Finite Group Databasebeta

← Group #13156544

Character table — Group #13156544

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size11112222222222222222224444444444444444444444448888888888121212121212121212121212121212121212121212121212121212121212121212121212242424242424242424363636363636727272727272216
order1222333446666666661212121233366666666612121212121212121212121236661212121212124488121212121212121212121212121212122424242424242424242424242424242441212121212121212882424242444121212122
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-11-1-111-1
χ41111111111111111111111111111111111111111111111111111111111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-11
χ511111111111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111111-1-1-1-1-1-11-111-1-1-1
χ611111111111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111
χ711111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-11
χ811111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1
χ92222222-2-2222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-22-2002222-2-2-2-22222-2-2-2-200000000000000000000000000000000000000
χ102222222-2-2222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2200-2-2-2-22222-2-2-2-2222200000000000000000000000000000000000000
χ11222222-12222-122-122-122222-1-122-12-1-1-1-1-1-1-1222-1-1-1-1222-1-1-1-1-1-1-1-1-1-1220022-1-122-1-1-1-1-1-1-1-1-1-10000000000000000222-1-1-1-1-1-10000000200-1-10
χ12222222-12222-122-122-122222-1-122-12-1-1-1-1-1-1-1222-1-1-1-1222-1-1-1-1-1-1-1-1-1-1220022-1-122-1-1-1-1-1-1-1-1-1-10000000000000000-2-2-21111110000000-200110
χ13222222-12222-122-122-122222-1-122-12-1-1-1-1-1-1-1222-1-1-1-1222-1-1-1-1-1-1-1-1-1-1-2-200-2-211-2-211111111110000000000000000222-1-1-1-1-1-10000000-200110
χ14222222-12222-122-122-122222-1-122-12-1-1-1-1-1-1-1222-1-1-1-1222-1-1-1-1-1-1-1-1-1-1-2-200-2-211-2-211111111110000000000000000-2-2-21111110000000200-1-10
χ15222222-1-2-222-122-122-1-2-2-2-22-1-122-12-1-1-1-1-111-2-2-21111-2-2-2-1-1-1-11111112-20022-1-1-2-211-1-1-1-111110000000000000000000−i3i3−i3−i3i3i30000000000−i3i30
χ16222222-1-2-222-122-122-1-2-2-2-22-1-122-12-1-1-1-1-111-2-2-21111-2-2-2-1-1-1-11111112-20022-1-1-2-211-1-1-1-111110000000000000000000i3−i3i3i3−i3−i30000000000i3−i30
χ17222222-1-2-222-122-122-1-2-2-2-22-1-122-12-1-1-1-1-111-2-2-21111-2-2-2-1-1-1-1111111-2200-2-21122-1-11111-1-1-1-10000000000000000000−i3i3−i3−i3i3i30000000000i3−i30
χ18222222-1-2-222-122-122-1-2-2-2-22-1-122-12-1-1-1-1-111-2-2-21111-2-2-2-1-1-1-1111111-2200-2-21122-1-11111-1-1-1-10000000000000000000i3−i3i3i3−i3−i30000000000−i3i30
χ1922222-12222-12-1-12222-1-1-1-1-12-1-1-12-12-1-1-12222-1-1-1-1-1-12-1-1-1-1-1-122-1-1-1-12222-1-122-1-122-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100000000022-1-1-1-10000000
