Finite Group Databasebeta

← Group #13167812

Character table — Group #13167812

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117
size11222222222222222444444444444444444444444666666668888888888812121212121212121212121212121212121212121212121212121212121212121212181824242424363636363636363636484872727272108108
order12333466688121224242424333666121212121212242424242424242424242424224466663612121224242424242424666666881212121212121212242424242424242424242424242424242466121222446812242461266121224
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-11111111111111111111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-11-111-1-111111111111111-111-1-11-11-11-111-1-111-1-1111111-1-1-1-1-1-1-1-111111-11-1-1-1-1-1-1111-11-1-1-1
χ4111111111111111111111111111111111111111111-11-111-1-111111111111-1-11-111-1-11-11-11-111-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-1-1-1-1-11-1111
χ511111111111111111111111111111111111111111-11-11-1-1111111111111111-11-1-111-11-11-11-1-111-1-111-1-1-1-1-1-1111111-1-11111-11-11-1-1-1-1-111-11-11-1-1
χ611111111111111111111111111111111111111111-11-11-1-11111111111111-1-1-11-1-111-11-11-11-1-111-1-111-1-1-1-1-1-1111111-1-1-1-1-1-11-11-1-1-1-1-1-1-1-11-11-111
χ711111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111111-1-1-1-111
χ811111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111-1-11111-1-1
χ9111111111-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-11-1111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-11-11-1-11-111-1-1-11
χ10111111111-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-11111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1111-11-1-1-11-1-1111-1
χ11111111111-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-111111-1-1-1-1-1-11-11-111-1-1-111-11-111-1-1-1-111-1-1-1-1-1-1111111-1-111-1-11-1-11-11-1111-11-1-111-1
χ12111111111-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-111111-1-1-1-1-1-1-111-111-1-1-111-11-111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-111-111-1-11-111-11-111-1-11
χ13111111111-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-11111111-1-1-1-1-1-11-1-11-1-1111-1-11-11-1-11111-1-1111111-1-1-1-1-1-1-1-111-1-1-111-1-11-1111-1-111-11-1
χ14111111111-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-11111111-1-1-1-1-1-1-11-11-1-1111-1-11-11-1-11111-1-1111111-1-1-1-1-1-1-1-1-1-1111-1-11-11-111-111-1-11-11
χ15111111111-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-11-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1111-11-1-11-1-1-111-11
χ16111111111-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-11-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111111111-1-11111-1-11-11-1-1-1111-1-11-1
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χ2022222-222200-2-20000222222-2-2-2-2-2-2000000000000-2-222-2-2-2-222-2-2-200000000-2-2-2-2-2-200222222220000000000000000-2200000000-2020000000000
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χ222222-1222-1222222222-1-12-1-12-122-1-1222222-1-1-1-1-1-1020200-1-1-1-1-1-1-1-1-1-1-1-1-1-2-20200-1-102020-100-1-10022000000-1-1-1-1-1-100-21-210-20-20000011010100
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χ242222-1222-1222222222-1-12-1-12-122-1-1222222-1-1-1-1-1-10-20-20011-1-1-1-1-1-1-1-1-1-1-1-2-20-200110-20-201001100-2-200000011111100-21-21020200000110-10-100
χ252222-1222-1-2-222-2-2-2-22-1-12-1-12-122-1-1-2-2-2-2-2-2111111020200-1-1-1-1-1-1-11111112-20200-1-10-2020-100-1-100-2-2000000111111002-1-21020-200000-110-10100
