Finite Group Databasebeta

← Group #13161776

Character table — Group #13161776

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size112222222222244444444444444444444444444448888888888888888888888888888888888888363636363636363636363636727272727272727272727272
order1223334466612123333366666666121212121212121212121212121212666668121212121224242424242424242424242424242424242424242424242424242244444412121212266668121212122424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111-11-1-1-1111111-11-1-1-1-11-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111111111-11-11-1-1-1-1-1-1-1-11-1111-1-11-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-11-1-11111
χ51111111111111111111111111111111111111111111111-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-111-1-1-11111-1-1
χ61111111111111111111111111111111111111111111111-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-1-1-1-1-1-111-11111-1-1-111
χ71111111111111111111111111111111111111111111111-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1111111-1-11-1-11-11-1-111
χ81111111111111111111111111111111111111111111111-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-111-1-1-111-1-1
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χ10222222-2-2222-2-22222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222220-2-2-2-2-2000000000000000000000000000000-2200000000000000-2200
χ1122222-1222-12222-1-1-1-12-12-1-1-1-122-1-1222-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-102020000000020-1-1-100-10000
χ1222222-1222-12222-1-1-1-12-12-1-1-1-122-1-1222-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10-20-200000000-201110010000
χ1322222-1222-12222-1-1-1-12-12-1-1-1-122-1-1222-1-1-1-1-1-1-1-122-1-1-1-1-22-1-1-1-1-2-2-2-2-2-2-2-2111111111111111111020200000000-20-11100-10000
χ1422222-1222-12222-1-1-1-12-12-1-1-1-122-1-1222-1-1-1-1-1-1-1-122-1-1-1-1-22-1-1-1-1-2-2-2-2-2-2-2-21111111111111111110-20-200000000201-1-10010000
χ152222-1222-122-1-1-12-1-1-122-12-1-1-1-1-1222-1-122-1-1-1-1-1-12-12-1-1-12-12-1-1-1-1-122-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-120200022-1-1-1-10-10000-100000
χ162222-1222-122-1-1-12-1-1-122-12-1-1-1-1-1222-1-122-1-1-1-1-1-12-12-1-1-12-12-1-1-1-1-122-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-20-2000-2-21111010000100000
χ172222-1222-122-1-1-12-1-1-122-12-1-1-1-1-1222-1-122-1-1-1-1-1-12-12-1-1-1-2-12-1-1-111-2-21111-2-2-2-2-2-2111111111111202000-2-211110-10000-100000
χ182222-1222-122-1-1-12-1-1-122-12-1-1-1-1-1222-1-122-1-1-1-1-1-12-12-1-1-1-2-12-1-1-111-2-21111-2-2-2-2-2-2111111111111-20-200022-1-1-1-1010000100000
χ19222-1222222-122-1-12-1-1-12-1-12-1-12222-1-1-1-1-122-1-1-1-1-1-1-12-1-12-1-12-1-122-1-1-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-100002200000000000200-1-1-1-1
χ20222-1222222-122-1-12-1-1-12-1-12-1-12222-1-1-1-1-122-1-1-1-1-1-1-12-1-12-1-12-1-122-1-1-1-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-10000-2-200000000000-2001111
χ21222-1222222-122-1-12-1-1-12-1-12-1-12222-1-1-1-1-122-1-1-1-1-1-1-12-1-1-2-1-12-1-1-2-2111111-2-21111-2-2-2-21111111100002200000000000-200-1-111
χ22222-1222222-122-1-12-1-1-12-1-12-1-12222-1-1-1-1-122-1-1-1-1-1-1-12-1-1-2-1-12-1-1-2-2111111-2-21111-2-2-2-2111111110000-2-20000000000020011-1-1
χ23222-122-2-222-1-2-2-1-12-1-1-12-1-12-1-12-2-2-211111-2-211111-1-12-1-1011-211003−333−3−30033−3−300003333−3−3−3−300002-200000000000000-113−3
χ24222-122-2-222-1-2-2-1-12-1-1-12-1-12-1-12-2-2-211111-2-211111-1-12-1-1011-211003−333−3−30033−3−300003333−3−3−3−30000-22000000000000001-1−33
