Finite Group Databasebeta

← Group #13157085

Character table — Group #13157085

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144
size111122444444444488888888888899991818181818181818181836363636363611112244444444448888888888889999181818181818181818183636363636361111224444444444888888888888999918181818181818181818363636363636
order12224433446666661212121212121212121212124444448888888822888836661212331212666666121212121212121212121212121212121212242424242424242466242424243666121233121266666612121212121212121212121212121212121224242424242424246624242424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-1iiii−i−i−i−i-1-1ii−i−i1111111111111111111111111111-1-1-1-1-1-1iiii−i−i−i−i-1-1ii−i−i1111111111111111111111111111-1-1-1-1-1-1iiii−i−i−i−i-1-1ii−i−i
χ41111111111111111111111111111-1-1-1-1-1-1−i−i−i−iiiii-1-1−i−iii1111111111111111111111111111-1-1-1-1-1-1−i−i−i−iiiii-1-1−i−iii1111111111111111111111111111-1-1-1-1-1-1−i−i−i−iiiii-1-1−i−iii
χ511111111-1-11111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-111111111-1-11111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-111111111-1-11111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1
χ611111111-1-11111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111111111-1-11111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111111111-1-11111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111
χ711111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i11−i−iii11111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i11−i−iii11111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i11−i−iii
χ811111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii11ii−i−i11111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii11ii−i−i11111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii11ii−i−i
χ911-1-11-111i−i-1-111-1-111-1-1iiii−i−i−i−ii−ii−ii−iζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ131-1ζ5+ζ13−ζ5−ζ13ζ7+ζ23−ζ7−ζ2311-1-11-111i−i-1-111-1-111-1-1iiii−i−i−i−ii−ii−ii−iζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ131-1ζ5+ζ13−ζ5−ζ13ζ7+ζ23−ζ7−ζ2311-1-11-111i−i-1-111-1-111-1-1iiii−i−i−i−ii−ii−ii−iζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ131-1ζ5+ζ13−ζ5−ζ13ζ7+ζ23−ζ7−ζ23
χ1011-1-11-111i−i-1-111-1-111-1-1iiii−i−i−i−ii−ii−ii−i−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ131-1−ζ5−ζ13ζ5+ζ13−ζ7−ζ23ζ7+ζ2311-1-11-111i−i-1-111-1-111-1-1iiii−i−i−i−ii−ii−ii−i−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ131-1−ζ5−ζ13ζ5+ζ13−ζ7−ζ23ζ7+ζ2311-1-11-111i−i-1-111-1-111-1-1iiii−i−i−i−ii−ii−ii−i−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ131-1−ζ5−ζ13ζ5+ζ13−ζ7−ζ23ζ7+ζ23
χ1111-1-11-111i−i-1-111-1-111-1-1iiii−i−i−i−i−ii−ii−iiζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23-11−ζ7−ζ23ζ7+ζ23−ζ5−ζ13ζ5+ζ1311-1-11-111i−i-1-111-1-111-1-1iiii−i−i−i−i−ii−ii−iiζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23-11−ζ7−ζ23ζ7+ζ23−ζ5−ζ13ζ5+ζ1311-1-11-111i−i-1-111-1-111-1-1iiii−i−i−i−i−ii−ii−iiζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23-11−ζ7−ζ23ζ7+ζ23−ζ5−ζ13ζ5+ζ13
