Finite Group Databasebeta

← Group #13157133

Character table — Group #13157133

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155C156C157C158C159C160C161C162
size111122444444444444444444444444444444444418181818363636363636363636361111224444444444444444444444444444444444181818183636363636363636363611112244444444444444444444444444444444441818181836363636363636363636
order12222233446666666666666612121212121212121212121212121212444444888888883666663312126666666666666612121212121212121212121212121212121212121212242424242424242436666633121266666666666666121212121212121212121212121212121212121212122424242424242424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-1-1-1iiii−i−i−i−i1111111111111111111111111111111111111111-1-1-1-1-1-1iiii−i−i−i−i1111111111111111111111111111111111111111-1-1-1-1-1-1iiii−i−i−i−i
χ41111111111111111111111111111111111111111-1-1-1-1-1-1−i−i−i−iiiii1111111111111111111111111111111111111111-1-1-1-1-1-1−i−i−i−iiiii1111111111111111111111111111111111111111-1-1-1-1-1-1−i−i−i−iiiii
χ511111111-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-111111111-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-111111111-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-1
χ611111111-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111111111-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111111111-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111
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χ811111111-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111−i−iiiii−i−i11111111-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111−i−iiiii−i−i11111111-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111−i−iiiii−i−i
χ91-11-11-111i−i111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i1-11-1i−i1-1i−i1-1i−i1-11-11-111i−i111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i1-11-1i−i1-1i−i1-1i−i1-11-11-111i−i111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i1-11-1i−i1-1i−i1-1i−i
χ101-11-11-111i−i111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i1-11-1i−i-11−ii-11−ii1-11-11-111i−i111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i1-11-1i−i-11−ii-11−ii1-11-11-111i−i111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i1-11-1i−i-11−ii-11−ii
χ111-11-11-111i−i111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-11-11−iii−i-11−ii1-11-11-11-111i−i111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-11-11−iii−i-11−ii1-11-11-11-111i−i111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-11-11−iii−i-11−ii1-1
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χ131-11-11-111−ii111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii1-11-1−ii1-1−ii1-1−ii1-11-11-111−ii111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii1-11-1−ii1-1−ii1-1−ii1-11-11-111−ii111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii1-11-1−ii1-1−ii1-1−ii
χ141-11-11-111−ii111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii1-11-1−ii-11i−i-11i−i1-11-11-111−ii111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii1-11-1−ii-11i−i-11i−i1-11-11-111−ii111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii1-11-1−ii-11i−i-11i−i
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χ161-11-11-111−ii111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-11-11i−i−ii-11i−i1-11-11-11-111−ii111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-11-11i−i−ii-11i−i1-11-11-11-111−ii111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-11-11i−i−ii-11i−i1-1