χ25222-122-2-222-1-2-2-1-12-1-1-12-1-12-1-12-2-2-211111-2-211111-1-12-1-1011-21100−33−3−33300−3−3330000−3−3−3−3333300002-200000000000000-11−33
χ26222-122-2-222-1-2-2-1-12-1-1-12-1-12-1-12-2-2-211111-2-211111-1-12-1-1011-21100−33−3−33300−3−3330000−3−3−3−333330000-22000000000000001-13−3
χ2722-22222-22222222222-2-222222-2-2-2222222222222-2-2-2-2-2-20-2-2-2-2-200000000000000000000000000020-2000000000020000-20000
χ2822-22222-22222222222-2-222222-2-2-2222222222222-2-2-2-2-2-20-2-2-2-2-2000000000000000000000000000-2020000000000-2000020000
χ2922-2222-22222-2-222222-2-222222-222-2-2-2-2-2-2-2-2-2-2-2-22-2-2-2-2-20222220000000000000000000000000020-2000000000020000-200000
χ3022-2222-22222-2-222222-2-222222-222-2-2-2-2-2-2-2-2-2-2-2-22-2-2-2-2-202222200000000000000000000000000-2020000000000-20000200000
χ3122-222-12-22-12222-1-1-1-1-212-1-1-1-1-2-21-1222-1-1-1-1-1-1-1-1-2-211110-2111100000000−i3i3−i3i3−i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3020-20000000000-1−i3i30010000
χ3222-222-12-22-12222-1-1-1-1-212-1-1-1-1-2-21-1222-1-1-1-1-1-1-1-1-2-211110-2111100000000−i3i3−i3i3−i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i30-20200000000001i3−i300-10000
χ3322-222-12-22-12222-1-1-1-1-212-1-1-1-1-2-21-1222-1-1-1-1-1-1-1-1-2-211110-2111100000000i3−i3i3−i3i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3020-20000000000-1i3−i30010000
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χ3622-22-12-22-12211-12-1-1-1-2-2-12-1-1-11-12-2-211-2-211111121-21110-12-1-1-13−3003−33−30000003−33−33−33−33−33−3-20200000−3−333010000-100000
χ3722-22-12-22-12211-12-1-1-1-2-2-12-1-1-11-12-2-211-2-211111121-21110-12-1-1-1−3300−33−33000000−33−33−33−33−33−3320-200000−3−3330-10000100000
χ3822-22-12-22-12211-12-1-1-1-2-2-12-1-1-11-12-2-211-2-211111121-21110-12-1-1-1−3300−33−33000000−33−33−33−33−33−33-2020000033−3−3010000-100000
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χ424444-2-244-2-24-2-2-2-21114-2-2-2111-2-2-2-24-2-2-2-21111114-2-2111-4-2-211122-4-42222222222-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000
χ434444-2-2-4-4-2-2422-2-21114-2-2-2111-2222-42222-1-1-1-1-1-1-4-2-2111022-1-1-1000000000000003i−3i−3i3i3i−3i−3i3i3i−3i−3i3i000000000000000000000000
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χ45444-24-2444-2-244-21-211-2-2-21-21144-2-2-2-2-211-2-21111-2-21-2114-21-21144-2-2-2-2-2-2-2-21111-2-2-2-211111111000000000000000000000000
χ46444-24-2444-2-244-21-211-2-2-21-21144-2-2-2-2-211-2-21111-2-21-211-4-21-211-4-422222222-1-1-1-12222-1-1-1-1-1-1-1-1000000000000000000000000
χ47444-24-2-4-44-2-2-4-4-21-211-2-2-21-2114-422222-1-122-1-1-1-12-21-21102-12-1-10023−232323−23−2300−3−3330000−3−3−3−33333000000000000000000000000
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χ49444-2-2444-24-2-2-21-2-211-241-2-211-2-244-211-2-2-2-21111-21-2-21141-2-211-2-2-2-2111144-2-2-2-2-2-2-2-211111111000000000000000000000000
χ50444-2-2444-24-2-2-21-2-211-241-2-211-2-244-211-2-2-2-21111-21-2-211-41-2-2112222-1-1-1-1-4-422222222-1-1-1-1-1-1-1-1000000000000000000000000
χ51444-2-24-4-4-24-2221-2-211-241-2-211-22-4-42-1-12222-1-1-1-121-2-2110-122-1-10023−23−3−333002323−23−230000−3−3−3−33333000000000000000000000000
χ52444-2-24-4-4-24-2221-2-211-241-2-211-22-4-42-1-12222-1-1-1-121-2-2110-122-1-100−232333−3−300−23−23232300003333−3−3−3−3000000000000000000000000
χ53444-2-2-244-2-2-2-2-2111−1−3i32−1+3i32-2-2111−1−3i32−1+3i32-2-2-2-2-2111111−1−3i32−1−3i32−1+3i32−1+3i32-2111−1−3i32−1+3i324111−1−3i32−1+3i32-2-2-2-21111-2-211111111−1−3i32−1+3i32−1+3i32−1−3i32−1+3i32−1−3i32−1−3i32−1+3i32000000000000000000000000
