Finite Group Databasebeta

← Group #13161774

Character table — Group #13161774

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size112222222222244444444444444444444444444448888888888888888888888888888888888888363636363636363636363636727272727272727272727272
order12233344666121233333666666661212121212121212121212121212126666681212121212242424242424242424242424242424242424242424242424242422224444121212122666666812122424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-11-1-111
χ3111111111111111111111111111111111111111111111111111111111111111111111111111111-1-11-11-1111111-11-1-1-1-1-1-11-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-11-11-1-1-1-1-1-11-1-1-1111-1-11-1-1
χ51111111111111111111111111111111111111111111111-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-11111-1-1-111-1-1
χ61111111111111111111111111111111111111111111111-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111-111-111-1-1-1-1-1
χ71111111111111111111111111111111111111111111111-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-1-1-1-111-1-1-11111-111
χ81111111111111111111111111111111111111111111111-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11111111-1-1-1-11-1-11-1111
χ9222222-2-2222-2-22222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222220-2-2-2-2-2000000000000000000000000002-20000000000002-200000000
χ10222222-2-2222-2-22222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222220-2-2-2-2-200000000000000000000000000-22000000000000-2200000000
χ1122222-12222-1222-1-1-1-12-12-1-1-1-122-12-122-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10002020000002000-1-1-100-100
χ1222222-12222-1222-1-1-1-12-12-1-1-1-122-12-122-1-1-1-1-1-1-1-122-1-1-1-122-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000-20-2000000-200011100100
χ1322222-12222-1222-1-1-1-12-12-1-1-1-122-12-122-1-1-1-1-1-1-1-122-1-1-1-1-22-1-1-1-1-2-2-2-2-2-2-2-2111111111111111111000202000000-2000-11100-100
χ1422222-12222-1222-1-1-1-12-12-1-1-1-122-12-122-1-1-1-1-1-1-1-122-1-1-1-1-22-1-1-1-1-2-2-2-2-2-2-2-2111111111111111111000-20-200000020001-1-100100
χ152222-1222-12222-12-1-1-1-12-12-1-1-1222-12-1-122-1-1-1-1-1-1-1-12-1-1-12-12-1-1-122-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-122000000000000-1-1000200-1-1
χ162222-1222-12222-12-1-1-1-12-12-1-1-1222-12-1-122-1-1-1-1-1-1-1-12-1-1-12-12-1-1-122-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-2-200000000000011000-20011
χ172222-1222-12222-12-1-1-1-12-12-1-1-1222-12-1-122-1-1-1-1-1-1-1-12-1-1-1-2-12-1-1-1-2-2111111-2-2-2-2-2-211111111111122000000000000-1-1000-20011
χ182222-1222-12222-12-1-1-1-12-12-1-1-1222-12-1-122-1-1-1-1-1-1-1-12-1-1-1-2-12-1-1-1-2-2111111-2-2-2-2-2-2111111111111-2-200000000000011000200-1-1
χ192222-12-2-2-122-2-2-12-1-1-1-12-12-1-1-12-2-21-211-2-21111111-12-1-1-101-211100333−3−3−3000000333333−3−3−3−3−3−32-2000000000000-110000003−3
χ202222-12-2-2-122-2-2-12-1-1-1-12-12-1-1-12-2-21-211-2-21111111-12-1-1-101-211100333−3−3−3000000333333−3−3−3−3−3−3-220000000000001-1000000−33
χ212222-12-2-2-122-2-2-12-1-1-1-12-12-1-1-12-2-21-211-2-21111111-12-1-1-101-211100−3−3−3333000000−3−3−3−3−3−33333332-2000000000000-11000000−33
χ222222-12-2-2-122-2-2-12-1-1-1-12-12-1-1-12-2-21-211-2-21111111-12-1-1-101-211100−3−3−3333000000−3−3−3−3−3−3333333-220000000000001-10000003−3
χ23222-122222-12-1-1-1-12-1-122-1-12-1-1-1-1222-1-1-1-122-1-1-1-12-1-12-1-12-1-12-1-1-1-12-1-12-1-122-1-1-1-122-1-1-1-122-1-1-1-100202022-1-1-1-10-1000000-1000
χ24222-122222-12-1-1-1-12-1-122-1-12-1-1-1-1222-1-1-1-122-1-1-1-12-1-12-1-12-1-12-1-1-1-12-1-12-1-122-1-1-1-122-1-1-1-122-1-1-1-100-20-20-2-21111010000001000
