Finite Group Databasebeta

← Group #13157078

Character table — Group #13157078

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99
size112444444444888888888888836363636727272721124444444448888888888888363636367272727211244444444488888888888883636363672727272
order122233666666466661212121212121212222444883666336666661266661212121212121212666121212242436663366666612666612121212121212126661212122424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111-1-1-1-111111111111111111111111111111-1-1-1-111111111111111111111111111111-1-1-1-1
χ31111111111111111111111111-1-1-1-1i−ii−i1111111111111111111111111-1-1-1-1i−ii−i1111111111111111111111111-1-1-1-1i−ii−i
χ41111111111111111111111111-1-1-1-1−ii−ii1111111111111111111111111-1-1-1-1−ii−ii1111111111111111111111111-1-1-1-1−ii−ii
χ5111111111111-11111-1-1-1-1-1-1-1-111-1-1i−i−ii111111111111-11111-1-1-1-1-1-1-1-111-1-1i−i−ii111111111111-11111-1-1-1-1-1-1-1-111-1-1i−i−ii
χ6111111111111-11111-1-1-1-1-1-1-1-111-1-1−iii−i111111111111-11111-1-1-1-1-1-1-1-111-1-1−iii−i111111111111-11111-1-1-1-1-1-1-1-111-1-1−iii−i
χ7111111111111-11111-1-1-1-1-1-1-1-1-1-11111-1-1111111111111-11111-1-1-1-1-1-1-1-1-1-11111-1-1111111111111-11111-1-1-1-1-1-1-1-1-1-11111-1-1
χ8111111111111-11111-1-1-1-1-1-1-1-1-1-111-1-111111111111111-11111-1-1-1-1-1-1-1-1-1-111-1-111111111111111-11111-1-1-1-1-1-1-1-1-1-111-1-111
χ9222-2222222220-2-2-2-200000000002-20000222-2222222220-2-2-2-200000000002-20000222-2222222220-2-2-2-200000000002-20000
χ10222-2222222220-2-2-2-20000000000-220000222-2222222220-2-2-2-20000000000-220000222-2222222220-2-2-2-20000000000-220000
χ1144441-21-211-2-2411-2-21111-2-2-2-20000000044441-21-211-2-2411-2-21111-2-2-2-20000000044441-21-211-2-2411-2-21111-2-2-2-200000000
χ1244441-21-211-2-2-411-2-2-1-1-1-122220000000044441-21-211-2-2-411-2-2-1-1-1-122220000000044441-21-211-2-2-411-2-2-1-1-1-1222200000000
χ134444-21-21-2-2114-2-211-2-2-2-21111000000004444-21-21-2-2114-2-211-2-2-2-21111000000004444-21-21-2-2114-2-211-2-2-2-2111100000000
χ144444-21-21-2-211-4-2-2112222-1-1-1-1000000004444-21-21-2-211-4-2-2112222-1-1-1-1000000004444-21-21-2-211-4-2-2112222-1-1-1-100000000
χ15444-41-21-211-2-20-1-12233-3-3000000000000444-41-21-211-2-20-1-12233-3-3000000000000444-41-21-211-2-20-1-12233-3-3000000000000
χ16444-41-21-211-2-20-1-122-3-333000000000000444-41-21-211-2-20-1-122-3-333000000000000444-41-21-211-2-20-1-122-3-333000000000000
χ17444-4-21-21-2-211022-1-1000033-3-300000000444-4-21-21-2-211022-1-1000033-3-300000000444-4-21-21-2-211022-1-1000033-3-300000000
χ18444-4-21-21-2-211022-1-10000-3-33300000000444-4-21-21-2-211022-1-10000-3-33300000000444-4-21-21-2-211022-1-10000-3-33300000000
χ1944-401-21-2-1-12203-3003−33−30023−230000000044-401-21-2-1-12203-3003−33−30023−230000000044-401-21-2-1-12203-3003−33−30023−2300000000
χ2044-401-21-2-1-12203-300−33−3300−23230000000044-401-21-2-1-12203-300−33−3300−23230000000044-401-21-2-1-12203-300−33−3300−232300000000