χ262222-1222-1-2-222-2-2-2-22-1-12-1-12-122-1-1-2-2-2-2-2-2111111020200-1-1-1-1-1-1-1111111-220200-1-10-2020-100-1-100-2-200000011111100-212-10-202000001-1010-100
χ272222-1222-1-2-222-2-2-2-22-1-12-1-12-122-1-1-2-2-2-2-2-21111110-20-20011-1-1-1-1-11111112-20-20011020-20100110022000000-1-1-1-1-1-1002-1-210-20200000-11010-100
χ282222-1222-1-2-222-2-2-2-22-1-12-1-12-122-1-1-2-2-2-2-2-21111110-20-20011-1-1-1-1-1111111-220-20011020-20100110022000000-1-1-1-1-1-100-212-1020-2000001-10-10100
χ29222-1222-1222222222-12-1-12-1-12-1-122-1-1-1-1-1-12222222020-1-100-1-1-1-1-1-1-1-1-1-1-12220-1-1002020-10-1-1002200-1-1-1-1-1-100000000-12-12202000000-1-1-10-1000
χ30222-1222-1222222222-12-1-12-1-12-1-122-1-1-1-1-1-12222222020-1-100-1-1-1-1-1-1-1-1-1-1-1-2-220-1-1002020-10-1-1002200-1-1-1-1-1-1000000001-21-2-20-200000011101000
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χ32222-1222-1222222222-12-1-12-1-12-1-122-1-1-1-1-1-1222222-20-201100-1-1-1-1-1-1-1-1-1-1-1-2-2-201100-20-20101100-2-200111111000000001-21-220200000011-10-1000
χ33222-1222-12-2-222-2-2-2-2-12-1-12-1-12-1-122111111-2-2-2-2-2-22020-1-100-1-1-1-1-11111112-220-1-100-2020-10-1-100-2-20011111100000000-121-220-2000000-11-101000
χ34222-1222-12-2-222-2-2-2-2-12-1-12-1-12-1-122111111-2-2-2-2-2-22020-1-100-1-1-1-1-1111111-2220-1-100-2020-10-1-100-2-200111111000000001-2-12-2020000001-110-1000
χ35222-1222-12-2-222-2-2-2-2-12-1-12-1-12-1-122111111-2-2-2-2-2-2-20-201100-1-1-1-1-11111112-2-20110020-201011002200-1-1-1-1-1-100000000-121-2-202000000-1110-1000
χ36222-1222-12-2-222-2-2-2-2-12-1-12-1-12-1-122111111-2-2-2-2-2-2-20-201100-1-1-1-1-1111111-22-20110020-201011002200-1-1-1-1-1-1000000001-2-1220-20000001-1-101000
χ3722-1222-12222-1-1-1-1-1-1-1-12-1-1222-1-1-1-122-1-1-1-122-1-1-1-122222222-1-12-1-122-1-1-1-100-1-1-1-1-1-122-1-122-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-12200000000-12-1-1-100000000
χ3822-1222-12222-1-1-1-1-1-1-1-12-1-1222-1-1-1-122-1-1-1-122-1-1-1-12-22-222-2-2-1-12-1-122-1-1-1-100-11-1-1112-2-112-2-1-111-1-11122-1-1-1-1-2-21111-2-2000000001-211100000000
χ3922-1222-12222-1-1-1-1-1-1-1-12-1-1222-1-1-1-122-1-1-1-122-1-1-1-1-22-22-2-222-1-12-1-122-1-1-1-1001-111-1-1-221-1-2211-1-111-1-1-2-2111122-1-1-1-1-2-2000000001-211100000000
χ4022-1222-12222-1-1-1-1-1-1-1-12-1-1222-1-1-1-122-1-1-1-122-1-1-1-1-2-2-2-2-2-2-2-2-1-12-1-122-1-1-1-100111111-2-211-2-211111111-2-21111-2-211112200000000-12-1-1-100000000
χ4122-1222-122-2-2-1-11111-1-12-1-1222-1-1-1-1-2-21111-2-2111122222222-1-12-1-1-2-2111100-1-1-1-1-1-1-2-2-1-122-1-1-1-11111-2-21111-2-211112200000000-1-2-11100000000
χ4222-1222-122-2-2-1-11111-1-12-1-1222-1-1-1-1-2-21111-2-211112-22-222-2-2-1-12-1-1-2-2111100-11-1-111-22-112-2-1-11111-1-1-2-2111122-1-1-1-1-2-200000000121-1-100000000
χ4322-1222-122-2-2-1-11111-1-12-1-1222-1-1-1-1-2-21111-2-21111-22-22-2-222-1-12-1-1-2-21111001-111-1-12-21-1-2211-1-1-1-11122-1-1-1-1-2-21111-2-200000000121-1-100000000
χ4422-1222-122-2-2-1-11111-1-12-1-1222-1-1-1-1-2-21111-2-21111-2-2-2-2-2-2-2-2-1-12-1-1-2-21111001111112211-2-21111-1-1-1-122-1-1-1-122-1-1-1-12200000000-1-2-11100000000
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χ4922-122-2-1220011−3−333-1-12-1-12-2-2111100−3−33300−3−33322-2-22222-1-1-21100−3−33300-1-1-1-1-1-10011-2-21111−33−3300−3−33300−3−333-220000000010-1−3300000000
χ5022-122-2-1220011−3−333-1-12-1-12-2-2111100−3−33300−3−3332-2-2222-2-2-1-1-21100−3−33300-11-1-111001-1-2211-1-1−333−300−3−3330033−3−32-200000000-1013−300000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.