Finite Group Databasebeta

← Group #13156501

Character table — Group #13156501

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117
size111122222222222222222244444444444444444444444488888888881212121212121212121212121212121212121212121212121212121212121212121212121212181824242424242424243636363636727272727272108108
order12223334466666666612121212333666666666121212121212121212121212366612121212121244888824242424242424242424242424242424242424242424242424242424242424244412121212121212122661212441212121244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-11-1-1-111-1-1
χ31111111111111111111111111111111111111111111111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111111111-1-1-1-1-1-1111-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-111
χ511111111111111111111111111111111111111111111111111111111-1-111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1
χ611111111111111111111111111111111111111111111111111111111-1-111-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-111
χ711111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11111
χ811111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111111-1-1
χ92222222-2-2222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-2000000000000000000000000000000000000002200000000-2-2-22200000000
χ102222222-2-2222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-200000000000000000000000000000000000000-2-200000000222-2-200000000
χ11222222-1222-1-1222-122-1-1-1-12-1-12-1-1-1-12-1-1222-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-1002222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122000000002-1-1-1-100000000
χ12222222-1222-1-1222-122-1-1-1-12-1-12-1-1-1-12-1-1222-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-10022-2-2-1-1-1-111112222-1-1-1-1-1-1-1-1-2-2-2-211111111-2-200000000-2111100000000
χ13222222-1222-1-1222-122-1-1-1-12-1-12-1-1-1-12-1-1222-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-100-2-2221111-1-1-1-1-2-2-2-2111111112222-1-1-1-1-1-1-1-1-2-200000000-2111100000000
χ14222222-1222-1-1222-122-1-1-1-12-1-12-1-1-1-12-1-1222-1-1-1-122-1-1-1-1-1-1-1-122-1-1-1-100-2-2-2-211111111-2-2-2-211111111-2-2-2-21111111122000000002-1-1-1-100000000
χ15222222-1-2-22-1-1222-12211112-1-12-1-1-1-12-1-12-2-21111-2-21111-1-1-1-1-2-2111100000033−3−333−3−300003333−3−3−3−300003333−3−3−3−32200000000-211-1-100000000
χ16222222-1-2-22-1-1222-12211112-1-12-1-1-1-12-1-12-2-21111-2-21111-1-1-1-1-2-2111100000033−3−3−3−33300003333−3−3−3−30000−3−3−3−33333-2-2000000002-1-11100000000
χ17222222-1-2-22-1-1222-12211112-1-12-1-1-1-12-1-12-2-21111-2-21111-1-1-1-1-2-21111000000−3−33333−3−30000−3−3−3−3333300003333−3−3−3−3-2-2000000002-1-11100000000
χ18222222-1-2-22-1-1222-12211112-1-12-1-1-1-12-1-12-2-21111-2-21111-1-1-1-1-2-21111000000−3−333−3−3330000−3−3−3−333330000−3−3−3−333332200000000-211-1-100000000
χ1922222-1222222-12-12-122222-12-1-122-1-1-12-1-1-1222-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-122002200002222000000000000-1-1-1-1-1-1-1-1-1-1-1-10022-1-1-1-1-1-10000002-1-10000
χ2022222-1222222-12-12-122222-12-1-122-1-1-12-1-1-1222-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-12200-2-20000-2-2-2-20000000000001111111111110022-1-1-1-1-1-1000000-2110000
χ2122222-1222222-12-12-122222-12-1-122-1-1-12-1-1-1222-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-1-2-2002200002222000000000000-1-1-1-1-1-1-1-1-1-1-1-100-2-2111111000000-2110000
χ2222222-1222222-12-12-122222-12-1-122-1-1-12-1-1-1222-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-1-2-200-2-20000-2-2-2-200000000000011111111111100-2-21111110000002-1-10000
