Finite Group Databasebeta

← Group #13156467

Character table — Group #13156467

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117
size1111222222222222222222444444444444444444444444668888888888121212121212121212121212121212121212121212121212121212121212121212121224242424242424242436363636363636367272727272108108
order12223334466666666612121212333666666666121212121212121212121212223666121212121212466666666881212121212121212242424242424242424242424242424244121212121212121244882424242441212121244
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
χ92222222-2-2222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-2222222-2-2-2-2-2-2-22222222200-2-2-2-2-2-2-2-20000000000000000000000000000000000000000
χ102222222-2-2222222222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-2-2-22-2-2-2-2-2-2-2-200222222220000000000000000000000000000000000000000
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
χ15222222-1-2-2222-122-1-12-2-2-2-22-1-122-1-1-12-1-1-1-211-2-21111-2-2-222-1-1-1-1111111-222-1-1-1-1-1-100-2-211111100000000000000000−i3i300−i3−i3i3i3000000000−i3i30000
χ16222222-1-2-2222-122-1-12-2-2-2-22-1-122-1-1-12-1-1-1-211-2-21111-2-2-222-1-1-1-1111111-222-1-1-1-1-1-100-2-211111100000000000000000i3−i300i3i3−i3−i3000000000i3−i30000
χ17222222-1-2-2222-122-1-12-2-2-2-22-1-122-1-1-12-1-1-1-211-2-21111-2-2-2-2-2-1-1-1-11111112-2-21111110022-1-1-1-1-1-100000000000000000−i3i300−i3−i3i3i3000000000i3−i30000
χ18222222-1-2-2222-122-1-12-2-2-2-22-1-122-1-1-12-1-1-1-211-2-21111-2-2-2-2-2-1-1-1-11111112-2-21111110022-1-1-1-1-1-100000000000000000i3−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
χ2322222-12-2-22-1-122-12221111-12-1-1-12-1-1-12-12-2-2-2111111-21122-1-1-1-1-2-21111-2-1-122-1-1-1-10011-2-2111133−3−300003333−3−3−3−3000000000000033−3−30000000
χ2422222-12-2-22-1-122-12221111-12-1-1-12-1-1-12-12-2-2-2111111-21122-1-1-1-1-2-21111-2-1-122-1-1-1-10011-2-21111−3−3330000−3−3−3−333330000000000000−3−3330000000
χ2522222-12-2-22-1-122-12221111-12-1-1-12-1-1-12-12-2-2-2111111-211-2-2-1-1-1-1-2-21111211-2-2111100-1-122-1-1-1-133−3−300003333−3−3−3−30000000000000−3−3330000000
χ2622222-12-2-22-1-122-12221111-12-1-1-12-1-1-12-12-2-2-2111111-211-2-2-1-1-1-1-2-21111211-2-2111100-1-122-1-1-1-1−3−3330000−3−3−3−33333000000000000033−3−30000000
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
χ3122-2-22220022-22-2-2-2-2-200002222-222-2-2-2-2-20000000000002-222-2-200000002-22-222-2-22−2000000002−22−222−2−222−2−222−2−2000000000002−22−22−20000000
χ3222-2-22220022-22-2-2-2-2-200002222-222-2-2-2-2-20000000000002-222-2-200000002-22-222-2-2−2200000000−22−22−2−222−2−222−2−22200000000000−22−22−220000000
χ3322-2-22220022-22-2-2-2-2-200002222-222-2-2-2-2-2000000000000-2222-2-20000000-22-22-2-2222−2000000002−22−222−2−222−2−222−2−200000000000−22−22−220000000
χ3422-2-22220022-22-2-2-2-2-200002222-222-2-2-2-2-2000000000000-2222-2-20000000-22-22-2-222−2200000000−22−22−2−222−2−222−2−222000000000002−22−22−20000000
χ3522-2-22-12002-112-21-2-2-23−33−3-12-1-112-111-21-20003−333−3−303−32-2-1-1110033−3−30-112-2-1-1112−23−30033−3−3ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ2322−2−2ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23000000000002−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ230000000
χ3622-2-22-12002-112-21-2-2-23−33−3-12-1-112-111-21-20003−333−3−303−32-2-1-1110033−3−30-112-2-1-111−223−30033−3−3−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−2−222−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ2300000000000−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ230000000
χ3722-2-22-12002-112-21-2-2-23−33−3-12-1-112-111-21-20003−333−3−303−3-22-1-1110033−3−301-1-2211-1-12−2−3300−3−333ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ2322−2−2ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ2300000000000−22−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ230000000
χ3822-2-22-12002-112-21-2-2-23−33−3-12-1-112-111-21-20003−333−3−303−3-22-1-1110033−3−301-1-2211-1-1−22−3300−3−333−ζ5+ζ7ζ5−ζ7−ζ13+ζ23ζ13−ζ23−2−222−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23000000000002−2ζ5−ζ7−ζ5+ζ7ζ13−ζ23−ζ13+ζ230000000
