Finite Group Databasebeta

← Group #13156570

Character table — Group #13156570

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size11112222222222222222224444444444444444444444448888888888121212121212121212121212121212121212121212121212121212121212121212121212242424242424242424363636363636727272727272216
order1222333446666666661212121233366666666612121212121212121212121236661212121212124488121212121212121212121212121212122424242424242424242424242424242441212121212121212882424242444121212124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-11-1-1-111-1
χ41111111111111111111111111111111111111111111111111111111111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-11
χ511111111111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111111111-1-1-1-1-1-1-1111-1-1-1
χ611111111111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1111
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
χ92222222-2-2222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-22-20022-2-222-2-22222-2-2-2-200000000000000000000000000000000000000
χ102222222-2-2222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2200-2-222-2-222-2-2-2-2222200000000000000000000000000000000000000
χ11222222-12222-1222-12-122222-1-122-12-1-1-1-1-1-1-1222-1-1-1-1222-1-1-1-1-1-1-1-1-1-122002222-1-1-1-1-1-1-1-1-1-1-1-10000000000000000222-1-1-1-1-1-10000002000-1-10
χ12222222-12222-1222-12-122222-1-122-12-1-1-1-1-1-1-1222-1-1-1-1222-1-1-1-1-1-1-1-1-1-122002222-1-1-1-1-1-1-1-1-1-1-1-10000000000000000-2-2-2111111000000-2000110
χ13222222-12222-1222-12-122222-1-122-12-1-1-1-1-1-1-1222-1-1-1-1222-1-1-1-1-1-1-1-1-1-1-2-200-2-2-2-21111111111110000000000000000222-1-1-1-1-1-1000000-2000110
χ14222222-12222-1222-12-122222-1-122-12-1-1-1-1-1-1-1222-1-1-1-1222-1-1-1-1-1-1-1-1-1-1-2-200-2-2-2-21111111111110000000000000000-2-2-21111110000002000-1-10
χ15222222-1-2-222-1222-12-1-2-2-2-22-1-122-12-1-1-1-1-111-2-2-21111-2-2-2-1-1-1-11111112-20022-2-2-1-111-1-1-1-111110000000000000000000−i3i3−i3−i3i3i30000000000−i3i30
χ16222222-1-2-222-1222-12-1-2-2-2-22-1-122-12-1-1-1-1-111-2-2-21111-2-2-2-1-1-1-11111112-20022-2-2-1-111-1-1-1-111110000000000000000000i3−i3i3i3−i3−i30000000000i3−i30
χ17222222-1-2-222-1222-12-1-2-2-2-22-1-122-12-1-1-1-1-111-2-2-21111-2-2-2-1-1-1-1111111-2200-2-22211-1-11111-1-1-1-10000000000000000000−i3i3−i3−i3i3i30000000000i3−i30
χ18222222-1-2-222-1222-12-1-2-2-2-22-1-122-12-1-1-1-1-111-2-2-21111-2-2-2-1-1-1-1111111-2200-2-22211-1-11111-1-1-1-10000000000000000000i3−i3i3i3−i3−i30000000000−i3i30
χ1922222-12222-12-1-12222-1-1-1-1-12-1-1-12-12-1-1-12222-1-1-1-1-1-12-1-1-1-1-1-122-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-100000000022-1-1-1-10000000