χ1211-1-11-111i−i-1-111-1-111-1-1iiii−i−i−i−i−ii−ii−ii−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23-11ζ7+ζ23−ζ7−ζ23ζ5+ζ13−ζ5−ζ1311-1-11-111i−i-1-111-1-111-1-1iiii−i−i−i−i−ii−ii−ii−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23-11ζ7+ζ23−ζ7−ζ23ζ5+ζ13−ζ5−ζ1311-1-11-111i−i-1-111-1-111-1-1iiii−i−i−i−i−ii−ii−ii−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23-11ζ7+ζ23−ζ7−ζ23ζ5+ζ13−ζ5−ζ13
χ1311-1-11-111−ii-1-111-1-111-1-1−i−i−i−iiiiii−ii−ii−iζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13-11−ζ5−ζ13ζ5+ζ13−ζ7−ζ23ζ7+ζ2311-1-11-111−ii-1-111-1-111-1-1−i−i−i−iiiiii−ii−ii−iζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13-11−ζ5−ζ13ζ5+ζ13−ζ7−ζ23ζ7+ζ2311-1-11-111−ii-1-111-1-111-1-1−i−i−i−iiiiii−ii−ii−iζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ23ζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13-11−ζ5−ζ13ζ5+ζ13−ζ7−ζ23ζ7+ζ23
χ1411-1-11-111−ii-1-111-1-111-1-1−i−i−i−iiiiii−ii−ii−i−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13-11ζ5+ζ13−ζ5−ζ13ζ7+ζ23−ζ7−ζ2311-1-11-111−ii-1-111-1-111-1-1−i−i−i−iiiiii−ii−ii−i−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13-11ζ5+ζ13−ζ5−ζ13ζ7+ζ23−ζ7−ζ2311-1-11-111−ii-1-111-1-111-1-1−i−i−i−iiiiii−ii−ii−i−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ23−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13-11ζ5+ζ13−ζ5−ζ13ζ7+ζ23−ζ7−ζ23
χ1511-1-11-111−ii-1-111-1-111-1-1−i−i−i−iiiii−ii−ii−iiζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ231-1ζ7+ζ23−ζ7−ζ23ζ5+ζ13−ζ5−ζ1311-1-11-111−ii-1-111-1-111-1-1−i−i−i−iiiii−ii−ii−iiζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ231-1ζ7+ζ23−ζ7−ζ23ζ5+ζ13−ζ5−ζ1311-1-11-111−ii-1-111-1-111-1-1−i−i−i−iiiii−ii−ii−iiζ5+ζ13ζ5+ζ13−ζ5−ζ13−ζ5−ζ13ζ7+ζ23ζ7+ζ23−ζ7−ζ23−ζ7−ζ231-1ζ7+ζ23−ζ7−ζ23ζ5+ζ13−ζ5−ζ13
χ1611-1-11-111−ii-1-111-1-111-1-1−i−i−i−iiiii−ii−ii−ii−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ231-1−ζ7−ζ23ζ7+ζ23−ζ5−ζ13ζ5+ζ1311-1-11-111−ii-1-111-1-111-1-1−i−i−i−iiiii−ii−ii−ii−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ231-1−ζ7−ζ23ζ7+ζ23−ζ5−ζ13ζ5+ζ1311-1-11-111−ii-1-111-1-111-1-1−i−i−i−iiiii−ii−ii−ii−ζ5−ζ13−ζ5−ζ13ζ5+ζ13ζ5+ζ13−ζ7−ζ23−ζ7−ζ23ζ7+ζ23ζ7+ζ231-1−ζ7−ζ23ζ7+ζ23−ζ5−ζ13ζ5+ζ13
χ172222-2-22200222222-2-2-2-2000000002222-2-2000000000000002222-2-22200222222-2-2-2-2000000002222-2-2000000000000002222-2-22200222222-2-2-2-2000000002222-2-200000000000000
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χ1922-2-2-222200-2-222-2-2-2-222000000002i−2i2i−2i−2i2i0000000000000022-2-2-222200-2-222-2-2-2-222000000002i−2i2i−2i−2i2i0000000000000022-2-2-222200-2-222-2-2-2-222000000002i−2i2i−2i−2i2i00000000000000
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χ242-22-200220022-2-2-2-2000000000000−2i2i2i−2i00−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000002-22-200220022-2-2-2-2000000000000−2i2i2i−2i00−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000002-22-200220022-2-2-2-2000000000000−2i2i2i−2i00−1−i1+i−1−i1+i−1+i1−i−1+i1−i000000
χ252-2-22002200-2-2-2-22200000000000022-2-200i2−i2−i2i2i2−i2−i2i20000002-2-22002200-2-2-2-22200000000000022-2-200i2−i2−i2i2i2−i2−i2i20000002-2-22002200-2-2-2-22200000000000022-2-200i2−i2−i2i2i2−i2−i2i2000000
χ262-2-22002200-2-2-2-22200000000000022-2-200−i2i2i2−i2−i2i2i2−i20000002-2-22002200-2-2-2-22200000000000022-2-200−i2i2i2−i2−i2i2i2−i20000002-2-22002200-2-2-2-22200000000000022-2-200−i2i2i2−i2−i2i2i2−i2000000
