Finite Group Databasebeta

← Group #13156489

Character table — Group #13156489

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117
size1111222222222222222222444444444444444444444444668888888888121212121212121212121212121212121212121212121212121212121212121212121224242424242424242436363636363636367272727272108108
order12223334466666666612121212333666666666121212121212121212121212443666121212121212266666666881212121212121212242424242424242424242424242424244121212121212121244882424242441212121244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1111-1-1-1-1
χ41111111111111111111111111111111111111111111111111111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111111111111111111111-1-11111111111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111111111111111111-1-1-1-1-1-1-1-1-111-1-1
χ61111111111111111111111111111111111111111111111-1-11111111111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-111
χ71111111111111111111111111111111111111111111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1111111-1-1-1-1-111
χ81111111111111111111111111111111111111111111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1
χ92222222-2-2222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-2222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-200222222220000000000000000000000000000000000000000
χ102222222-2-2222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-222222222200-2-2-2-2-2-2-2-20000000000000000000000000000000000000000
χ11222222-122222-122-1-1222222-1-122-1-1-12-1-1-12-1-122-1-1-1-122222-1-1-1-1-1-1-1-1-1-1222-1-1-1-1-1-10022-1-1-1-1-1-100000000000000002-1-122-1-1-1-1000000002-1-10000
χ12222222-122222-122-1-1222222-1-122-1-1-12-1-1-12-1-122-1-1-1-122222-1-1-1-1-1-1-1-1-1-1222-1-1-1-1-1-10022-1-1-1-1-1-10000000000000000-211-2-2111100000000-2110000
χ13222222-122222-122-1-1222222-1-122-1-1-12-1-1-12-1-122-1-1-1-1222-2-2-1-1-1-1-1-1-1-1-1-1-2-2-211111100-2-211111100000000000000002-1-122-1-1-1-100000000-2110000
χ14222222-122222-122-1-1222222-1-122-1-1-12-1-1-12-1-122-1-1-1-1222-2-2-1-1-1-1-1-1-1-1-1-1-2-2-211111100-2-21111110000000000000000-211-2-21111000000002-1-10000
χ15222222-1-2-2222-122-1-12-2-2-2-22-1-122-1-1-12-1-1-1-211-2-21111-2-2-222-1-1-1-1111111-2-2-21111110022-1-1-1-1-1-100000000000000000−i3i300−i3−i3i3i3000000000−i3i30000
χ16222222-1-2-2222-122-1-12-2-2-2-22-1-122-1-1-12-1-1-1-211-2-21111-2-2-222-1-1-1-1111111-2-2-21111110022-1-1-1-1-1-100000000000000000i3−i300i3i3−i3−i3000000000i3−i30000
χ17222222-1-2-2222-122-1-12-2-2-2-22-1-122-1-1-12-1-1-1-211-2-21111-2-2-2-2-2-1-1-1-1111111222-1-1-1-1-1-100-2-211111100000000000000000−i3i300−i3−i3i3i3000000000i3−i30000
χ18222222-1-2-2222-122-1-12-2-2-2-22-1-122-1-1-12-1-1-1-211-2-21111-2-2-2-2-2-1-1-1-1111111222-1-1-1-1-1-100-2-211111100000000000000000i3−i300i3i3−i3−i3000000000−i3i30000
χ1922222-12222-1-122-1222-1-1-1-1-12-1-1-12-1-1-12-12222-1-1-1-1-1-12-1-122-1-1-1-122-1-1-1-12-1-122-1-1-1-122-1-122-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-10000000000022-1-1-1-10000000
χ2022222-12222-1-122-1222-1-1-1-1-12-1-1-12-1-1-12-12222-1-1-1-1-1-12-1-122-1-1-1-122-1-1-1-12-1-122-1-1-1-1-2-2-1-122-1-1-1-11111-2-2-2-21111111100000000000-2-211110000000
χ2122222-12222-1-122-1222-1-1-1-1-12-1-1-12-1-1-12-12222-1-1-1-1-1-12-1-1-2-2-1-1-1-122-1-1-1-1-211-2-211112211-2-21111-1-1-1-12222-1-1-1-1-1-1-1-100000000000-2-211110000000
χ2222222-12222-1-122-1222-1-1-1-1-12-1-1-12-1-1-12-12222-1-1-1-1-1-12-1-1-2-2-1-1-1-122-1-1-1-1-211-2-21111-2-211-2-211111111-2-2-2-2111111110000000000022-1-1-1-10000000
χ2322222-12-2-22-1-122-12221111-12-1-1-12-1-1-12-12-2-2-2111111-21122-1-1-1-1-2-21111-211-2-2111100-1-122-1-1-1-133−3−300003333−3−3−3−3000000000000033−3−30000000