χ2022222-12222-12-1-12222-1-1-1-1-12-1-1-12-12-1-1-12222-1-1-1-1-1-12-1-1-1-1-1-122-1-1-1-122-2-2-1-1-1-12222-1-1-1-1-1-1-1-11111-2-2-2-211111111000000000-2-211110000000
χ2122222-12222-12-1-12222-1-1-1-1-12-1-1-12-12-1-1-12222-1-1-1-1-1-12-1-1-1-1-1-122-1-1-1-1-2-2221111-2-2-2-211111111-1-1-1-12222-1-1-1-1-1-1-1-1000000000-2-211110000000
χ2222222-12222-12-1-12222-1-1-1-1-12-1-1-12-12-1-1-12222-1-1-1-1-1-12-1-1-1-1-1-122-1-1-1-1-2-2-2-21111-2-2-2-2111111111111-2-2-2-21111111100000000022-1-1-1-10000000
χ2322222-12-2-22-12-1-122221111-12-1-1-12-12-1-1-12-2-2-2111111-211-1-1-1-1-2-211112-200-1-11122-2-2-1-1-1-1111133−3−300003333−3−3−3−30000000000033−3−30000000
χ2422222-12-2-22-12-1-122221111-12-1-1-12-12-1-1-12-2-2-2111111-211-1-1-1-1-2-211112-200-1-11122-2-2-1-1-1-11111−3−3330000−3−3−3−3333300000000000−3−3330000000
χ2522222-12-2-22-12-1-122221111-12-1-1-12-12-1-1-12-2-2-2111111-211-1-1-1-1-2-21111-220011-1-1-2-2221111-1-1-1-133−3−300003333−3−3−3−300000000000−3−3330000000
χ2622222-12-2-22-12-1-122221111-12-1-1-12-12-1-1-12-2-2-2111111-211-1-1-1-1-2-21111-220011-1-1-2-2221111-1-1-1-1−3−3330000−3−3−3−333330000000000033−3−30000000
χ272222-12222-12222-12-122222-1-12-1-1-1-1-1222-122-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1002200000000000000002222-1-1-1-1-1-1-1-1-1-1-1-12-1-122-1-1-1-100000002-1-1000
χ282222-12222-12222-12-122222-1-12-1-1-1-1-1222-122-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1002200000000000000002222-1-1-1-1-1-1-1-1-1-1-1-1-211-2-211110000000-211000
χ292222-12222-12222-12-122222-1-12-1-1-1-1-1222-122-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-100-2-20000000000000000-2-2-2-21111111111112-1-122-1-1-1-10000000-211000
χ302222-12222-12222-12-122222-1-12-1-1-1-1-1222-122-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-100-2-20000000000000000-2-2-2-2111111111111-211-2-2111100000002-1-1000
χ312-2-222222-2-222-2-2-2-22-222-2-2222-2-2-2222-2-2-22-2-2-2-222-2-22222-2-222-222-2-20000000000000000000000000000000000000000000002i−2i2i−2i2i−2i0000000
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χ332-2-22222-22-222-2-2-2-22-2-2-222222-2-2-2222-2-2-2-22222-2-222-2-2-22-2-22-22-2-222002i−2i00000000000000002i−2i2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i0000000000000000000000
χ342-2-22222-22-222-2-2-2-22-2-2-222222-2-2-2222-2-2-2-22222-2-222-2-2-22-2-22-22-2-22200−2i2i0000000000000000−2i2i−2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i0000000000000000000000
χ352-2-222-122-2-2-1211-2-22-2-1-111-12-111-2-12-111-22-2-211-1-1112-1-1-111-12-2-1-11100003−33−3000033−3−333−3−3−i3i3i3−i30000−i3−i3i3i3i3i3−i3−i30000000002i−2i−ii−ii0000000
