Finite Group Databasebeta

← Group #13155238

Character table — Group #13155238

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size112222222222222224444444444444444444444446666888888888881212121212121212121212121212121212121212121212121212121212121212121224242436363636363648484872727272144216
order123334666881212242424243336661212121212122424242424242424242424242412123612121224242424242466668121212161624242424242424244848484848484848484848484848484841212161648484848121212226662
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1111111-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-11111-111-1-1
χ41111111111111111111111111111111111111111111111111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111
χ511111111111111111111111111111111111111111-1-1-1-111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111111111111-1-1-1-1-1-1111-11-1-11-1
χ611111111111111111111111111111111111111111-1-1-1-111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-11-111-11
χ711111111111111111111111111111111111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-11
χ811111111111111111111111111111111111111111-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-111111-1
χ9222222222-2-222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-2222222222-2-2-2-2-2-22222-222200-2-2-2-2-2-2-2-20000000000000000000000000000000000
χ10222222222-2-222-2-2-2-2222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222-2-2-2-2-2-2-2-2-2-22-2-2-200222222220000000000000000000000000000000000
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χ1222222-222200-2-20000222222-2-2-2-2-2-20000000000002-2-2-222-2-2-200000022220-2-2-2−2200000000−2−222−2−2−2−2−2−2222222000−22−2−222000000000
χ1322222-222200-2-20000222222-2-2-2-2-2-2000000000000-222222-2-2-2000000-2-2-2-202222−20000000022−2−2222222−2−2−2−2−2−2000−22−2−222000000000
χ1422222-222200-2-20000222222-2-2-2-2-2-2000000000000-222222-2-2-2000000-2-2-2-20222−2200000000−2−222−2−2−2−2−2−22222220002−222−2−2000000000
χ152222-1222-1222222222-1-12-1-1222-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-12-1-1-122-1-10022-1-1-1-1-1-100000000000000002-1-10000002-1-120-1-100
χ162222-1222-1222222222-1-12-1-1222-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-12-1-1-122-1-10022-1-1-1-1-1-10000000000000000-211000000-211-201100
χ172222-1222-1222222222-1-12-1-1222-1-1-1-1-1-1-1-1-1222222-2-211-1-1-1-1-1-1-1-1-1-1-1-2111-2-21100-2-211111100000000000000002-1-10000002-1-1-201100
χ182222-1222-1222222222-1-12-1-1222-1-1-1-1-1-1-1-1-1222222-2-211-1-1-1-1-1-1-1-1-1-1-1-2111-2-21100-2-21111110000000000000000-211000000-21120-1-100