χ2022222-12222-12-1-12222-1-1-1-1-12-1-1-12-12-1-1-12222-1-1-1-1-1-12-1-1-1-1-1-122-1-1-1-122-2-2-1-122-1-122-1-1-1-1-1-1-1-11111-2-2-2-211111111000000000-2-211110000000
χ2122222-12222-12-1-12222-1-1-1-1-12-1-1-12-12-1-1-12222-1-1-1-1-1-12-1-1-1-1-1-122-1-1-1-1-2-22211-2-211-2-211111111-1-1-1-12222-1-1-1-1-1-1-1-1000000000-2-211110000000
χ2222222-12222-12-1-12222-1-1-1-1-12-1-1-12-12-1-1-12222-1-1-1-1-1-12-1-1-1-1-1-122-1-1-1-1-2-2-2-211-2-211-2-2111111111111-2-2-2-21111111100000000022-1-1-1-10000000
χ2322222-12-2-22-12-1-122221111-12-1-1-12-12-1-1-12-2-2-2111111-211-1-1-1-1-2-211112-200-1-12211-2-2-1-1-1-1111133−3−300003333−3−3−3−30000000000033−3−30000000
χ2422222-12-2-22-12-1-122221111-12-1-1-12-12-1-1-12-2-2-2111111-211-1-1-1-1-2-211112-200-1-12211-2-2-1-1-1-11111−3−3330000−3−3−3−3333300000000000−3−3330000000
χ2522222-12-2-22-12-1-122221111-12-1-1-12-12-1-1-12-2-2-2111111-211-1-1-1-1-2-21111-220011-2-2-1-1221111-1-1-1-133−3−300003333−3−3−3−300000000000−3−3330000000
χ2622222-12-2-22-12-1-122221111-12-1-1-12-12-1-1-12-2-2-2111111-211-1-1-1-1-2-21111-220011-2-2-1-1221111-1-1-1-1−3−3330000−3−3−3−333330000000000033−3−30000000
χ272222-12222-122222-1-122222-1-12-1-1-1-1-1222-122-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1002200000000000000002222-1-1-1-1-1-1-1-1-1-1-1-12-1-122-1-1-1-100000020-1-1000
χ282222-12222-122222-1-122222-1-12-1-1-1-1-1222-122-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1002200000000000000002222-1-1-1-1-1-1-1-1-1-1-1-1-211-2-21111000000-2011000
χ292222-12222-122222-1-122222-1-12-1-1-1-1-1222-122-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-100-2-20000000000000000-2-2-2-21111111111112-1-122-1-1-1-1000000-2011000
χ302222-12222-122222-1-122222-1-12-1-1-1-1-1222-122-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-100-2-20000000000000000-2-2-2-2111111111111-211-2-2111100000020-1-1000
χ312-22-22222-2-222-2-2-2-22-222-2-2222-2-2-2222-2-2-22-2-2-2-222-2-22222-2-222-222-2-20000000000000000000000000000000000000000000002i−2i2i−2i2i−2i0000000
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χ332-22-2222-22-222-2-2-2-22-2-2-222222-2-2-2222-2-2-2-22222-2-222-2-2-22-2-22-22-2-222002i−2i00000000000000002i−2i2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i0000000000000000000000
χ342-22-2222-22-222-2-2-2-22-2-2-222222-2-2-2222-2-2-2-22222-2-222-2-2-22-2-22-22-2-22200−2i2i0000000000000000−2i2i−2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i0000000000000000000000
χ352-22-22-122-2-2-1211-2-22-2-1-111-12-111-2-12-111-22-2-211-1-1112-1-1-111-12-2-1-11100003−3003−30033−3−333−3−3−i3i3i3−i30000−i3−i3i3i3i3i3−i3−i30000000002i−2i−ii−ii0000000