χ2144-401-21-2-1-1220-33003−3−3323−23000000000044-401-21-2-1-1220-33003−3−3323−23000000000044-401-21-2-1-1220-33003−3−3323−230000000000
χ2244-401-21-2-1-1220-3300−333−3−2323000000000044-401-21-2-1-1220-3300−333−3−2323000000000044-401-21-2-1-1220-3300−333−3−23230000000000
χ2344-404444-4-4-4-400000000000000000000044-404444-4-4-4-400000000000000000000044-404444-4-4-4-4000000000000000000000
χ2444-40-21-2122-1-10003-30023−233−3−330000000044-40-21-2122-1-10003-30023−233−3−330000000044-40-21-2122-1-10003-30023−233−3−3300000000
χ2544-40-21-2122-1-10003-300−2323−333−30000000044-40-21-2122-1-10003-300−2323−333−30000000044-40-21-2122-1-10003-300−2323−333−300000000
χ2644-40-21-2122-1-1000-3323−2300−33−330000000044-40-21-2122-1-1000-3323−2300−33−330000000044-40-21-2122-1-1000-3323−2300−33−3300000000
χ2744-40-21-2122-1-1000-33−2323003−33−30000000044-40-21-2122-1-1000-33−2323003−33−30000000044-40-21-2122-1-1000-33−2323003−33−300000000
χ284-40044-4-4000000000000000002-20000004-40044-4-4000000000000000002-20000004-40044-4-4000000000000000002-2000000
χ294-40044-4-400000000000000000-220000004-40044-4-400000000000000000-220000004-40044-4-400000000000000000-22000000
χ308-8002-4-246-6000000000000000000000008-8002-4-246-6000000000000000000000008-8002-4-246-600000000000000000000000
χ318-8002-4-24-66000000000000000000000008-8002-4-24-66000000000000000000000008-8002-4-24-6600000000000000000000000
χ328-800-424-2006-60000000000000000000008-800-424-2006-60000000000000000000008-800-424-2006-6000000000000000000000
χ338-800-424-200-660000000000000000000008-800-424-200-660000000000000000000008-800-424-200-66000000000000000000000
χ34111111111111111111111111111111111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32
χ3511111111111111111111111111111-1-1-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32
χ361111111111111111111111111-1-1-1-1i−ii−i−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32ζ7−ζ7ζ7−ζ7−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32ζ11−ζ11ζ11−ζ11
χ371111111111111111111111111-1-1-1-1−ii−ii−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−ζ7ζ7−ζ7ζ7−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−ζ11ζ11−ζ11ζ11
χ38111111111111-11111-1-1-1-1-1-1-1-111-1-1i−i−ii−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i321−i321−i32−1+i32−1+i321−i321−i32ζ7−ζ7−ζ7ζ7−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32ζ11−ζ11−ζ11ζ11
χ39111111111111-11111-1-1-1-1-1-1-1-111-1-1−iii−i−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i321−i321−i32−1+i32−1+i321−i321−i32−ζ7ζ7ζ7−ζ7−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32−ζ11ζ11ζ11−ζ11
χ40111111111111-11111-1-1-1-1-1-1-1-1-1-11111-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32
χ41111111111111-11111-1-1-1-1-1-1-1-1-1-111-1-111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32