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χ202-22-2-22220022-2-2-2-2-2-22222-2-20000000000000000-2-22200000000002-22-2-22220022-2-2-2-2-2-22222-2-20000000000000000-2-22200000000002-22-2-22220022-2-2-2-2-2-22222-2-20000000000000000-2-2220000000000
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χ11411111111-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111−1−i32−1−i32−1−i32−1−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−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−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+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−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i32
χ11511111111-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111ii−i−i−i−iii−1−i32−1−i32−1−i32−1−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−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32ζ11ζ11−ζ11−ζ11−ζ11−ζ11ζ11ζ11−1+i32−1+i32−1+i32−1+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+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32ζ7ζ7−ζ7−ζ7−ζ7−ζ7ζ7ζ7
χ11611111111-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111−i−iiiii−i−i−1−i32−1−i32−1−i32−1−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−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−ζ11−ζ11ζ11ζ11ζ11ζ11−ζ11−ζ11−1+i32−1+i32−1+i32−1+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+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−ζ7−ζ7ζ7ζ7ζ7ζ7−ζ7−ζ7
χ1171-11-11-111i−i111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i1-11-1i−i1-1i−i1-1i−i−1−i321+i32−1−i321+i32−1−i321+i32−1−i32−1−i32ζ11−ζ11−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i321+i32ζ11ζ11ζ11ζ11ζ11ζ11ζ11ζ11−ζ11−ζ11−ζ11−ζ11−ζ11−ζ11−ζ11−ζ11−1−i321+i32−1−i321+i32ζ11−ζ11−1−i321+i32ζ11−ζ11−1−i321+i32ζ11−ζ11−1+i321−i32−1+i321−i32−1+i321−i32−1+i32−1+i32ζ7−ζ7−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i321−i321−i32ζ7ζ7ζ7ζ7ζ7ζ7ζ7ζ7−ζ7−ζ7−ζ7−ζ7−ζ7−ζ7−ζ7−ζ7−1+i321−i32−1+i321−i32ζ7−ζ7−1+i321−i32ζ7−ζ7−1+i321−i32ζ7−ζ7
χ1181-11-11-111i−i111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i1-11-1i−i-11−ii-11−ii−1−i321+i32−1−i321+i32−1−i321+i32−1−i32−1−i32ζ11−ζ11−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i321+i32ζ11ζ11ζ11ζ11ζ11ζ11ζ11ζ11−ζ11−ζ11−ζ11−ζ11−ζ11−ζ11−ζ11−ζ11−1−i321+i32−1−i321+i32ζ11−ζ111+i32−1−i32−ζ11ζ111+i32−1−i32−ζ11ζ11−1+i321−i32−1+i321−i32−1+i321−i32−1+i32−1+i32ζ7−ζ7−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i321−i321−i32ζ7ζ7ζ7ζ7ζ7ζ7ζ7ζ7−ζ7−ζ7−ζ7−ζ7−ζ7−ζ7−ζ7−ζ7−1+i321−i32−1+i321−i32ζ7−ζ71−i32−1+i32−ζ7ζ71−i32−1+i32−ζ7ζ7
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χ1544-4-44001-200-123-300-12-33001-2−i3i3−i3i300−2i32i3i3−i3i3−i3002i3−2i300000000000000−2−2i32+2i32+2i3−2−2i300−1−i321+i3001+i32−1−i3−3−3i323+3i32001+i32−1−i33+3i32−3−3i3200−1−i321+i3−3+i323−i32−3+i323−i3200−3+i33−i33−i32−3+i323−i32−3+i32003−i3−3+i300000000000000−2+2i32−2i32−2i3−2+2i300−1+i321−i3001−i32−1+i3−3+3i323−3i32001−i32−1+i33−3i32−3+3i3200−1+i321−i33+i32−3−i323+i32−3−i32003+i3−3−i3−3−i323+i32−3−i323+i3200−3−i33+i300000000000000