χ362-22-22-122-2-2-1211-2-22-2-1-111-12-111-2-12-111-22-2-211-1-1112-1-1-111-12-2-1-11100003−3003−30033−3−333−3−3i3−i3−i3i30000i3i3−i3−i3−i3−i3i3i3000000000−2i2ii−ii−i0000000
χ372-22-22-122-2-2-1211-2-22-2-1-111-12-111-2-12-111-22-2-211-1-1112-1-1-111-12-2-1-1110000−3300−3300−3−333−3−333−i3i3i3−i30000−i3−i3i3i3i3i3−i3−i3000000000−2i2ii−ii−i0000000
χ382-22-22-122-2-2-1211-2-22-2-1-111-12-111-2-12-111-22-2-211-1-1112-1-1-111-12-2-1-1110000−3300−3300−3−333−3−333i3−i3−i3i30000i3i3−i3−i3−i3−i3i3i30000000002i−2i−ii−ii0000000
χ392-22-22-12-22-2-1211-2-22-211-1-1-12-111-2-12-111-2-222-1-111-1-1-211-111-1-2211-1-1002i−2i3−300−330033−3−3−3−333−ii−ii2i2i−2i−2i−i−iii−i−iii00000000000i3−i3−i3i30000000
χ402-22-22-12-22-2-1211-2-22-211-1-1-12-111-2-12-111-2-222-1-111-1-1-211-111-1-2211-1-1002i−2i−33003−300−3−33333−3−3−ii−ii2i2i−2i−2i−i−iii−i−iii00000000000−i3i3i3−i30000000
χ412-22-22-12-22-2-1211-2-22-211-1-1-12-111-2-12-111-2-222-1-111-1-1-211-111-1-2211-1-100−2i2i3−300−330033−3−3−3−333i−ii−i−2i−2i2i2iii−i−iii−i−i00000000000−i3i3i3−i30000000
χ422-22-22-12-22-2-1211-2-22-211-1-1-12-111-2-12-111-2-222-1-111-1-1-211-111-1-2211-1-100−2i2i−33003−300−3−33333−3−3i−ii−i−2i−2i2i2iii−i−iii−i−i00000000000i3−i3−i3i30000000
χ432-22-2-122-22122-2-2-21-1-2-2-222-1-12111-1-12-2-21-22-1-1-1-2-222111-111-11-111-1-1002i−2i00000000000000002i−2i2i−2i−i−iii−i−iii−i−iii03−3003−33−300000000−i3i3000
χ442-22-2-122-22122-2-2-21-1-2-2-222-1-12111-1-12-2-21-22-1-1-1-2-222111-111-11-111-1-1002i−2i00000000000000002i−2i2i−2i−i−iii−i−iii−i−iii0−3300−33−3300000000i3−i3000
χ452-22-2-122-22122-2-2-21-1-2-2-222-1-12111-1-12-2-21-22-1-1-1-2-222111-111-11-111-1-100−2i2i0000000000000000−2i2i−2i2iii−i−iii−i−iii−i−i03−3003−33−300000000i3−i3000
χ462-22-2-122-22122-2-2-21-1-2-2-222-1-12111-1-12-2-21-22-1-1-1-2-222111-111-11-111-1-100−2i2i0000000000000000−2i2i−2i2iii−i−iii−i−iii−i−i0−3300−33−3300000000−i3i3000
χ4744444-2-2444-2-2-2-2-244-2-2-2-2-2-2-21-2-2-2-2-2111-2-2-24-2-211114-2-21111-2-211114400-2-2-2-2-2-2-2-21111111100000000000000000000000000000000000000
χ4844444-2-2444-2-2-2-2-244-2-2-2-2-2-2-21-2-2-2-2-2111-2-2-24-2-211114-2-21111-2-21111-4-40022222222-1-1-1-1-1-1-1-100000000000000000000000000000000000000
χ4944444-2-2-4-44-2-2-2-2-244-22222-2-21-2-2-2-2-2111-222-422-1-1-1-1-422111122-1-1-1-14-400-2-2-2-222221111-1-1-1-100000000000000000000000000000000000000
χ5044444-2-2-4-44-2-2-2-2-244-22222-2-21-2-2-2-2-2111-222-422-1-1-1-1-422111122-1-1-1-1-44002222-2-2-2-2-1-1-1-1111100000000000000000000000000000000000000
χ514444-244-4-4-244444-2-24-4-4-4-4-2-24-2-2-2-2-2444-2-4-4222-4-4-4-4222-2-2-2-22222220000000000000000000000000000000000000000000000000000000000
