Finite Group Databasebeta

← Group #13161766

Character table — Group #13161766

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size112222222222244444444444444444444444444448888888888888888888888888888888888888181836363636363636363672727272727272727272727272
order12233344666121233333666666661212121212121212121212121212126666681212121212242424242424242424242424242424242424242424242424242488248882424242424666812121224242424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111-1-11-1-11111-1-1-1-1-11-1-1-111-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-11-1111-11-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-111-1-1-1-1-11-1-1-1-1-111-1-111
χ51111111111111111111111111111111111111111111111-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-11-1-1-11-1-1-1-111
χ61111111111111111111111111111111111111111111111-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11-1-1111111-111-1-111-1-1-1-1
χ71111111111111111111111111111111111111111111111-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-1111111-1-1
χ81111111111111111111111111111111111111111111111-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11-1-1111-1-1-11111
χ9222222-2-2222-2-22222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222220-2-2-2-2-200000000000000000000000000000002i−2i0000000000000002i−2i
χ10222222-2-2222-2-22222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222220-2-2-2-2-20000000000000000000000000000000−2i2i000000000000000−2i2i
χ1122222-1222-12222-1-1-1-122-12-1-1-1-1-1-1222-1-1-1-1-1-1-1-1222-1-1-1-122-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10022000000020-1-1-10-1000000
χ1222222-1222-12222-1-1-1-122-12-1-1-1-1-1-1222-1-1-1-1-1-1-1-1222-1-1-1-122-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100-2-20000000-2011101000000
χ1322222-1222-12222-1-1-1-122-12-1-1-1-1-1-1222-1-1-1-1-1-1-1-1222-1-1-1-1-22-1-1-1-1-2-2-2-2-2-2-2-211111111111111111100220000000-20-1110-1000000
χ1422222-1222-12222-1-1-1-122-12-1-1-1-1-1-1222-1-1-1-1-1-1-1-1222-1-1-1-1-22-1-1-1-1-2-2-2-2-2-2-2-211111111111111111100-2-20000000201-1-101000000
χ152222-122222-122-12-1-1-12-12-12-1-1-122-1-1-122-1-1-1-1-1-12-1-12-1-1-12-12-1-1-122-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1000002200000200000-1-100-1-1
χ162222-122222-122-12-1-1-12-12-12-1-1-122-1-1-122-1-1-1-1-1-12-1-12-1-1-12-12-1-1-122-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-100000-2-200000-200000110011
χ172222-122222-122-12-1-1-12-12-12-1-1-122-1-1-122-1-1-1-1-1-12-1-12-1-1-1-2-12-1-1-1-2-2111111-2-2-2-2-2-2111111111111000002200000-2000001100-1-1
χ182222-122222-122-12-1-1-12-12-12-1-1-122-1-1-122-1-1-1-1-1-12-1-12-1-1-1-2-12-1-1-1-2-2111111-2-2-2-2-2-211111111111100000-2-200000200000-1-10011
χ192222-12-2-222-1-2-2-12-1-1-12-12-12-1-1-1-2-2111-2-2111111-21-12-1-1-101-211100333−3−3−3000000333333−3−3−3−3−3−3000002i−2i00000000000−i3i300−ii
χ202222-12-2-222-1-2-2-12-1-1-12-12-12-1-1-1-2-2111-2-2111111-21-12-1-1-101-211100333−3−3−3000000333333−3−3−3−3−3−300000−2i2i00000000000i3−i300i−i
χ212222-12-2-222-1-2-2-12-1-1-12-12-12-1-1-1-2-2111-2-2111111-21-12-1-1-101-211100−3−3−3333000000−3−3−3−3−3−3333333000002i−2i00000000000i3−i300−ii