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χ382-2-222-122-2-2-1211-2-22-2-1-111-12-111-2-12-111-22-2-211-1-1112-1-1-111-12-2-1-1110000−33−330000−3−333−3−333i3−i3−i3i30000i3i3−i3−i3−i3−i3i3i30000000002i−2i−ii−ii0000000
χ392-2-222-12-22-2-1211-2-22-211-1-1-12-111-2-12-111-2-222-1-111-1-1-211-111-1-2211-1-1002i−2i3−3−33000033−3−3−3−333−ii−ii2i2i−2i−2i−i−iii−i−iii00000000000i3−i3−i3i30000000
χ402-2-222-12-22-2-1211-2-22-211-1-1-12-111-2-12-111-2-222-1-111-1-1-211-111-1-2211-1-1002i−2i−333−30000−3−33333−3−3−ii−ii2i2i−2i−2i−i−iii−i−iii00000000000−i3i3i3−i30000000
χ412-2-222-12-22-2-1211-2-22-211-1-1-12-111-2-12-111-2-222-1-111-1-1-211-111-1-2211-1-100−2i2i3−3−33000033−3−3−3−333i−ii−i−2i−2i2i2iii−i−iii−i−i00000000000−i3i3i3−i30000000
χ422-2-222-12-22-2-1211-2-22-211-1-1-12-111-2-12-111-2-222-1-111-1-1-211-111-1-2211-1-100−2i2i−333−30000−3−33333−3−3i−ii−i−2i−2i2i2iii−i−iii−i−i00000000000i3−i3−i3i30000000
χ432-2-22-122-22122-2-21-2-1-2-2-222-1-12111-1-12-2-21-22-1-1-1-2-222111-111-11-111-1-1002i−2i00000000000000002i−2i2i−2i−i−iii−i−iii−i−iii03−3003−33−300000000−i3i3000
χ442-2-22-122-22122-2-21-2-1-2-2-222-1-12111-1-12-2-21-22-1-1-1-2-222111-111-11-111-1-1002i−2i00000000000000002i−2i2i−2i−i−iii−i−iii−i−iii0−3300−33−3300000000i3−i3000
χ452-2-22-122-22122-2-21-2-1-2-2-222-1-12111-1-12-2-21-22-1-1-1-2-222111-111-11-111-1-100−2i2i0000000000000000−2i2i−2i2iii−i−iii−i−iii−i−i03−3003−33−300000000i3−i3000
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χ4744444-2-2444-2-2-2-24-24-2-2-2-2-2-2-21-2-2-2-2-2111-2-2-24-2-211114-2-21111-2-211114400-2-2-2-2-2-2-2-21111111100000000000000000000000000000000000000
χ4844444-2-2444-2-2-2-24-24-2-2-2-2-2-2-21-2-2-2-2-2111-2-2-24-2-211114-2-21111-2-21111-4-40022222222-1-1-1-1-1-1-1-100000000000000000000000000000000000000
χ4944444-2-2-4-44-2-2-2-24-24-22222-2-21-2-2-2-2-2111-222-422-1-1-1-1-422111122-1-1-1-14-400-2-222-2-2221111-1-1-1-100000000000000000000000000000000000000
χ5044444-2-2-4-44-2-2-2-24-24-22222-2-21-2-2-2-2-2111-222-422-1-1-1-1-422111122-1-1-1-1-440022-2-222-2-2-1-1-1-1111100000000000000000000000000000000000000
χ514444-244-4-4-24444-24-24-4-4-4-4-2-24-2-2-2-2-2444-2-4-4222-4-4-4-4222-2-2-2-22222220000000000000000000000000000000000000000000000000000000000
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
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χ564444-2-2444-2-24-2-2-24-24-2-2-2-21-2-211-21-2-2-2-2-244-211-2-2-2-2-2111111-2-2111100440000000000000000-2-2-2-2-2-2-2-2111111110000000000000000000000
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χ594444-2-24-4-4-2-24-2-2-24-2422221-2-211-21-2-2-2-2-2-4-42-1-122222-1-1111122-1-1-1-100000000000000000000−23−23232300003333−3−3−3−30000000000000000000000