χ25222-122222-12-1-1-1-12-1-122-1-12-1-1-1-1222-1-1-1-122-1-1-1-12-1-12-1-1-2-1-12-1-111-211-211-2-21111-2-21111-2-21111002020-2-211110-1000000-1000
χ26222-122222-12-1-1-1-12-1-122-1-12-1-1-1-1222-1-1-1-122-1-1-1-12-1-12-1-1-2-1-12-1-111-211-211-2-21111-2-21111-2-2111100-20-2022-1-1-1-1010000001000
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χ2822-22222-22222222222-2-222222-2-2-2222222222222-2-2-2-2-2-20-2-2-2-2-200000000000000000000000000000-2020000000000-20000200
χ2922-2222-22222-2-222222-2-222222-222-2-2-2-2-2-2-2-2-2-2-2-22-2-2-2-2-2022222000000000000000000000000000020-2000000002000000-2000
χ3022-2222-22222-2-222222-2-222222-222-2-2-2-2-2-2-2-2-2-2-2-22-2-2-2-2-20222220000000000000000000000000000-20200000000-20000002000
χ3122-222-12-222-1222-1-1-1-1-212-1-1-1-1-2-212-122-1-1-1-1-1-1-1-1-2-211110-2111100000000−i3i3−i3−i3i3i3−i3i3−i3−i3i3i3−i3i3−i3−i3i3i300020-20000000000-1−i3i300100
χ3222-222-12-222-1222-1-1-1-1-212-1-1-1-1-2-212-122-1-1-1-1-1-1-1-1-2-211110-2111100000000−i3i3−i3−i3i3i3−i3i3−i3−i3i3i3−i3i3−i3−i3i3i3000-20200000000001i3−i300-100
χ3322-222-12-222-1222-1-1-1-1-212-1-1-1-1-2-212-122-1-1-1-1-1-1-1-1-2-211110-2111100000000i3−i3i3i3−i3−i3i3−i3i3i3−i3−i3i3−i3i3i3−i3−i300020-20000000000-1i3−i300100
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χ3522-2-122-222-1211-1-12-1-1-2-2-1-12-1-11-12-2-21111-2-21111211-2110-1-12-1-13−303−303−3003−33−3003−33−3003−33−30020-200033−3−30-10000001000
χ3622-2-122-222-1211-1-12-1-1-2-2-1-12-1-11-12-2-21111-2-21111211-2110-1-12-1-13−303−303−3003−33−3003−33−3003−33−300-202000−3−33301000000-1000
χ3722-2-122-222-1211-1-12-1-1-2-2-1-12-1-11-12-2-21111-2-21111211-2110-1-12-1-1−330−330−3300−33−3300−33−3300−33−330020-2000−3−3330-10000001000
χ3822-2-122-222-1211-1-12-1-1-2-2-1-12-1-11-12-2-21111-2-21111211-2110-1-12-1-1−330−330−3300−33−3300−33−3300−33−3300-20200033−3−301000000-1000
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χ414444-2-244-24-244-2-2111-2-2-2-211144-2-2-2-2-2-2-2111111-2-2-2111-4-2-2111-4-4222222222222-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000
χ424444-2-2-4-4-24-2-4-4-2-2111-2-2-2-21114-42222222-1-1-1-1-1-12-2-2111022-1-1-100232323−23−23−23000000−3−3−3−3−3−3333333000000000000000000000000
χ434444-2-2-4-4-24-2-4-4-2-2111-2-2-2-21114-42222222-1-1-1-1-1-12-2-2111022-1-1-100−23−23−23232323000000333333−3−3−3−3−3−3000000000000000000000000
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χ45444-24-2444-2-2-2-2-21-2114-2-21-211-2-2-24-2-2-211-2-211114-21-2114-21-211-2-24-2-24-2-2-2-21111-2-21111-2-21111000000000000000000000000
χ46444-24-2444-2-2-2-2-21-2114-2-21-211-2-2-24-2-2-211-2-211114-21-211-4-21-21122-422-42222-1-1-1-122-1-1-1-122-1-1-1-1000000000000000000000000
χ47444-24-2-4-44-2-222-21-2114-2-21-211-222-4222-1-122-1-1-1-1-4-21-21102-12-1-100000000003i−3i−3i3i003i−3i−3i3i003i−3i−3i3i000000000000000000000000
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χ49444-2-2444-2-24-2-21-2-211-241-2-211-2-24-2411-2-2-2-21111-21-2-21141-2-211-2-2-211-21144-2-2-2-2-2-21111-2-21111000000000000000000000000
χ50444-2-2444-2-24-2-21-2-211-241-2-211-2-24-2411-2-2-2-21111-21-2-211-41-2-211222-1-12-1-1-4-4222222-1-1-1-122-1-1-1-1000000000000000000000000
χ51444-2-24-4-4-2-24221-2-211-241-2-211-22-42-4-1-12222-1-1-1-121-2-2110-122-1-10023−3−3−23330000002323−3−3−3−3−23−233333000000000000000000000000
χ52444-2-24-4-4-2-24221-2-211-241-2-211-22-42-4-1-12222-1-1-1-121-2-2110-122-1-100−233323−3−3000000−23−2333332323−3−3−3−3000000000000000000000000