χ3922-2-22-12002-112-21-2-2-2−33−33-12-1-112-111-21-2000−33−3−3330−332-2-1-11100−3−3330-112-2-1-1112−2−3300−3−333ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ722−2−2ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ7000000000002−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ70000000
χ4022-2-22-12002-112-21-2-2-2−33−33-12-1-112-111-21-2000−33−3−3330−332-2-1-11100−3−3330-112-2-1-111−22−3300−3−333−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−2−222−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ700000000000−22−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ70000000
χ4122-2-22-12002-112-21-2-2-2−33−33-12-1-112-111-21-2000−33−3−3330−33-22-1-11100−3−33301-1-2211-1-12−23−30033−3−3ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ722−2−2ζ13−ζ23ζ13−ζ23−ζ13+ζ23−ζ13+ζ23ζ5−ζ7ζ5−ζ7−ζ5+ζ7−ζ5+ζ700000000000−22−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ70000000
χ4222-2-22-12002-112-21-2-2-2−33−33-12-1-112-111-21-2000−33−3−3330−33-22-1-11100−3−33301-1-2211-1-1−223−30033−3−3−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7−2−222−ζ13+ζ23−ζ13+ζ23ζ13−ζ23ζ13−ζ23−ζ5+ζ7−ζ5+ζ7ζ5−ζ7ζ5−ζ7000000000002−2ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ70000000
χ432-22-22222-2-2-2-2-222-22-222-2-2222-2-2-2-2-2222-2-22-2-2-22-22-2222002-2-222-22-22-2000000000000000000000000000000000000000000002i−2i0000000002i−2i00
χ442-22-22222-2-2-2-2-222-22-222-2-2222-2-2-2-2-2222-2-22-2-2-22-22-2222002-2-222-22-22-200000000000000000000000000000000000000000000−2i2i000000000−2i2i00
χ452-22-2222-22-2-2-2-222-22-2-2-222222-2-2-2-2-2222-22-2222-22-22-2-2-2002-2-22-22-22-220000000000000000000000000000000000000000000000000000000002i−2i
χ462-22-2222-22-2-2-2-222-22-2-2-222222-2-2-2-2-2222-22-2222-22-22-2-2-2002-2-22-22-22-22000000000000000000000000000000000000000000000000000000000−2i2i
χ472-22-2-1222-21-2-2-2-12-22122-2-2-1-12111-2-2-1-12112-2112-22-2-1-1-100-111-1-11-11-1100000000000000000000000−i3i3−i3i3−i3i3−i3i3−i3i3−i3i30003−33−33−32i−2i000000000−ii00
χ482-22-2-1222-21-2-2-2-12-22122-2-2-1-12111-2-2-1-12112-2112-22-2-1-1-100-111-1-11-11-1100000000000000000000000−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3000−33−33−33−2i2i000000000i−i00
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χ5144444-2-2444-2-2-24-2-2-24-2-2-2-2-2-21-2-2-211-2-21-24-2-2-2-211114-2-2441111-2-211114-2-2-2-2111100-2-2-2-211110000000000000000000000000000000000000000
χ5244444-2-2444-2-2-24-2-2-24-2-2-2-2-2-21-2-2-211-2-21-24-2-2-2-211114-2-2-4-41111-2-21111-42222-1-1-1-1002222-1-1-1-10000000000000000000000000000000000000000
χ5344444-2-2-4-44-2-2-24-2-2-242222-2-21-2-2-211-2-21-2-42222-1-1-1-1-42244111122-1-1-1-1-4-2-2-2-21111002222-1-1-1-10000000000000000000000000000000000000000
χ5444444-2-2-4-44-2-2-24-2-2-242222-2-21-2-2-211-2-21-2-42222-1-1-1-1-422-4-4111122-1-1-1-142222-1-1-1-100-2-2-2-211110000000000000000000000000000000000000000
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
χ564444-24-244-244-2-24-2-2-24444-21-2-2-21-2-2-21-21-2-2-2-2-2-2-2-2-2-2-2-2001111111111000000000000000000000000000000000004-2-2-2-21111000000000000000
χ574444-24-244-244-2-24-2-2-24444-21-2-2-21-2-2-21-21-2-2-2-2-2-2-2-2-2-2-2-200111111111100000000000000000000000000000000000-42222-1-1-1-1000000000000000
χ584444-24-2-4-4-244-2-24-2-2-2-4-4-4-4-21-2-2-21-2-2-21-21222222222222001111-1-1-1-1-1-1000000000000000000000000000000000000−2i32i300i3i3−i3−i3000000000000000
χ594444-24-2-4-4-244-2-24-2-2-2-4-4-4-4-21-2-2-21-2-2-21-21222222222222001111-1-1-1-1-1-10000000000000000000000000000000000002i3−2i300−i3−i3i3i3000000000000000
χ604444-2-2444-2-2-24-2-244-2-2-2-2-21-2-211-2-2-21-2-2-2-24411-2-2-2-2-211001111-2-211110000000004400000000-2-2-2-2-2-2-2-211111111000000000000000000000000
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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χ6944-4-44-2-2004-22-2-4222-4−2323−2323-2-21-22-21-122-12000−232333−3−30−2323-4411-1-10033−3−302-22-2-1-1110023−2300−3−3330000000000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.