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χ282-2-22002200-2-2-2-222000000000000-2-22200−222−22−2−220000002-2-22002200-2-2-2-222000000000000-2-22200−222−22−2−220000002-2-22002200-2-2-2-222000000000000-2-22200−222−22−2−22000000
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χ304444441-2-4-41-21-21-21-21-2-1-122-1-122000000000000000000004444441-2-4-41-21-21-21-21-2-1-122-1-122000000000000000000004444441-2-4-41-21-21-21-21-2-1-122-1-12200000000000000000000
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χ344444-4-41-2001-21-21-2-12-12-3300-3300000000000000000000004444-4-41-2001-21-21-2-12-12-3300-3300000000000000000000004444-4-41-2001-21-21-2-12-12-3300-330000000000000000000000
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χ4044-4-44-4-21−4i4i2-1-212-1-212-12i2i−i−i−2i−2iii0000000000000000000044-4-44-4-21−4i4i2-1-212-1-212-12i2i−i−i−2i−2iii0000000000000000000044-4-44-4-21−4i4i2-1-212-1-212-12i2i−i−i−2i−2iii00000000000000000000
χ4144-4-4-441-200-121-2-12-121-23i−3i00−3i3i000000000000000000000044-4-4-441-200-121-2-12-121-23i−3i00−3i3i000000000000000000000044-4-4-441-200-121-2-12-121-23i−3i00−3i3i0000000000000000000000
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χ991111111111111111111111111111-1-1-1-1-1-1iiii−i−i−i−i-1-1ii−i−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−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32ζ22ζ22ζ22ζ22−ζ22−ζ22−ζ22−ζ221+i321+i32ζ22ζ22−ζ22−ζ22−1+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−i321−i321−i32ζ14ζ14ζ14ζ14−ζ14−ζ14−ζ14−ζ141−i321−i32ζ14ζ14−ζ14−ζ14
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χ10111111111-1-11111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1−1−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−i321+i321+i321+i321+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−i321+i321+i321+i321+i321+i321+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+i321−i321−i321−i321−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+i321−i321−i321−i321−i321−i321−i32
χ10211111111-1-11111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111−1−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−i321+i321+i321+i321+i321+i321+i321+i321+i32−1−i32−1−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−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+i321−i321−i321−i321−i321−i321−i321−i321−i32−1+i32−1+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+i32
χ10311111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i11−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−i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i32ζ22ζ22ζ22ζ22−ζ22−ζ22−ζ22−ζ22−1−i32−1−i32−ζ22−ζ22ζ22ζ22−1+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+i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i32ζ14ζ14ζ14ζ14−ζ14−ζ14−ζ14−ζ14−1+i32−1+i32−ζ14−ζ14ζ14ζ14
χ10411111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii11ii−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−i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i32−ζ22−ζ22−ζ22−ζ22ζ22ζ22ζ22ζ22−1−i32−1−i32ζ22ζ22−ζ22−ζ22−1+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+i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i32−ζ14−ζ14−ζ14−ζ14ζ14ζ14ζ14ζ14−1+i32−1+i32ζ14ζ14−ζ14−ζ14
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.