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χ834-44-44-2-2004222-2-42-4-2−232323−23-2-212-2-222-1-11200023−233−3−330−23231-11-1003−3−3300000000−2323003−3−33-333-300000000000000000000000000000000000000
χ844-44-4-24400-2-4-4-442-4240000-2-242-2-222-4-442000000000000-22-22000000000000000000000000000000i6−i6−i6i6i6−i6−i6i6i6−i6−i6i60000000000000000000000
χ854-44-4-24400-2-4-4-442-4240000-2-242-2-222-4-442000000000000-22-22000000000000000000000000000000−i6i6i6−i6−i6i6i6−i6−i6i6i6−i60000000000000000000000
χ864-44-4-2-2400-22-42-22-42423−23−23231-2-2-11-2-1222-220003−323−23−23230−331-11-100−333−3000000000000000000000000i6−i6−i6i6−2ζ5−2ζ7−ζ13−ζ232ζ5+2ζ7+ζ13+ζ232ζ5+2ζ7+ζ13+ζ23−2ζ5−2ζ7−ζ13−ζ23ζ5+ζ7+2ζ13+2ζ23−ζ5−ζ7−2ζ13−2ζ23−ζ5−ζ7−2ζ13−2ζ23ζ5+ζ7+2ζ13+2ζ230000000000000000000000
χ874-44-4-2-2400-22-42-22-42423−23−23231-2-2-11-2-1222-220003−323−23−23230−331-11-100−333−3000000000000000000000000−i6i6i6−i62ζ5+2ζ7+ζ13+ζ23−2ζ5−2ζ7−ζ13−ζ23−2ζ5−2ζ7−ζ13−ζ232ζ5+2ζ7+ζ13+ζ23−ζ5−ζ7−2ζ13−2ζ23ζ5+ζ7+2ζ13+2ζ23ζ5+ζ7+2ζ13+2ζ23−ζ5−ζ7−2ζ13−2ζ230000000000000000000000
χ884-44-4-2-2400-22-42-22-424−232323−231-2-2-11-2-1222-22000−33−232323−2303−31-11-1003−3−33000000000000000000000000i6−i6−i6i6ζ5+ζ7+2ζ13+2ζ23−ζ5−ζ7−2ζ13−2ζ23−ζ5−ζ7−2ζ13−2ζ23ζ5+ζ7+2ζ13+2ζ23−2ζ5−2ζ7−ζ13−ζ232ζ5+2ζ7+ζ13+ζ232ζ5+2ζ7+ζ13+ζ23−2ζ5−2ζ7−ζ13−ζ230000000000000000000000
χ894-44-4-2-2400-22-42-22-424−232323−231-2-2-11-2-1222-22000−33−232323−2303−31-11-1003−3−33000000000000000000000000−i6i6i6−i6−ζ5−ζ7−2ζ13−2ζ23ζ5+ζ7+2ζ13+2ζ23ζ5+ζ7+2ζ13+2ζ23−ζ5−ζ7−2ζ13−2ζ232ζ5+2ζ7+ζ13+ζ23−2ζ5−2ζ7−ζ13−ζ23−2ζ5−2ζ7−ζ13−ζ232ζ5+2ζ7+ζ13+ζ230000000000000000000000
χ904-4-4444-24-4-44-2-4-4-424244-4-44-2-2-4-424-2-2222-22-4-4-4-2-222444-222-2-22-2-2220000000000000000000000000000000000000000000000000000000000
χ914-4-4444-2-44-44-2-4-4-4242-4-4444-2-2-4-424-2-22222-244422-2-2-4-4-4-222-22-222-2-20000000000000000000000000000000000000000000000000000000000
χ924-4-444-2-24-4-4-2-222-4242-2-222-2-21222-2-21-1-12-22-42211-1-14-2-21-1-11-2211-1-1000023−2323−230000−3−333−3−33300000000000000000000000000000000000000
χ934-4-444-2-24-4-4-2-222-4242-2-222-2-21222-2-21-1-12-22-42211-1-14-2-21-1-11-2211-1-10000−2323−2323000033−3−333−3−300000000000000000000000000000000000000
χ944-4-444-2-2-44-4-2-222-424222-2-2-2-21222-2-21-1-122-24-2-2-1-111-4221-1-112-2-1-111000023−23−23230000−3−33333−3−300000000000000000000000000000000000000
χ954-4-444-2-2-44-4-2-222-424222-2-2-2-21222-2-21-1-122-24-2-2-1-111-4221-1-112-2-1-1110000−232323−23000033−3−3−3−33300000000000000000000000000000000000000
χ964-4-44-2444-4244-4-42-4-2-444-4-4-2-24222-2-24-4-424-422244-4-4-2-2-2-222-2-22-2-2220000000000000000000000000000000000000000000000000000000000
χ974-4-44-24-24-424-2-4-422-2244-4-4-21-222-1-21-222-1-22222-2-222-2-2-21-1-111-111-1-1000000000000000000000000000000000000000003i−3i−3i3i0000000000000