χ222222-12-2-222-1-2-2-12-1-1-12-12-12-1-1-1-2-2111-2-2111111-21-12-1-1-101-211100−3−3−3333000000−3−3−3−3−3−333333300000−2i2i00000000000−i3i300i−i
χ23222-12222-122-1-1-1-12-1-1-122-1-12-1-1222-1-1-1-122-1-1-1-1-12-1-12-1-12-1-12-1-1-1-12-1-12-1-122-1-1-1-122-1-1-1-122-1-1-1-12200200-1-1-1-1000002000-1-100
χ24222-12222-122-1-1-1-12-1-1-122-1-12-1-1222-1-1-1-122-1-1-1-1-12-1-12-1-12-1-12-1-1-1-12-1-12-1-122-1-1-1-122-1-1-1-122-1-1-1-1-2-200-200111100000-20001100
χ25222-12222-122-1-1-1-12-1-1-122-1-12-1-1222-1-1-1-122-1-1-1-1-12-1-12-1-1-2-1-12-1-111-211-211-2-21111-2-21111-2-211112200200-1-1-1-100000-20001100
χ26222-12222-122-1-1-1-12-1-1-122-1-12-1-1222-1-1-1-122-1-1-1-1-12-1-12-1-1-2-1-12-1-111-211-211-2-21111-2-21111-2-21111-2-200-2001111000002000-1-100
χ2722-22222-22222222222-2-2-222222-2222222222222-2-2-2-2-2-2-20-2-2-2-2-200000000000000000000000000002-20000000002000-2000000
χ2822-22222-22222222222-2-2-222222-2222222222222-2-2-2-2-2-2-20-2-2-2-2-20000000000000000000000000000-22000000000-20002000000
χ2922-2222-22222-2-222222-2-2-2222222-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2-2-2022222000000000000000000000000002200-20022-2-20000000000000
χ3022-2222-22222-2-222222-2-2-2222222-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2-2-202222200000000000000000000000000-2-200200-2-2220000000000000
χ3122-222-12-22-12222-1-1-1-1-2-212-1-1-1-11-1222-1-1-1-1-1-1-1-1-2-2-211110-2111100000000−i3i3−i3−i3i3i3−i3i3−i3−i3i3i3−i3i3−i3−i3i3i3002-2000000000-1−i3i301000000
χ3222-222-12-22-12222-1-1-1-1-2-212-1-1-1-11-1222-1-1-1-1-1-1-1-1-2-2-211110-2111100000000−i3i3−i3−i3i3i3−i3i3−i3−i3i3i3−i3i3−i3−i3i3i300-220000000001i3−i30-1000000
χ3322-222-12-22-12222-1-1-1-1-2-212-1-1-1-11-1222-1-1-1-1-1-1-1-1-2-2-211110-2111100000000i3−i3i3i3−i3−i3i3−i3i3i3−i3−i3i3−i3i3i3−i3−i3002-2000000000-1i3−i301000000
χ3422-222-12-22-12222-1-1-1-1-2-212-1-1-1-11-1222-1-1-1-1-1-1-1-1-2-2-211110-2111100000000i3−i3i3i3−i3−i3i3−i3i3i3−i3−i3i3−i3i3i3−i3−i300-220000000001−i3i30-1000000
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χ3622-2-122-22-12211-1-12-1-11-2-2-1-12-1-12-2-21111-2-21111-1211-2110-1-12-1-13−303−303−3003−33−3003−33−3003−33−3-2-20020011-1-1000000000−3300
χ3722-2-122-22-12211-1-12-1-11-2-2-1-12-1-12-2-21111-2-21111-1211-2110-1-12-1-1−330−330−3300−33−3300−33−3300−33−332200-200-1-111000000000−3300
χ3822-2-122-22-12211-1-12-1-11-2-2-1-12-1-12-2-21111-2-21111-1211-2110-1-12-1-1−330−330−3300−33−3300−33−3300−33−33-2-20020011-1-10000000003−300
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χ414444-2-2444-2-244-2-21114-2-2-2-2111-2-2-2-2-2-2-21111114-2-2-2111-4-2-2111-4-4222222222222-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000
χ424444-2-2-4-44-2-2-4-4-2-21114-2-2-2-21112222222-1-1-1-1-1-1-42-2-2111022-1-1-100232323−23−23−23000000−3−3−3−3−3−3333333000000000000000000000000
χ434444-2-2-4-44-2-2-4-4-2-21114-2-2-2-21112222222-1-1-1-1-1-1-42-2-2111022-1-1-100−23−23−23232323000000333333−3−3−3−3−3−3000000000000000000000000