χ232222-12222-1222-1222-12222-1-12-1-1-122-1-12-12-1-1-1222-1-1-122-1-1-1-1-1-1-1-1-1-122220022220000-1-1-1-1-1-1-1-1-1-1-1-100000000000000-1-122-1-1-1-1000002000-1-100
χ242222-12222-1222-1222-12222-1-12-1-1-122-1-12-12-1-1-1222-1-1-122-1-1-1-1-1-1-1-1-1-122-2-200-2-2-2-2000011111111111100000000000000-1-122-1-1-1-100000-20001100
χ252222-12222-1222-1222-12222-1-12-1-1-122-1-12-12-1-1-1222-1-1-122-1-1-1-1-1-1-1-1-1-1-2-2220022220000-1-1-1-1-1-1-1-1-1-1-1-10000000000000011-2-2111100000-20001100
χ262222-12222-1222-1222-12222-1-12-1-1-122-1-12-12-1-1-1222-1-1-122-1-1-1-1-1-1-1-1-1-1-2-2-2-200-2-2-2-200001111111111110000000000000011-2-21111000002000-1-100
χ272-22-22222-2-2-2-22-2-22-2222-2-2222-2-2-2-2-2222-22-2-2-222-2222-2-22-2-222-222-2-2000000000000000000000000000000000000000000000000000000000002i−2i
χ282-22-22222-2-2-2-22-2-22-2222-2-2222-2-2-2-2-2222-22-2-2-222-2222-2-22-2-222-222-2-200000000000000000000000000000000000000000000000000000000000−2i2i
χ292-22-2222-22-2-2-22-2-22-22-2-222222-2-2-2-2-2222-2-2222-2-22-2-2-2222-2-22-22-2-2222i−2i000000000000000000000000000000000000002i−2i2i−2i2i2i−2i−2i0000000000000
χ302-22-2222-22-2-2-22-2-22-22-2-222222-2-2-2-2-2222-2-2222-2-22-2-2-2222-2-22-22-2-222−2i2i00000000000000000000000000000000000000−2i2i−2i2i−2i−2i2i2i0000000000000
χ312-22-22-12-22-2-2-2-1-21212-2-222-12-11-2-211-12-11122211-1-2-2-2-1-1-111-11-111-1-12i−2i000000000000000000000000−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3002i−2i−ii−i−iii00000003−30000
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χ332-22-22-12-22-2-2-2-1-21212-2-222-12-11-2-211-12-11122211-1-2-2-2-1-1-111-11-111-1-1−2i2i000000000000000000000000−i3−i3i3i3−i3−i3i3i3−i3−i3i3i300−2i2ii−iii−i−i0000000−330000
χ342-22-22-12-22-2-2-2-1-21212-2-222-12-11-2-211-12-11122211-1-2-2-2-1-1-111-11-111-1-1−2i2i000000000000000000000000i3i3−i3−i3i3i3−i3−i3i3i3−i3−i300−2i2ii−iii−i−i00000003−30000
χ352-22-2-122-221-2-221-22-2-1-2-222-1-12111-2-2-1-121-2-1-1-1-2-2211122-111-11-111-1-12i−2i00000000000033−3−333−3−333−3−300000000000000−ii2i−2i−i−iii000000000−i3i300
χ362-22-2-122-221-2-221-22-2-1-2-222-1-12111-2-2-1-121-2-1-1-1-2-2211122-111-11-111-1-12i−2i000000000000−3−333−3−333−3−33300000000000000−ii2i−2i−i−iii000000000i3−i300
χ372-22-2-122-221-2-221-22-2-1-2-222-1-12111-2-2-1-121-2-1-1-1-2-2211122-111-11-111-1-1−2i2i00000000000033−3−333−3−333−3−300000000000000i−i−2i2iii−i−i000000000i3−i300
χ382-22-2-122-221-2-221-22-2-1-2-222-1-12111-2-2-1-121-2-1-1-1-2-2211122-111-11-111-1-1−2i2i000000000000−3−333−3−333−3−33300000000000000i−i−2i2iii−i−i000000000−i3i300
χ392-2-222220022-2-2-2-2-22-2000022222-22-2-2-2-2-200000000000022-2-2000000002−2−i2i22−22−2−i2i2−i2i22−22−22−22−22−22−2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i22i−2i000000000002i−2i00000000
χ402-2-222220022-2-2-2-2-22-2000022222-22-2-2-2-2-200000000000022-2-2000000002−2i2−i22−22−2i2−i2i2−i22−22−22−22−22−22−2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2−2i2i00000000000−2i2i00000000
χ412-2-222220022-2-2-2-2-22-2000022222-22-2-2-2-2-200000000000022-2-200000000−22−i2i2−22−22−i2i2−i2i2−22−22−22−22−22−22−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−2i2i00000000000−2i2i00000000
χ422-2-222220022-2-2-2-2-22-2000022222-22-2-2-2-2-200000000000022-2-200000000−22i2−i2−22−22i2−i2i2−i2−22−22−22−22−22−22i2−i2i2−i2i2−i2i2−i2i2−i2i2−i22i−2i000000000002i−2i00000000
χ432-2-2222-1002-11-2-2-212-23−33−32-1-12-11-11-211-2003−33−3003−33−3-1-111003−33−3002−2−i2i2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ72−22−2ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23−i2i2−i2i2ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ72i−2i000000000−i3i3−ii00000000
