χ562-2-2222-1-1-2-21122-2-22-1-10-21-1-1-21121i3−i300i3i3−i3−i3−2i2i00−2i2i3−33−3-111-10i3−i300i3i3−i3−i3000i−i0000i−i3−3−2i2i−2i2iii−i−i3−33−32-20000000000i−i3−30000-11i3−i300000000
χ5744444-2-2-24-2-2-24-24-2-2-214-2-2-21-211-2-2-2-2-2-21111444400-2-2-2-211114-2-2-2-21111000-2-2-2-2000000-2-2001111111100000000000000000000000000000000
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χ904-44-44-2-22-4-22-2-4242-2-210-222-121-12-20000−3i3i3i−3i004-400-2-22211-1-100000−3i3i3i−3i00000-220000000000−3i3i3i−3i11-1-100000000000000000000000000000000
χ914-44-44-2-22-4-22-2-4242-2-210-222-121-12-20000−3i3i3i−3i00-440022-2-211-1-100000−3i3i3i−3i000002-200000000003i−3i−3i3i-1-11100000000000000000000000000000000
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χ964-4-444-2-2-2-42224-2-42-2-21022-212-1-1-22−2i32i300i3i3−i3−i34i−4i000023−2323−231-1-110−2i32i300i3i3−i3−i3000−2i2i00000000−2i2i00ii−i−i−33−3300000000000000000000000000000000
χ974-4-444-2-2-2-42224-2-42-2-21022-212-1-1-22−2i32i300i3i3−i3−i3−4i4i0000−2323−23231-1-110−2i32i300i3i3−i3−i30002i−2i000000002i−2i00−i−iii3−33−300000000000000000000000000000000
χ984-4-444-2-2-2-42224-2-42-2-21022-212-1-1-222i3−2i300−i3−i3i3i34i−4i0000−2323−23231-1-1102i3−2i300−i3−i3i3i3000−2i2i00000000−2i2i00ii−i−i3−33−300000000000000000000000000000000
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χ1004-4-44-24442-4-4-4-242-4-2-24022-242-4-4-220000000000004i−4i0000-222-20000000000000000004i−4i0000−2i2i00000000000000000000−2i2i000000000000000000
χ1014-4-44-24442-4-4-4-242-4-2-24022-242-4-4-22000000000000−4i4i0000-222-2000000000000000000−4i4i00002i−2i000000000000000000002i−2i000000000000000000
χ1024-4-44-24-2-22-422-242-4-21-202-11-2222-2-1−2i32i300−2i3−2i32i32i300004i−4i00001-1-110i3−i300i3i3−i3−i3000000000−2i2i23−2300−2i2i00000000000000000000i−i−330000000000000000
χ1034-4-44-24-2-22-422-242-4-21-202-11-2222-2-1−2i32i300−2i3−2i32i32i30000−4i4i00001-1-110i3−i300i3i3−i3−i30000000002i−2i−2323002i−2i00000000000000000000−ii3−30000000000000000
χ1044-4-44-24-2-22-422-242-4-21-202-11-2222-2-12i3−2i3002i32i3−2i3−2i300004i−4i00001-1-110−i3i300−i3−i3i3i3000000000−2i2i−232300−2i2i00000000000000000000i−i3−30000000000000000
χ1054-4-44-24-2-22-422-242-4-21-202-11-2222-2-12i3−2i3002i32i3−2i3−2i30000−4i4i00001-1-110−i3i300−i3−i3i3i30000000002i−2i23−23002i−2i00000000000000000000−ii−330000000000000000
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χ1078888-4-4-4-4-4-4-4-4-4-4-4-4222-82222222224444-2-2-2-20000000000-1-1-1-14-2-2-2-21111000000000000000000000000000000000000000000000000000000000
χ10888-8-8-48-44-4-8-444-848-42-4042-24-44-44-20000000000000000002-22-2000000000000000000000000000000000000000000000000000000000000000000
χ10988-8-8-4-4-44-44-44444-42220-22-2-22-22-2-20043−43−2323−23230000000000-11-11000−23233−33−3000000000000000000000000000000000000000000000000000000000
χ11088-8-8-4-4-44-44-44444-42220-22-2-22-22-2-200−434323−2323−230000000000-11-1100023−23−33−33000000000000000000000000000000000000000000000000000000000
χ1118-88-8-48-44484-44-8-4-8-42-40-4-2-244-444200000000000000000022-2-2000000000000000000000000000000000000000000000000000000000000000000
χ1128-88-8-4-48-84-4-8844-442-4-402444-2-44-2-400000000000000000022-2-2000000000000000000000000000000000000000000000000000000000000000000
χ1138-88-8-4-4-444-44-444-4422202-2-2-2-22-2-2200006i−6i−6i6i0000000000-1-11100000−3i3i3i−3i000000000000000000000000000000000000000000000000000000000
χ1148-88-8-4-4-444-44-444-4422202-2-2-2-22-2-220000−6i6i6i−6i0000000000-1-111000003i−3i−3i3i000000000000000000000000000000000000000000000000000000000
χ1158-8-88-4-48844-8-8-4-4442-4-40-24-4-4-244240000000000000000002-2-22000000000000000000000000000000000000000000000000000000000000000000
χ1168-8-88-4-4-4-44444-4-4442220-2-222-2-2-22-2−4i34i3002i32i3−2i3−2i30000000000-111-102i3−2i300−i3−i3i3i3000000000000000000000000000000000000000000000000000000000
χ1178-8-88-4-4-4-44444-4-4442220-2-222-2-2-22-24i3−4i300−2i3−2i32i32i30000000000-111-10−2i32i300i3i3−i3−i3000000000000000000000000000000000000000000000000000000000

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