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χ45444-24-244-2-24-2-2-21-211-24-2-21-211-2-24-2-211-2-21111-24-21-2114-21-211-2-24-2-24-2-2-2-21111-2-21111-2-21111000000000000000000000000
χ46444-24-244-2-24-2-2-21-211-24-2-21-211-2-24-2-211-2-21111-24-21-211-4-21-21122-422-42222-1-1-1-122-1-1-1-122-1-1-1-1000000000000000000000000
χ47444-24-2-4-4-2-2422-21-211-24-2-21-21122-422-1-122-1-1-1-12-4-21-21102-12-1-100000000003i−3i−3i3i003i−3i−3i3i003i−3i−3i3i000000000000000000000000
χ48444-24-2-4-4-2-2422-21-211-24-2-21-21122-422-1-122-1-1-1-12-4-21-21102-12-1-10000000000−3i3i3i−3i00−3i3i3i−3i00−3i3i3i−3i000000000000000000000000
χ49444-2-2444-24-2-2-21-2-211-2-241-2-21144-211-2-2-2-21111-2-21-2-21141-2-211-2-2-211-21144-2-2-2-2-2-21111-2-21111000000000000000000000000
χ50444-2-2444-24-2-2-21-2-211-2-241-2-21144-211-2-2-2-21111-2-21-2-211-41-2-211222-1-12-1-1-4-4222222-1-1-1-122-1-1-1-1000000000000000000000000
χ51444-2-24-4-4-24-2221-2-211-2-241-2-211-4-42-1-12222-1-1-1-1221-2-2110-122-1-10023−3−3−23330000002323−3−3−3−3−23−233333000000000000000000000000
χ52444-2-24-4-4-24-2221-2-211-2-241-2-211-4-42-1-12222-1-1-1-1221-2-2110-122-1-100−233323−3−3000000−23−2333332323−3−3−3−3000000000000000000000000
χ53444-2-2-244-2-2-2-2-2111−1−3i32−1+3i32-2-2-2111−1−3i32−1+3i32-2-2-2111111−1−3i32−1−3i32−1+3i32−1+3i32-2-2111−1−3i32−1+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+3i32-2-2-2111−1−3i32−1+3i32-2-2-2111111−1−3i32−1−3i32−1+3i32−1+3i32-2-2111−1−3i32−1+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+3i32−1−3i32-2-2-2111−1+3i32−1−3i32-2-2-2111111−1+3i32−1+3i32−1−3i32−1−3i32-2-2111−1+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+3i32−1−3i32-2-2-2111−1+3i32−1−3i32-2-2-2111111−1+3i32−1+3i32−1−3i32−1−3i32-2-2111−1+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+3i32-2-2-2111−1−3i32−1+3i32222-1-1-1-1-1-11+3i321+3i321−3i321−3i3222111−1−3i32−1+3i320-1-1-11+3i321−3i320023−3−3−2333003i−3i−3i3i−3−3ζ14+2ζ22−2ζ14−ζ22−2ζ14−ζ22ζ14+2ζ22332ζ14+ζ22−ζ14−2ζ22−ζ14−2ζ222ζ14+ζ22000000000000000000000000
χ58444-2-2-2-4-4-2-2-222111−1−3i32−1+3i32-2-2-2111−1−3i32−1+3i32222-1-1-1-1-1-11+3i321+3i321−3i321−3i3222111−1−3i32−1+3i320-1-1-11+3i321−3i3200−233323−3−300−3i3i3i−3i33−ζ14−2ζ222ζ14+ζ222ζ14+ζ22−ζ14−2ζ22−3−3−2ζ14−ζ22ζ14+2ζ22ζ14+2ζ22−2ζ14−ζ22000000000000000000000000
χ59444-2-2-2-4-4-2-2-222111−1+3i32−1−3i32-2-2-2111−1+3i32−1−3i32222-1-1-1-1-1-11−3i321−3i321+3i321+3i3222111−1+3i32−1−3i320-1-1-11−3i321+3i320023−3−3−233300−3i3i3i−3i−3−3−2ζ14−ζ22ζ14+2ζ22ζ14+2ζ22−2ζ14−ζ2233−ζ14−2ζ222ζ14+ζ222ζ14+ζ22−ζ14−2ζ22000000000000000000000000
χ60444-2-2-2-4-4-2-2-222111−1+3i32−1−3i32-2-2-2111−1+3i32−1−3i32222-1-1-1-1-1-11−3i321−3i321+3i321+3i3222111−1+3i32−1−3i320-1-1-11−3i321+3i3200−233323−3−3003i−3i−3i3i332ζ14+ζ22−ζ14−2ζ22−ζ14−2ζ222ζ14+ζ22−3−3ζ14+2ζ22−2ζ14−ζ22−2ζ14−ζ22ζ14+2ζ22000000000000000000000000
χ6144-444-2-444-24-4-44-2-2-2-2-4-424-2-2-2-2-22-4-4-42222222244-4222204-2-2-2-200000000000000000000000000000000000000000000000000
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χ6344-44-24-4444-2-4-4-24-2-2-2-42-4-24-2-2-24-4222-4-42222224-22-42220-24-2-2-200000000000000000000000000000000000000000000000000