χ192222-1222-1-2-222-2-2-2-22-1-12-1-1222-1-1-1111111-2-2-2-2-2-222-1-1-1-1-1-1-11111112-1-1-1-22-1-100-2-211111100000000000000000−i3i30000000−i3i300−i3i300
χ202222-1222-1-2-222-2-2-2-22-1-12-1-1222-1-1-1111111-2-2-2-2-2-222-1-1-1-1-1-1-11111112-1-1-1-22-1-100-2-211111100000000000000000i3−i30000000i3−i300i3−i300
χ212222-1222-1-2-222-2-2-2-22-1-12-1-1222-1-1-1111111-2-2-2-2-2-2-2-211-1-1-1-1-1111111-21112-2110022-1-1-1-1-1-100000000000000000−i3i30000000−i3i300i3−i300
χ222222-1222-1-2-222-2-2-2-22-1-12-1-1222-1-1-1111111-2-2-2-2-2-2-2-211-1-1-1-1-1111111-21112-2110022-1-1-1-1-1-100000000000000000i3−i30000000i3−i300−i3i300
χ23222-1222-1222222222-1-12-12-1-1-1-1222222222-1-1-1-1-1-10000-1-1-1-1-1-1-1-1-1-1-10000000022000000002222-1-1-1-1-1-1-1-1-1-1-1-1222000000-1-1-10200-10
χ24222-1222-1222222222-1-12-12-1-1-1-1222222222-1-1-1-1-1-10000-1-1-1-1-1-1-1-1-1-1-10000000022000000002222-1-1-1-1-1-1-1-1-1-1-1-1-2-2-20000001110-20010
χ25222-1222-1222222222-1-12-12-1-1-1-1222222222-1-1-1-1-1-10000-1-1-1-1-1-1-1-1-1-1-100000000-2-200000000-2-2-2-2111111111111222000000-1-1-10-20010
χ26222-1222-1222222222-1-12-12-1-1-1-1222222222-1-1-1-1-1-10000-1-1-1-1-1-1-1-1-1-1-100000000-2-200000000-2-2-2-2111111111111-2-2-20000001110200-10
χ2722-1222-12222-1-1-1-1-1-1-12-1-1-122-1-12-1-122-1-1-1-122-1-1-1-12222-1-12-1-122-1-1-1-1-12-1-12-1-1-122-1-122-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-100022-1-1-1-1000000000
χ2822-1222-12222-1-1-1-1-1-1-12-1-1-122-1-12-1-122-1-1-1-122-1-1-1-12222-1-12-1-122-1-1-1-1-12-1-12-1-1-1-2-2-1-122-1-1-1-11111-2-21111-2-21111000-2-21111000000000
χ2922-1222-12222-1-1-1-1-1-1-12-1-1-122-1-12-1-122-1-1-1-122-1-1-1-1-2-2-2-2-1-12-1-122-1-1-1-11-211-21112211-2-21111-1-1-1-122-1-1-1-122-1-1-1-1000-2-21111000000000
χ3022-1222-12222-1-1-1-1-1-1-12-1-1-122-1-12-1-122-1-1-1-122-1-1-1-1-2-2-2-2-1-12-1-122-1-1-1-11-211-2111-2-211-2-211111111-2-21111-2-2111100022-1-1-1-1000000000
χ3122-1222-122-2-2-1-11111-12-1-1-122-1-12-1-1-2-21111-2-211112222-1-12-1-1-2-21111-12-1-1-2-1-1-10011-2-211113−33−30033−3−30033−3−3000003−33−3000000000
χ3222-1222-122-2-2-1-11111-12-1-1-122-1-12-1-1-2-21111-2-211112222-1-12-1-1-2-21111-12-1-1-2-1-1-10011-2-21111−33−3300−3−33300−3−33300000−33−33000000000
χ3322-1222-122-2-2-1-11111-12-1-1-122-1-12-1-1-2-21111-2-21111-2-2-2-2-1-12-1-1-2-211111-211211100-1-122-1-1-1-13−33−30033−3−30033−3−300000−33−33000000000
χ3422-1222-122-2-2-1-11111-12-1-1-122-1-12-1-1-2-21111-2-21111-2-2-2-2-1-12-1-1-2-211111-211211100-1-122-1-1-1-1−33−3300−3−33300−3−333000003−33−3000000000