χ984-4-44-24-24-424-2-4-422-2244-4-4-21-222-1-21-222-1-22222-2-222-2-2-21-1-111-111-1-100000000000000000000000000000000000000000−3i3i3i−3i0000000000000
χ994-4-44-24-2-4424-2-4-422-22-4-444-21-222-1-21-222-12-2-2-2-222-2-22221-1-11-11-1-111000000000000000000000000000000000000023−2300−33−330000000000000
χ1004-4-44-24-2-4424-2-4-422-22-4-444-21-222-1-21-222-12-2-2-2-222-2-22221-1-11-11-1-1110000000000000000000000000000000000000−2323003−33−30000000000000
χ1014-4-44-2-244-42-24222-4-2-4-2-2221-2-2-1-121-2-22224-42-1-1-2-222-2111-1-11-2211-1-100000000000000000000−2i32i32i3−2i30000i3i3−i3−i3−i3−i3i3i30000000000000000000000
χ1024-4-44-2-244-42-24222-4-2-4-2-2221-2-2-1-121-2-22224-42-1-1-2-222-2111-1-11-2211-1-1000000000000000000002i3−2i3−2i32i30000−i3−i3i3i3i3i3−i3−i30000000000000000000000
χ1034-4-44-2-24-442-24222-4-2-422-2-21-2-2-1-121-2-2222-44-21122-2-22-1-11-1-112-2-1-111004i−4i0000000000000000−2i2i−2i2i−2i−2i2i2iii−i−iii−i−i0000000000000000000000
χ1044-4-44-2-24-442-24222-4-2-422-2-21-2-2-1-121-2-2222-44-21122-2-22-1-11-1-112-2-1-11100−4i4i00000000000000002i−2i2i−2i2i2i−2i−2i−i−iii−i−iii0000000000000000000000
χ1058888-4-4-488-4-4-4-4-4-4-4-4-4-4-4-4-4222222222222-4-4-4222222-422-1-1-1-122-1-1-1-10000000000000000000000000000000000000000000000000000000000
χ1068888-4-4-4-8-8-4-4-4-4-4-4-4-4-44444222222222222444-2-2-2-2-2-24-2-2-1-1-1-1-2-211110000000000000000000000000000000000000000000000000000000000
χ10788-8-8-48-4004-848-8-4-4440000-42-4-44-24-24-44200000000000022-2-20000000000000000000000000000000000000000000000000000000000000000
χ10888-8-8-4-4-400444-44-4-44443−4343−432222-2-2-2-2-22-22000−2323−2323−23230−2323-1-111003−33−30000000000000000000000000000000000000000000000000000000000
χ10988-8-8-4-4-400444-44-4-444−4343−43432222-2-2-2-2-22-2200023−2323−2323−23023−23-1-11100−33−330000000000000000000000000000000000000000000000000000000000
χ1108-88-8-48-400-4-84-88444-40000-42-44-424-244-4-20000000000002-22-20000000000000000000000000000000000000000000000000000000000000000
χ1118-88-8-4-4-400-4444-4444-443−43−4343222-222-2-2-2-22-200023−23−232323−230−2323-11-11003−3−330000000000000000000000000000000000000000000000000000000000
χ1128-88-8-4-4-400-4444-4444-4−434343−43222-222-2-2-2-22-2000−232323−23−2323023−23-11-1100−333−30000000000000000000000000000000000000000000000000000000000
χ1138-8-88-4-4-48-84-4-44444-44-4-444222-2-2-2222-2-2-2-444-2-222-2-2-422-111-12-2-1-1110000000000000000000000000000000000000000000000000000000000
χ1148-8-88-4-4-4-884-4-44444-4444-4-4222-2-2-2222-2-2-24-4-422-2-2224-2-2-111-1-2211-1-10000000000000000000000000000000000000000000000000000000000

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