χ42222-2222222220-2-2-2-200000000002-20000−1+i3−1+i3−1+i31−i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i301−i31−i31−i31−i30000000000−1+i31−i30000−1−i3−1−i3−1−i31+i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i301+i31+i31+i31+i30000000000−1−i31+i30000
χ43222-2222222220-2-2-2-20000000000-220000−1+i3−1+i3−1+i31−i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i301−i31−i31−i31−i300000000001−i3−1+i30000−1−i3−1−i3−1−i31+i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i301+i31+i31+i31+i300000000001+i3−1−i30000
χ4444441-21-211-2-2411-2-21111-2-2-2-200000000−2+2i3−2+2i3−2+2i3−2+2i3−1+i321−i3−1+i321−i3−1+i32−1+i321−i31−i3−2+2i3−1+i32−1+i321−i31−i3−1+i32−1+i32−1+i32−1+i321−i31−i31−i31−i300000000−2−2i3−2−2i3−2−2i3−2−2i3−1−i321+i3−1−i321+i3−1−i32−1−i321+i31+i3−2−2i3−1−i32−1−i321+i31+i3−1−i32−1−i32−1−i32−1−i321+i31+i31+i31+i300000000
χ4544441-21-211-2-2-411-2-2-1-1-1-1222200000000−2+2i3−2+2i3−2+2i3−2+2i3−1+i321−i3−1+i321−i3−1+i32−1+i321−i31−i32−2i3−1+i32−1+i321−i31−i31−i321−i321−i321−i32−1+i3−1+i3−1+i3−1+i300000000−2−2i3−2−2i3−2−2i3−2−2i3−1−i321+i3−1−i321+i3−1−i32−1−i321+i31+i32+2i3−1−i32−1−i321+i31+i31+i321+i321+i321+i32−1−i3−1−i3−1−i3−1−i300000000
χ464444-21-21-2-2114-2-211-2-2-2-2111100000000−2+2i3−2+2i3−2+2i3−2+2i31−i3−1+i321−i3−1+i321−i31−i3−1+i32−1+i32−2+2i31−i31−i3−1+i32−1+i321−i31−i31−i31−i3−1+i32−1+i32−1+i32−1+i3200000000−2−2i3−2−2i3−2−2i3−2−2i31+i3−1−i321+i3−1−i321+i31+i3−1−i32−1−i32−2−2i31+i31+i3−1−i32−1−i321+i31+i31+i31+i3−1−i32−1−i32−1−i32−1−i3200000000
χ474444-21-21-2-211-4-2-2112222-1-1-1-100000000−2+2i3−2+2i3−2+2i3−2+2i31−i3−1+i321−i3−1+i321−i31−i3−1+i32−1+i322−2i31−i31−i3−1+i32−1+i32−1+i3−1+i3−1+i3−1+i31−i321−i321−i321−i3200000000−2−2i3−2−2i3−2−2i3−2−2i31+i3−1−i321+i3−1−i321+i31+i3−1−i32−1−i322+2i31+i31+i3−1−i32−1−i32−1−i3−1−i3−1−i3−1−i31+i321+i321+i321+i3200000000
χ48444-41-21-211-2-20-1-12233-3-3000000000000−2+2i3−2+2i3−2+2i32−2i3−1+i321−i3−1+i321−i3−1+i32−1+i321−i31−i301−i321−i32−1+i3−1+i3−3+3i32−3+3i323−3i323−3i32000000000000−2−2i3−2−2i3−2−2i32+2i3−1−i321+i3−1−i321+i3−1−i32−1−i321+i31+i301+i321+i32−1−i3−1−i3−3−3i32−3−3i323+3i323+3i32000000000000
χ49444-41-21-211-2-20-1-122-3-333000000000000−2+2i3−2+2i3−2+2i32−2i3−1+i321−i3−1+i321−i3−1+i32−1+i321−i31−i301−i321−i32−1+i3−1+i33−3i323−3i32−3+3i32−3+3i32000000000000−2−2i3−2−2i3−2−2i32+2i3−1−i321+i3−1−i321+i3−1−i32−1−i321+i31+i301+i321+i32−1−i3−1−i33+3i323+3i32−3−3i32−3−3i32000000000000
χ50444-4-21-21-2-211022-1-1000033-3-300000000−2+2i3−2+2i3−2+2i32−2i31−i3−1+i321−i3−1+i321−i31−i3−1+i32−1+i320−1+i3−1+i31−i321−i320000−3+3i32−3+3i323−3i323−3i3200000000−2−2i3−2−2i3−2−2i32+2i31+i3−1−i321+i3−1−i321+i31+i3−1−i32−1−i320−1−i3−1−i31+i321+i320000−3−3i32−3−3i323+3i323+3i3200000000