χ2422222-12-2-22-1-122-12221111-12-1-1-12-1-1-12-12-2-2-2111111-21122-1-1-1-1-2-21111-211-2-2111100-1-122-1-1-1-1−3−3330000−3−3−3−333330000000000000−3−3330000000
χ2522222-12-2-22-1-122-12221111-12-1-1-12-1-1-12-12-2-2-2111111-211-2-2-1-1-1-1-2-211112-1-122-1-1-1-10011-2-2111133−3−300003333−3−3−3−30000000000000−3−3330000000
χ2622222-12-2-22-1-122-12221111-12-1-1-12-1-1-12-12-2-2-2111111-211-2-2-1-1-1-1-2-211112-1-122-1-1-1-10011-2-21111−3−3330000−3−3−3−33333000000000000033−3−30000000
χ272222-12222-1222-1222-12222-1-12-1-1-122-1-12-1-122-1-12222-1-1-100-1-1-1-1-1-1-1-1-1-100000000022000000002222-1-1-1-1-1-1-1-1-1-1-1-1222-1-1-1-1-1-122000000000-1-100
χ282222-12222-1222-1222-12222-1-12-1-1-122-1-12-1-122-1-12222-1-1-100-1-1-1-1-1-1-1-1-1-100000000022000000002222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2111111-2-20000000001100
χ292222-12222-1222-1222-12222-1-12-1-1-122-1-12-1-122-1-12222-1-1-100-1-1-1-1-1-1-1-1-1-1000000000-2-200000000-2-2-2-2111111111111222-1-1-1-1-1-1-2-20000000001100
χ302222-12222-1222-1222-12222-1-12-1-1-122-1-12-1-122-1-12222-1-1-100-1-1-1-1-1-1-1-1-1-1000000000-2-200000000-2-2-2-2111111111111-2-2-211111122000000000-1-100
χ3122-2-22222-2-2-2-2-222-22-222-2-2222-2-2-2-2-2222-2-22-2-2-222-2-2222002-2-222-222-2-2000000000000000000000000000000000000000000002i−2i0000000002i−2i00
χ3222-2-22222-2-2-2-2-222-22-222-2-2222-2-2-2-2-2222-2-22-2-2-222-2-2222002-2-222-222-2-200000000000000000000000000000000000000000000−2i2i000000000−2i2i00
χ3322-2-2222-22-2-2-2-222-22-2-2-222222-2-2-2-2-2222-22-2222-2-222-2-2-2002-2-22-22-2-2220000000000000000000000000000000000000000000000000000000002i−2i
χ3422-2-2222-22-2-2-2-222-22-2-2-222222-2-2-2-2-2222-22-2222-2-222-2-2-2002-2-22-22-2-222000000000000000000000000000000000000000000000000000000000−2i2i
χ3522-2-2-1222-21-2-2-2-12-22122-2-2-1-12111-2-2-1-12112-21122-2-2-1-1-100-111-1-11-1-11100000000000000000000000−i3−i3i3i3−i3−i3i3i3−i3−i3i3i30003−33−33−32i−2i000000000−ii00
χ3622-2-2-1222-21-2-2-2-12-22122-2-2-1-12111-2-2-1-12112-21122-2-2-1-1-100-111-1-11-1-11100000000000000000000000−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3000−33−33−33−2i2i000000000i−i00
χ3722-2-2-1222-21-2-2-2-12-22122-2-2-1-12111-2-2-1-12112-21122-2-2-1-1-100-111-1-11-1-11100000000000000000000000i3i3−i3−i3i3i3−i3−i3i3i3−i3−i30003−33−33−3−2i2i000000000i−i00
χ3822-2-2-1222-21-2-2-2-12-22122-2-2-1-12111-2-2-1-12112-21122-2-2-1-1-100-111-1-11-1-11100000000000000000000000i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3000−33−33−332i−2i000000000−ii00
χ392-22-222200-22-2-2-2-22-2200002222-2-22-2-2-2-220000000000002i−2i22-2-20000000000000002−22i−2i2i−2i2i2i−2i−2i2−22−22−22−22−22−22−22−200000000000−i2i2−i2i2−i2i20000000
χ402-22-222200-22-2-2-2-22-2200002222-2-22-2-2-2-220000000000002i−2i22-2-2000000000000000−222i−2i2i−2i2i2i−2i−2i−22−22−22−22−22−22−22−2200000000000i2−i2i2−i2i2−i20000000
χ412-22-222200-22-2-2-2-22-2200002222-2-22-2-2-2-22000000000000−2i2i22-2-20000000000000002−2−2i2i−2i2i−2i−2i2i2i2−22−22−22−22−22−22−22−200000000000i2−i2i2−i2i2−i20000000
χ422-22-222200-22-2-2-2-22-2200002222-2-22-2-2-2-22000000000000−2i2i22-2-2000000000000000−22−2i2i−2i2i−2i−2i2i2i−22−22−22−22−22−22−22−2200000000000−i2i2−i2i2−i2i20000000
χ432-22-22-1200-2-11-2-212-223−33−3-12-1-11-2-111-2120003−33−33−303−32i−2i-1-111003−33−30−i3i300−i3−i3i3i32−2−ii2i−2i−i−iiiζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ232−22−2ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ2300000000000−i2i2ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70000000
χ442-22-22-1200-2-11-2-212-223−33−3-12-1-11-2-111-2120003−33−33−303−32i−2i-1-111003−33−30−i3i300−i3−i3i3i3−22−ii2i−2i−i−iii−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−22−22−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ2300000000000i2−i2−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70000000