χ524444-24-244-24-244-2-2-2-24444-21-2-2-21-21-2-2-21-2-2-2-2-2-2-2-2-2-2-2-211111111110000000000000000000000000000000000004-2-2-2-211110000000000000
χ534444-24-244-24-244-2-2-2-24444-21-2-2-21-21-2-2-21-2-2-2-2-2-2-2-2-2-2-2-21111111111000000000000000000000000000000000000-42222-1-1-1-10000000000000
χ544444-24-2-4-4-24-244-2-2-2-2-4-4-4-4-21-2-2-21-21-2-2-212222222222221111-1-1-1-1-1-1000000000000000000000000000000000000000−2i32i3i3i3−i3−i30000000000000
χ554444-24-2-4-4-24-244-2-2-2-2-4-4-4-4-21-2-2-21-21-2-2-212222222222221111-1-1-1-1-1-10000000000000000000000000000000000000002i3−2i3−i3−i3i3i30000000000000
χ564444-2-2444-2-24-2-24-2-24-2-2-2-21-2-211-21-2-2-2-2-244-211-2-2-2-2-2111111-2-2111100440000000000000000-2-2-2-2-2-2-2-2111111110000000000000000000000
χ574444-2-2444-2-24-2-24-2-24-2-2-2-21-2-211-21-2-2-2-2-244-211-2-2-2-2-2111111-2-2111100-4-4000000000000000022222222-1-1-1-1-1-1-1-10000000000000000000000
χ584444-2-24-4-4-2-24-2-24-2-2422221-2-211-21-2-2-2-2-2-4-42-1-122222-1-1111122-1-1-1-1000000000000000000002323−23−230000−3−3−3−333330000000000000000000000
χ594444-2-24-4-4-2-24-2-24-2-2422221-2-211-21-2-2-2-2-2-4-42-1-122222-1-1111122-1-1-1-100000000000000000000−23−23232300003333−3−3−3−30000000000000000000000
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χ6344-4-44-240042-4-224-4-4-423−2323−23-24-2-2242-42-22-400023−2323−2323−23023−23-2-2220023−2323−230000000000000000000000000000000000000000000000000000000000
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χ7144-4-4-2-2400-22-4-22422-423−2323−231-2-21-1-2-122-222000−3323−2323−230−3311-1-100−33−33000000000000000000000000i6−i6i6−i6−2ζ5−2ζ7−ζ13−ζ232ζ5+2ζ7+ζ13+ζ23−2ζ5−2ζ7−ζ13−ζ232ζ5+2ζ7+ζ13+ζ23ζ5+ζ7+2ζ13+2ζ23−ζ5−ζ7−2ζ13−2ζ23ζ5+ζ7+2ζ13+2ζ23−ζ5−ζ7−2ζ13−2ζ230000000000000000000000
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χ764-44-444-2-44-44-2-4-42-442-4-4444-2-2-4-424-2-22222-244422-2-2-4-4-4-222-22-222-2-20000000000000000000000000000000000000000000000000000000000
χ774-44-44-2-24-4-4-2-2222-442-2-222-2-21222-2-21-1-12-22-42211-1-14-2-21-1-11-2211-1-1000023−230023−2300−3−333−3−33300000000000000000000000000000000000000
χ784-44-44-2-24-4-4-2-2222-442-2-222-2-21222-2-21-1-12-22-42211-1-14-2-21-1-11-2211-1-10000−232300−23230033−3−333−3−300000000000000000000000000000000000000
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χ1118-88-8-4-4-4-884-4-44444-4444-4-4222-2-2-2222-2-2-24-4-422-2-2224-2-2-111-1-2211-1-10000000000000000000000000000000000000000000000000000000000
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χ1148-8-88-4-4-4004444-44-44-4−434343−43222-22-2-2-2-2-222000−232323−23−2323023−23-11-1100−333−30000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.