χ51444-4-21-21-2-211022-1-10000-3-33300000000−2+2i3−2+2i3−2+2i32−2i31−i3−1+i321−i3−1+i321−i31−i3−1+i32−1+i320−1+i3−1+i31−i321−i3200003−3i323−3i32−3+3i32−3+3i3200000000−2−2i3−2−2i3−2−2i32+2i31+i3−1−i321+i3−1−i321+i31+i3−1−i32−1−i320−1−i3−1−i31+i321+i3200003+3i323+3i32−3−3i32−3−3i3200000000
χ5244-401-21-2-1-12203-3003−33−30023−2300000000−2+2i3−2+2i32−2i30−1+i321−i3−1+i321−i31−i321−i32−1+i3−1+i30−3+3i323−3i3200−ζ7−2ζ11ζ7+2ζ11−ζ7−2ζ11ζ7+2ζ1100−2ζ7−4ζ112ζ7+4ζ1100000000−2−2i3−2−2i32+2i30−1−i321+i3−1−i321+i31+i321+i32−1−i3−1−i30−3−3i323+3i32002ζ7+ζ11−2ζ7−ζ112ζ7+ζ11−2ζ7−ζ11004ζ7+2ζ11−4ζ7−2ζ1100000000
χ5344-401-21-2-1-12203-300−33−3300−232300000000−2+2i3−2+2i32−2i30−1+i321−i3−1+i321−i31−i321−i32−1+i3−1+i30−3+3i323−3i3200ζ7+2ζ11−ζ7−2ζ11ζ7+2ζ11−ζ7−2ζ11002ζ7+4ζ11−2ζ7−4ζ1100000000−2−2i3−2−2i32+2i30−1−i321+i3−1−i321+i31+i321+i32−1−i3−1−i30−3−3i323+3i3200−2ζ7−ζ112ζ7+ζ11−2ζ7−ζ112ζ7+ζ1100−4ζ7−2ζ114ζ7+2ζ1100000000
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χ9144-40-21-2122-1-10003-300−2323−333−300000000−2−2i3−2−2i32+2i301+i3−1−i321+i3−1−i32−1−i3−1−i31+i321+i32000−3−3i323+3i3200−4ζ7−2ζ114ζ7+2ζ11−2ζ7−ζ112ζ7+ζ112ζ7+ζ11−2ζ7−ζ1100000000−2+2i3−2+2i32−2i301−i3−1+i321−i3−1+i32−1+i3−1+i31−i321−i32000−3+3i323−3i32002ζ7+4ζ11−2ζ7−4ζ11ζ7+2ζ11−ζ7−2ζ11−ζ7−2ζ11ζ7+2ζ1100000000
χ9244-40-21-2122-1-1000-3323−2300−33−3300000000−2−2i3−2−2i32+2i301+i3−1−i321+i3−1−i32−1−i3−1−i31+i321+i320003+3i32−3−3i324ζ7+2ζ11−4ζ7−2ζ1100−2ζ7−ζ112ζ7+ζ11−2ζ7−ζ112ζ7+ζ1100000000−2+2i3−2+2i32−2i301−i3−1+i321−i3−1+i32−1+i3−1+i31−i321−i320003−3i32−3+3i32−2ζ7−4ζ112ζ7+4ζ1100ζ7+2ζ11−ζ7−2ζ11ζ7+2ζ11−ζ7−2ζ1100000000
χ9344-40-21-2122-1-1000-33−2323003−33−300000000−2−2i3−2−2i32+2i301+i3−1−i321+i3−1−i32−1−i3−1−i31+i321+i320003+3i32−3−3i32−4ζ7−2ζ114ζ7+2ζ11002ζ7+ζ11−2ζ7−ζ112ζ7+ζ11−2ζ7−ζ1100000000−2+2i3−2+2i32−2i301−i3−1+i321−i3−1+i32−1+i3−1+i31−i321−i320003−3i32−3+3i322ζ7+4ζ11−2ζ7−4ζ1100−ζ7−2ζ11ζ7+2ζ11−ζ7−2ζ11ζ7+2ζ1100000000
χ944-40044-4-4000000000000000002-2000000−2−2i32+2i300−2−2i3−2−2i32+2i32+2i300000000000000000−1−i31+i3000000−2+2i32−2i300−2+2i3−2+2i32−2i32−2i300000000000000000−1+i31−i3000000
χ954-40044-4-400000000000000000-22000000−2−2i32+2i300−2−2i3−2−2i32+2i32+2i3000000000000000001+i3−1−i3000000−2+2i32−2i300−2+2i3−2+2i32−2i32−2i3000000000000000001−i3−1+i3000000
χ968-8002-4-246-600000000000000000000000−4−4i34+4i300−1−i32+2i31+i3−2−2i3−3−3i33+3i300000000000000000000000−4+4i34−4i300−1+i32−2i31−i3−2+2i3−3+3i33−3i300000000000000000000000
χ978-8002-4-24-6600000000000000000000000−4−4i34+4i300−1−i32+2i31+i3−2−2i33+3i3−3−3i300000000000000000000000−4+4i34−4i300−1+i32−2i31−i3−2+2i33−3i3−3+3i300000000000000000000000
χ988-800-424-2006-6000000000000000000000−4−4i34+4i3002+2i3−1−i3−2−2i31+i300−3−3i33+3i3000000000000000000000−4+4i34−4i3002−2i3−1+i3−2+2i31−i300−3+3i33−3i3000000000000000000000
χ998-800-424-200-66000000000000000000000−4−4i34+4i3002+2i3−1−i3−2−2i31+i3003+3i3−3−3i3000000000000000000000−4+4i34−4i3002−2i3−1+i3−2+2i31−i3003−3i3−3+3i3000000000000000000000

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