χ452-22-22-1200-2-11-2-212-223−33−3-12-1-11-2-111-2120003−33−33−303−3−2i2i-1-111003−33−30i3−i300i3i3−i3−i32−2i−i−2i2iii−i−iζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ232−22−2ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ2300000000000i2−i2−ζ13−ζ23ζ13+ζ23−ζ5−ζ7ζ5+ζ70000000
χ462-22-22-1200-2-11-2-212-223−33−3-12-1-11-2-111-2120003−33−33−303−3−2i2i-1-111003−33−30i3−i300i3i3−i3−i3−22i−i−2i2iii−i−i−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−22−22−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ2300000000000−i2i2ζ13+ζ23−ζ13−ζ23ζ5+ζ7−ζ5−ζ70000000
χ472-22-22-1200-2-11-2-212-22−33−33-12-1-11-2-111-212000−33−33−330−332i−2i-1-11100−33−330i3−i300i3i3−i3−i32−2−ii2i−2i−i−iiiζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ72−22−2ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ700000000000−i2i2ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000000
χ482-22-22-1200-2-11-2-212-22−33−33-12-1-11-2-111-212000−33−33−330−332i−2i-1-11100−33−330i3−i300i3i3−i3−i3−22−ii2i−2i−i−iii−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−22−22−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ700000000000i2−i2−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000000
χ492-22-22-1200-2-11-2-212-22−33−33-12-1-11-2-111-212000−33−33−330−33−2i2i-1-11100−33−330−i3i300−i3−i3i3i32−2i−i−2i2iii−i−iζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ72−22−2ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7ζ5−ζ7−ζ5+ζ700000000000i2−i2−ζ5−ζ7ζ5+ζ7−ζ13−ζ23ζ13+ζ230000000
χ502-22-22-1200-2-11-2-212-22−33−33-12-1-11-2-111-212000−33−33−330−33−2i2i-1-11100−33−330−i3i300−i3−i3i3i3−22i−i−2i2iii−i−i−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−22−22−ζ13+ζ23ζ13−ζ23−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−ζ5+ζ7ζ5−ζ700000000000−i2i2ζ5+ζ7−ζ5−ζ7ζ13+ζ23−ζ13−ζ230000000
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χ5344444-2-2-4-44-2-2-24-2-2-242222-2-21-2-2-211-2-21-2-42222-1-1-1-1-42244111122-1-1-1-1-42222-1-1-1-100-2-2-2-211110000000000000000000000000000000000000000
χ5444444-2-2-4-44-2-2-24-2-2-242222-2-21-2-2-211-2-21-2-42222-1-1-1-1-422-4-4111122-1-1-1-14-2-2-2-21111002222-1-1-1-10000000000000000000000000000000000000000
χ554444-244-4-4-2444-2444-2-4-4-4-4-2-24-2-2-244-2-24-22-4-422-4-4-4-422200-2-2-2-222222200000000000000000000000000000000000000000000000000000000000
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χ614444-2-2444-2-2-24-2-244-2-2-2-2-21-2-211-2-2-21-2-2-2-24411-2-2-2-2-211001111-2-21111000000000-4-40000000022222222-1-1-1-1-1-1-1-1000000000000000000000000
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χ1088888-4-4-488-4-4-4-4-4-4-4-4-4-4-4-4-4222222222222-4-4-4222222-42200-1-1-1-122-1-1-1-100000000000000000000000000000000000000000000000000000000000
χ1098888-4-4-4-8-8-4-4-4-4-4-4-4-4-44444222222222222444-2-2-2-2-2-24-2-200-1-1-1-1-2-2111100000000000000000000000000000000000000000000000000000000000
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χ11188-8-8-4-4-4-884444-4-44-4444-4-4222-2-2-2-2-2222-2-44-422-2-2224-2-200-111-1-2211-1-100000000000000000000000000000000000000000000000000000000000
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χ1148-88-8-4-4-4004-44444-44-4−4343−43432222-2-22-2-2-2-2200023−2323−2323−23023−2300-1-11100−33−3300000000000000000000000000000000000000000000000000000000000
χ1158-8-88-48-400-4-88-44-84440000-42-44-424-44-24-2000000000000002-22-200000000000000000000000000000000000000000000000000000000000000000
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χ1178-8-88-4-4-400-44-4-444444−434343−43222-222-22-2-2-2-2000−232323−23−2323023−2300-11-1100−333−300000000000000000000000000000000000000000000000000000000000

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