χ442-2-2222-1002-11-2-2-212-23−33−32-1-12-11-11-211-2003−33−3003−33−3-1-111003−33−3002−2i2−i2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ72−22−2ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23i2−i2i2−i2−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−2i2i000000000i3−i3i−i00000000
χ452-2-2222-1002-11-2-2-212-23−33−32-1-12-11-11-211-2003−33−3003−33−3-1-111003−33−300−22−i2i2−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7−22−22−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−i2i2−i2i2ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7−2i2i000000000i3−i3i−i00000000
χ462-2-2222-1002-11-2-2-212-23−33−32-1-12-11-11-211-2003−33−3003−33−3-1-111003−33−300−22i2−i2−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−22−22−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23i2−i2i2−i2−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ72i−2i000000000−i3i3−ii00000000
χ472-2-2222-1002-11-2-2-212-2−33−332-1-12-11-11-211-200−33−3300−33−33-1-11100−33−33002−2−i2i2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ232−22−2ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7−i2i2−i2i2ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ232i−2i000000000i3−i3−ii00000000
χ482-2-2222-1002-11-2-2-212-2−33−332-1-12-11-11-211-200−33−3300−33−33-1-11100−33−33002−2i2−i2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ232−22−2ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7i2−i2i2−i2−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ23−2i2i000000000−i3i3i−i00000000
χ492-2-2222-1002-11-2-2-212-2−33−332-1-12-11-11-211-200−33−3300−33−33-1-11100−33−3300−22−i2i2−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23−22−22−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−i2i2−i2i2ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ23ζ13+ζ23−ζ13−ζ23−2i2i000000000−i3i3i−i00000000
χ502-2-2222-1002-11-2-2-212-2−33−332-1-12-11-11-211-200−33−3300−33−33-1-11100−33−3300−22i2−i2−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−22−22−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7i2−i2i2−i2−ζ5−ζ7ζ5+ζ7−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ23−ζ13−ζ23ζ13+ζ232i−2i000000000i3−i3−ii00000000
χ5144444-24-4-4444-24-24-24-4-4-4-4-24-2-244-2-2-24-2-22-4-4-4222-4-4-422-2-2-2-22222220000000000000000000000000000000000000000000000000000000000000
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χ564444-244-4-4-2444-2444-2-4-4-4-4-2-24-2-2-244-2-24-2-4222-4-4-4222-4-4-2-2-2-22222220000000000000000000000000000000000000000000000000000000000000
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χ584444-24-244-2-2-24-24-24-2-2-2-2-2-21-2-211-2-2-21-2-24-211-2-24-211-2-21111-2-2111100-4-400222200002222-1-1-1-1-1-1-1-100000000000000000000000000000000000
χ594444-24-2-4-4-2-2-24-24-24-22222-21-2-211-2-2-21-2-2-42-1-122-42-1-122111122-1-1-1-10000002323−23−2300000000−3−3−3−3333300000000000000000000000000000000000
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χ614444-2-2444-244-2-2-24-2-244441-2-21-2-2-2-21-2-21-2-2-2-2-2-2-2-2-2-2-2-211111111114400000000000000000000000000000000000000-2-2-2-211110000000000000
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χ634444-2-24-4-4-244-2-2-24-2-2-4-4-4-41-2-21-2-2-2-21-2-212222222222221111-1-1-1-1-1-1000000000000000000000000000000000000000000003-33-30000000000000
χ644444-2-24-4-4-244-2-2-24-2-2-4-4-4-41-2-21-2-2-2-21-2-212222222222221111-1-1-1-1-1-100000000000000000000000000000000000000000000-33-330000000000000
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χ6844-4-44-2400-4-4424-2-42-40000-24-22-442-22-42-2000000000000-22-22000000000000000000000000000000006−6−666−6−666−6−6600000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.