χ54444-2-2-244-2-2-2-2-2111−1−3i32−1+3i32-2-2111−1−3i32−1+3i32-2-2-2-2-2111111−1−3i32−1−3i32−1+3i32−1+3i32-2111−1−3i32−1+3i32-4111−1−3i32−1+3i322222-1-1-1-122-1-1-1-1-1-1-1-11+3i321−3i321−3i321+3i321−3i321+3i321+3i321−3i32000000000000000000000000
χ55444-2-2-244-2-2-2-2-2111−1+3i32−1−3i32-2-2111−1+3i32−1−3i32-2-2-2-2-2111111−1+3i32−1+3i32−1−3i32−1−3i32-2111−1+3i32−1−3i324111−1+3i32−1−3i32-2-2-2-21111-2-211111111−1+3i32−1−3i32−1−3i32−1+3i32−1−3i32−1+3i32−1+3i32−1−3i32000000000000000000000000
χ56444-2-2-244-2-2-2-2-2111−1+3i32−1−3i32-2-2111−1+3i32−1−3i32-2-2-2-2-2111111−1+3i32−1+3i32−1−3i32−1−3i32-2111−1+3i32−1−3i32-4111−1+3i32−1−3i322222-1-1-1-122-1-1-1-1-1-1-1-11−3i321+3i321+3i321−3i321+3i321−3i321−3i321+3i32000000000000000000000000
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χ58444-2-2-2-4-4-2-2-222111−1−3i32−1+3i32-2-2111−1−3i32−1+3i32-22222-1-1-1-1-1-11+3i321+3i321−3i321−3i322111−1−3i32−1+3i320-1-1-11+3i321−3i3200−232333−3−30033−3−3−3i3i3i−3i−ζ7−2ζ112ζ7+ζ112ζ7+ζ11−ζ7−2ζ11−2ζ7−ζ11ζ7+2ζ11ζ7+2ζ11−2ζ7−ζ11000000000000000000000000
χ59444-2-2-2-4-4-2-2-222111−1+3i32−1−3i32-2-2111−1+3i32−1−3i32-22222-1-1-1-1-1-11−3i321−3i321+3i321+3i322111−1+3i32−1−3i320-1-1-11−3i321+3i320023−23−3−33300−3−333−3i3i3i−3i−2ζ7−ζ11ζ7+2ζ11ζ7+2ζ11−2ζ7−ζ11−ζ7−2ζ112ζ7+ζ112ζ7+ζ11−ζ7−2ζ11000000000000000000000000
χ60444-2-2-2-4-4-2-2-222111−1+3i32−1−3i32-2-2111−1+3i32−1−3i32-22222-1-1-1-1-1-11−3i321−3i321+3i321+3i322111−1+3i32−1−3i320-1-1-11−3i321+3i3200−232333−3−30033−3−33i−3i−3i3i2ζ7+ζ11−ζ7−2ζ11−ζ7−2ζ112ζ7+ζ11ζ7+2ζ11−2ζ7−ζ11−2ζ7−ζ11ζ7+2ζ11000000000000000000000000
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χ7544-4-2-24-44-24-2221-2-2112-41-2-2112-24-42-1-12222-1-1-1-1-2-122-1-101-2-21123−2300−33−3300000023−2323−23−33−33−33−33000000000000000000000000
χ7644-4-2-24-44-24-2221-2-2112-41-2-2112-24-42-1-12222-1-1-1-1-2-122-1-101-2-211−2323003−33−3000000−2323−23233−33−33−33−3000000000000000000000000
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χ854-4044400-4-4-4004444400-4-4-4-4-4000000000000000000000000000000000000000000000000000000000002i−2i2i−2i2i−2i000000000000
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χ928-808-4-40044-843−43-4-42220044-2-2-20000043−4300−2323−2323−232300000000000000000000000000000000000000000000000000000000000000
χ938-808-4-40044-8−4343-4-42220044-2-2-200000−43430023−2323−2323−2300000000000000000000000000000000000000000000000000000000000000
χ948-80-48800-8-8400-4-48-4-40044-84400000000000000000000000000000000000000000000000000000000000000000000000000000
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χ968-80-48-400-84400-42-422004-24-2-20000000−6i6i00−6i6i6i−6i00000000000000000000000000000000000000000000000000000000000000
χ978-80-4-48004-8443−432-4-42200-244-2-200000−23230043−43−2323−232300000000000000000000000000000000000000000000000000000000000000
χ988-80-4-48004-84−43432-4-42200-244-2-20000023−2300−434323−2323−2300000000000000000000000000000000000000000000000000000000000000
χ998-80-4-4-40044443−43222−1−3i3−1+3i300-2-2-21+3i31−3i300000−23236i−6i−23232ζ7+4ζ11−2ζ7−4ζ11−4ζ7−2ζ114ζ7+2ζ1100000000000000000000000000000000000000000000000000000000000000
χ1008-80-4-4-40044443−43222−1+3i3−1−3i300-2-2-21−3i31+3i300000−2323−6i6i−2323−4ζ7−2ζ114ζ7+2ζ112ζ7+4ζ11−2ζ7−4ζ1100000000000000000000000000000000000000000000000000000000000000
χ1018-80-4-4-400444−4343222−1−3i3−1+3i300-2-2-21+3i31−3i30000023−23−6i6i23−23−2ζ7−4ζ112ζ7+4ζ114ζ7+2ζ11−4ζ7−2ζ1100000000000000000000000000000000000000000000000000000000000000
χ1028-80-4-4-400444−4343222−1+3i3−1−3i300-2-2-21−3i31+3i30000023−236i−6i23−234ζ7+2ζ11−4ζ7−2ζ11−2ζ7−4ζ112ζ7+4ζ1100000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.