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+3i32-2-2-211-211-2-2111111−1−3i32−1+3i32−1+3i32−1−3i3211−1+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+3i32222-1-12-1-122-1-1-1-1-1-11+3i321−3i321−3i321+3i32-1-11−3i321+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+3i32−1−3i32-2-2-211-211-2-2111111−1+3i32−1−3i32−1−3i32−1+3i3211−1−3i32−1+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+3i32−1−3i32222-1-12-1-122-1-1-1-1-1-11−3i321+3i321+3i321−3i32-1-11+3i321−3i321−3i321+3i32000000000000000000000000
χ57444-2-2-2-4-4-2-2-222111−1−3i32−1+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+3i321−3i320023−3−3−2333003i−3i−3i3i−3−3ζ7+2ζ11−2ζ7−ζ11−2ζ7−ζ11ζ7+2ζ11332ζ7+ζ11−ζ7−2ζ11−ζ7−2ζ112ζ7+ζ11000000000000000000000000
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+3i321−3i3200−233323−3−300−3i3i3i−3i33−ζ7−2ζ112ζ7+ζ112ζ7+ζ11−ζ7−2ζ11−3−3−2ζ7−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+3i320023−3−3−233300−3i3i3i−3i−3−3−2ζ7−ζ11ζ7+2ζ11ζ7+2ζ11−2ζ7−ζ1133−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+3i3200−233323−3−3003i−3i−3i3i332ζ7+ζ11−ζ7−2ζ11−ζ7−2ζ112ζ7+ζ11−3−3ζ7+2ζ11−2ζ7−ζ11−2ζ7−ζ11ζ7+2ζ11000000000000000000000000
χ6144-444-2-4444-2-4-44-2-2-2-2-424-2-2-2-2-44-2-42-4-4222222224-4222204-2-2-2-200000000000000000000000000000000000000000000000000
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χ6944-4-24-24-44-2-2-2-2-21-211-42-21-2112224-2-2-211-2-21111-42-12-1-102-12-1-100000000−2i32i3i3i3−i3−i3−2i32i3i3i3−i3−i3−2i32i3i3i3−i3−i3000000000000000000000000
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χ7244-4-24-2-444-2-222-21-211-42-21-2112-2-2-4222-1-122-1-1-1-142-12-1-10-21-211−23230−23230−2323003−33−3003−33−3003−33−3000000000000000000000000
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χ7544-4-2-24-44-2-24221-2-2112-41-2-2112-242-4-1-12222-1-1-1-1-2-122-1-101-2-21123−230−330−330023−2323−2300−33−3300−33−33000000000000000000000000
χ7644-4-2-24-44-2-24221-2-2112-41-2-2112-242-4-1-12222-1-1-1-1-2-122-1-101-2-211−232303−303−300−2323−2323003−33−3003−33−3000000000000000000000000
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χ918-8088-400-8-84008-4-4-4-400-8444400000000000000000000000000000000000000000000000000000000000000000000000000000
χ928-808-48004-8-800-48-4-4-4004-844400000000000000000000000000000000000000000000000000000000000000000000000000000
χ938-808-4-4004-8400-4-42220044-2-2-20000000006i−6i6i−6i−6i6i00000000000000000000000000000000000000000000000000000000000000
χ948-808-4-4004-8400-4-42220044-2-2-2000000000−6i6i−6i6i6i−6i00000000000000000000000000000000000000000000000000000000000000
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χ978-80-4-480044-843−432-4-42200-244-2-200000−232343−4300−2323−232300000000000000000000000000000000000000000000000000000000000000
χ988-80-4-480044-8−43432-4-42200-244-2-20000023−23−43430023−2323−2300000000000000000000000000000000000000000000000000000000000000
χ998-80-4-4-40044443−43222−1−3i3−1+3i300-2-2-21+3i31−3i300000−2323−23236i−6i2ζ7+4ζ11−2ζ7−4ζ11−4ζ7−2ζ114ζ7+2ζ1100000000000000000000000000000000000000000000000000000000000000
χ1008-80-4-4-40044443−43222−1+3i3−1−3i300-2-2-21−3i31+3i300000−2323−2323−6i6i−4ζ7−2ζ114ζ7+2ζ112ζ7+4ζ11−2ζ7−4ζ1100000000000000000000000000000000000000000000000000000000000000
χ1018-80-4-4-400444−4343222−1−3i3−1+3i300-2-2-21+3i31−3i30000023−2323−23−6i6i−2ζ7−4ζ112ζ7+4ζ114ζ7+2ζ11−4ζ7−2ζ1100000000000000000000000000000000000000000000000000000000000000
χ1028-80-4-4-400444−4343222−1+3i3−1−3i300-2-2-21−3i31+3i30000023−2323−236i−6i4ζ7+2ζ11−4ζ7−2ζ11−2ζ7−4ζ112ζ7+4ζ1100000000000000000000000000000000000000000000000000000000000000

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