χ3522-122-2-122001133−3−3-12-1-1-12-211-2110033−3−30033−3−32-2-2-2-1-1-2110033−3−3-12-1-101112−23−30033−3−3ζ10−ζ14ζ26−ζ46−ζ10+ζ14−ζ26+ζ4622ζ10−ζ14ζ10−ζ14ζ26−ζ46ζ26−ζ46−2−2−ζ10+ζ14−ζ10+ζ14−ζ26+ζ46−ζ26+ζ460002−2ζ10−ζ14ζ26−ζ46−ζ10+ζ14−ζ26+ζ46000000000
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χ3722-122-2-122001133−3−3-12-1-1-12-211-2110033−3−30033−3−3-2222-1-1-2110033−3−31-2110-1-1-12−2−3300−3−333ζ10−ζ14ζ26−ζ46−ζ10+ζ14−ζ26+ζ4622ζ10−ζ14ζ10−ζ14ζ26−ζ46ζ26−ζ46−2−2−ζ10+ζ14−ζ10+ζ14−ζ26+ζ46−ζ26+ζ46000−22−ζ10+ζ14−ζ26+ζ46ζ10−ζ14ζ26−ζ46000000000
χ3822-122-2-122001133−3−3-12-1-1-12-211-2110033−3−30033−3−3-2222-1-1-2110033−3−31-2110-1-1-1−22−3300−3−333−ζ10+ζ14−ζ26+ζ46ζ10−ζ14ζ26−ζ46−2−2−ζ10+ζ14−ζ10+ζ14−ζ26+ζ46−ζ26+ζ4622ζ10−ζ14ζ10−ζ14ζ26−ζ46ζ26−ζ460002−2ζ10−ζ14ζ26−ζ46−ζ10+ζ14−ζ26+ζ46000000000
χ3922-122-2-1220011−3−333-12-1-1-12-211-21100−3−33300−3−3332-2-2-2-1-1-21100−3−333-12-1-101112−2−3300−3−333ζ26−ζ46ζ10−ζ14−ζ26+ζ46−ζ10+ζ1422ζ26−ζ46ζ26−ζ46ζ10−ζ14ζ10−ζ14−2−2−ζ26+ζ46−ζ26+ζ46−ζ10+ζ14−ζ10+ζ140002−2ζ26−ζ46ζ10−ζ14−ζ26+ζ46−ζ10+ζ14000000000
χ4022-122-2-1220011−3−333-12-1-1-12-211-21100−3−33300−3−3332-2-2-2-1-1-21100−3−333-12-1-10111−22−3300−3−333−ζ26+ζ46−ζ10+ζ14ζ26−ζ46ζ10−ζ14−2−2−ζ26+ζ46−ζ26+ζ46−ζ10+ζ14−ζ10+ζ1422ζ26−ζ46ζ26−ζ46ζ10−ζ14ζ10−ζ14000−22−ζ26+ζ46−ζ10+ζ14ζ26−ζ46ζ10−ζ14000000000
χ4122-122-2-1220011−3−333-12-1-1-12-211-21100−3−33300−3−333-2222-1-1-21100−3−3331-2110-1-1-12−23−30033−3−3ζ26−ζ46ζ10−ζ14−ζ26+ζ46−ζ10+ζ1422ζ26−ζ46ζ26−ζ46ζ10−ζ14ζ10−ζ14−2−2−ζ26+ζ46−ζ26+ζ46−ζ10+ζ14−ζ10+ζ14000−22−ζ26+ζ46−ζ10+ζ14ζ26−ζ46ζ10−ζ14000000000
χ4222-122-2-1220011−3−333-12-1-1-12-211-21100−3−33300−3−333-2222-1-1-21100−3−3331-2110-1-1-1−223−30033−3−3−ζ26+ζ46−ζ10+ζ14ζ26−ζ46ζ10−ζ14−2−2−ζ26+ζ46−ζ26+ζ46−ζ10+ζ14−ζ10+ζ1422ζ26−ζ46ζ26−ζ46ζ10−ζ14ζ10−ζ140002−2ζ26−ζ46ζ10−ζ14−ζ26+ζ46−ζ10+ζ14000000000
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χ46444-24-44-2400-4-40000-2-24-24-2222-4-4-40000000000000000-2-22220000000000000022−22000000002222−22−22−2−2−2−2−2−2222222000000000000000000
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χ50444-2-244-2-2-4-444-4-4-4-4-21-2-2-21-2-2-2-2-2-2222222222222000011111-1-1-1-1-1-100000000000000000000000000000000000−2i32i30000000i3−i3000000
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χ5544-24-24-24-2-4-4-2-22222-2-21-21-24-2-2-21122-1-1-1-1-4-42222-4-42211-21122-1-1-1-122-1-142-1-100-2-2-2-211110000000000000000000000000000000000
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χ5944-24-2-4-24-20022−23−232323-2-21-21-2-4222-1-10033−3−300−23−232323-44-2-2112-1-10033−3−322-1-10-2110023−2300−3−3330000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 48 (ζ48 = 1); i = ζ12.