χ1554-4-44001-200-123-300-12-33001-2i3−i3i3−i3002i3−2i3−i3i3−i3i300−2i32i300000000000000−2−2i32+2i32+2i3−2−2i300−1−i321+i3001+i32−1−i3−3−3i323+3i32001+i32−1−i33+3i32−3−3i3200−1−i321+i33−i32−3+i323−i32−3+i32003−i3−3+i3−3+i323−i32−3+i323−i3200−3+i33−i300000000000000−2+2i32−2i32−2i3−2+2i300−1+i321−i3001−i32−1+i3−3+3i323−3i32001−i32−1+i33−3i32−3+3i3200−1+i321−i3−3−i323+i32−3−i323+i3200−3−i33+i33+i32−3−i323+i32−3−i32003+i3−3−i300000000000000
χ1564-4-44001-200-12-3300-123-3001-2−i3i3i3−i3−2i32i300i3−i3−i3i32i3−2i30000000000000000−2−2i32+2i32+2i3−2−2i300−1−i321+i3001+i32−1−i33+3i32−3−3i32001+i32−1−i3−3−3i323+3i3200−1−i321+i3−3+i323−i323−i32−3+i32−3+i33−i3003−i32−3+i32−3+i323−i323−i3−3+i30000000000000000−2+2i32−2i32−2i3−2+2i300−1+i321−i3001−i32−1+i33−3i32−3+3i32001−i32−1+i3−3+3i323−3i3200−1+i321−i33+i32−3−i32−3−i323+i323+i3−3−i300−3−i323+i323+i32−3−i32−3−i33+i30000000000000000
χ1574-4-44001-200-12-3300-123-3001-2i3−i3−i3i32i3−2i300−i3i3i3−i3−2i32i30000000000000000−2−2i32+2i32+2i3−2−2i300−1−i321+i3001+i32−1−i33+3i32−3−3i32001+i32−1−i3−3−3i323+3i3200−1−i321+i33−i32−3+i32−3+i323−i323−i3−3+i300−3+i323−i323−i32−3+i32−3+i33−i30000000000000000−2+2i32−2i32−2i3−2+2i300−1+i321−i3001−i32−1+i33−3i32−3+3i32001−i32−1+i3−3+3i323−3i3200−1+i321−i3−3−i323+i323+i32−3−i32−3−i33+i3003+i32−3−i32−3−i323+i323+i3−3−i30000000000000000
χ1584-4-44004400-4-40000-4-4000044000000000000000000000000000000−2−2i32+2i32+2i3−2−2i300−2−2i3−2−2i3002+2i32+2i300002+2i32+2i30000−2−2i3−2−2i3000000000000000000000000000000−2+2i32−2i32−2i3−2+2i300−2+2i3−2+2i3002−2i32−2i300002−2i32−2i30000−2+2i3−2+2i3000000000000000000000000000000
χ1594-4-4400-21002-1003-32-100-33-2100−2i32i3−i3i3i3−i3002i3−2i3i3−i3−i3i300000000000000−2−2i32+2i32+2i3−2−2i3001+i3−1−i3200−1−i31+i3200−3−3i323+3i32−1−i31+i32003+3i32−3−3i321+i3−1−i3200−3+i33−i3−3+i323−i323−i32−3+i32003−i3−3+i33−i32−3+i32−3+i323−i3200000000000000−2+2i32−2i32−2i3−2+2i3001−i3−1+i3200−1+i31−i3200−3+3i323−3i32−1+i31−i32003−3i32−3+3i321−i3−1+i32003+i3−3−i33+i32−3−i32−3−i323+i3200−3−i33+i3−3−i323+i323+i32−3−i3200000000000000
χ1604-4-4400-21002-1003-32-100-33-21002i3−2i3i3−i3−i3i300−2i32i3−i3i3i3−i300000000000000−2−2i32+2i32+2i3−2−2i3001+i3−1−i3200−1−i31+i3200−3−3i323+3i32−1−i31+i32003+3i32−3−3i321+i3−1−i32003−i3−3+i33−i32−3+i32−3+i323−i3200−3+i33−i3−3+i323−i323−i32−3+i3200000000000000−2+2i32−2i32−2i3−2+2i3001−i3−1+i3200−1+i31−i3200−3+3i323−3i32−1+i31−i32003−3i32−3+3i321−i3−1+i3200−3−i33+i3−3−i323+i323+i32−3−i32003+i3−3−i33+i32−3−i32−3−i323+i3200000000000000
χ1614-4-4400-21002-100-332-1003-3-21−2i32i300i3−i3i3−i32i3−2i300−i3i3−i3i300000000000000−2−2i32+2i32+2i3−2−2i3001+i3−1−i3200−1−i31+i32003+3i32−3−3i32−1−i31+i3200−3−3i323+3i321+i3−1−i32−3+i33−i3003−i32−3+i323−i32−3+i323−i3−3+i300−3+i323−i32−3+i323−i3200000000000000−2+2i32−2i32−2i3−2+2i3001−i3−1+i3200−1+i31−i32003−3i32−3+3i32−1+i31−i3200−3+3i323−3i321−i3−1+i323+i3−3−i300−3−i323+i32−3−i323+i32−3−i33+i3003+i32−3−i323+i32−3−i3200000000000000
χ1624-4-4400-21002-100-332-1003-3-212i3−2i300−i3i3−i3i3−2i32i300i3−i3i3−i300000000000000−2−2i32+2i32+2i3−2−2i3001+i3−1−i3200−1−i31+i32003+3i32−3−3i32−1−i31+i3200−3−3i323+3i321+i3−1−i323−i3−3+i300−3+i323−i32−3+i323−i32−3+i33−i3003−i32−3+i323−i32−3+i3200000000000000−2+2i32−2i32−2i3−2+2i3001−i3−1+i3200−1+i31−i32003−3i32−3+3i32−1+i31−i3200−3+3i323−3i321−i3−1+i32−3−i33+i3003+i32−3−i323+i32−3−i323+i3−3−i300−3−i323+i32−3−i323+i3200000000000000

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