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χ7444-4-2-244-4-24-2-2-21-2-21122-41-2-211-44-211-2-2-2-2111122-122-1-10-122-1-1000-3303-300000000-33-33003-33-3000000000000000000000000
χ7544-4-2-24-44-24-2221-2-21122-41-2-2114-42-1-12222-1-1-1-1-2-2-122-1-101-2-21123−230−330−330023−2323−2300−33−3300−33−33000000000000000000000000
χ7644-4-2-24-44-24-2221-2-21122-41-2-2114-42-1-12222-1-1-1-1-2-2-122-1-101-2-211−232303−303−300−2323−2323003−33−3003−33−3000000000000000000000000
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χ8444-4-2-2-2-44-2-2-222111−1+3i32−1−3i32222111−1+3i32−1−3i32-222-1-1-1-1-1-11−3i321−3i321+3i321+3i32-2-2-1-1-11−3i321+3i320111−1+3i32−1−3i32−232303−303−3003−33−33i−3i2ζ14+ζ22ζ14+2ζ22−ζ14−2ζ22−2ζ14−ζ22−3i3i−ζ14−2ζ22−2ζ14−ζ222ζ14+ζ22ζ14+2ζ22000000000000000000000000
χ854-4044400-4-4-40044444000-4-4-4-4-40000000000000000000000000000000000000000000000000000−2i22i200000−2i22i2000000000000000
χ864-4044400-4-4-40044444000-4-4-4-4-400000000000000000000000000000000000000000000000000002i2−2i2000002i2−2i2000000000000000
χ874-40-244002-4-423−23-2-24-2-200022-42200023−2323−230023−2323−23000000000000000000000000000000000000000−2i22i200000i2−i2i6−i60000000000000
χ884-40-244002-4-423−23-2-24-2-200022-42200023−2323−230023−2323−230000000000000000000000000000000000000002i2−2i200000−i2i2−i6i60000000000000
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χ918-8088-400-84-8008-4-4-4-4000-844440000000000000000000000000000000000000000000000000000000000000000000000000000
χ928-808-4800-8-8400-48-4-4-40004-84440000000000000000000000000000000000000000000000000000000000000000000000000000
χ938-808-4-400-84400-4-422200044-2-2-200000006i−6i6i−6i−6i6i000000000000000000000000000000000000000000000000000000000000000
χ948-808-4-400-84400-4-422200044-2-2-20000000−6i6i−6i6i6i−6i000000000000000000000000000000000000000000000000000000000000000
χ958-80-48-40044-843−43-42-4220004-24-2-200043−43−232300−2323−2323000000000000000000000000000000000000000000000000000000000000000
χ968-80-48-40044-8−4343-42-4220004-24-2-2000−434323−230023−2323−23000000000000000000000000000000000000000000000000000000000000000
χ978-80-4-48004-8443−432-4-422000-244-2-2000−232343−4300−2323−2323000000000000000000000000000000000000000000000000000000000000000
χ988-80-4-48004-84−43432-4-422000-244-2-200023−23−43430023−2323−23000000000000000000000000000000000000000000000000000000000000000
χ998-80-4-4-40044443−43222−1−3i3−1+3i3000-2-2-21+3i31−3i3000−2323−23236i−6i2ζ14+4ζ22−2ζ14−4ζ22−4ζ14−2ζ224ζ14+2ζ22000000000000000000000000000000000000000000000000000000000000000
χ1008-80-4-4-40044443−43222−1+3i3−1−3i3000-2-2-21−3i31+3i3000−2323−2323−6i6i−4ζ14−2ζ224ζ14+2ζ222ζ14+4ζ22−2ζ14−4ζ22000000000000000000000000000000000000000000000000000000000000000
χ1018-80-4-4-400444−4343222−1−3i3−1+3i3000-2-2-21+3i31−3i300023−2323−23−6i6i−2ζ14−4ζ222ζ14+4ζ224ζ14+2ζ22−4ζ14−2ζ22000000000000000000000000000000000000000000000000000000000000000
χ1028-80-4-4-400444−4343222−1+3i3−1−3i3000-2-2-21−3i31+3i300023−2323−236i−6i4ζ14+2ζ22−4ζ14−2ζ22−2ζ14−4ζ222ζ14+4ζ22000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.