Finite Group Databasebeta

← Group #13161491

Character table — Group #13161491

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153
size111122222222222222222222222244444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444363636363636363636363636363636363636363636363636727272727272
order122233344446666666661212121212121212333334666666666666666121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121212121244448888121212121212121224242424242424244412121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111-1-11111111111111-1-1-1-11111111-111111111111111111-1-1-1-1-1-111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11-111-1-1
χ61111111-1-11111111111111-1-1-1-11111111-111111111111111111-1-1-1-1-1-111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111-11-1-111
χ71111111-1-11111111111111-1-1-1-11111111-111111111111111111-1-1-1-1-1-111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1-11-1-111
χ81111111-1-11111111111111-1-1-1-11111111-111111111111111111-1-1-1-1-1-111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-111111-111-1-1
χ9222222222-2-2222222222-2-22222-2-222222-2222222222222222-2-22222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2000000000000000000000000000000
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χ13222222-122-2-222222-1-1-12-2-2-1-1-1-1-2-22-1-1-1-1-2222-1-1-1-1-1-1-1-1-1-1-1-1-2-22222-2-21111-2-2-2-2-2-211111111111111112222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2111111111111111100000000−i3−i3i3i3−i3−i3i3i300000000000000
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χ15222222-1-2-22222222-1-1-12221111222-1-1-1-1-2222-1-1-1-1-1-1-1-1-1-1-1-122-2-2-2-2-2-2-1-111-2-22222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-21111111111111111-2-2-2-2111111111111111122-2-20000-1-1-1-1111100000000000000
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χ2322222-12-2-222222-1-1222-122-2-2-2-222-12-1-1-1-2-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-2-211-2-222-2-211-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-11111-2-2-2-21111111111111111-2-2-2-21111111111110000000000000000000000002-2-1-111
χ2422222-12-2-222222-1-1222-122-2-2-2-222-12-1-1-1-2-1-1-1222-1-1-1-1-1-1-1-1-1-1-1-2-211-2-222-2-211-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-11111-2-2-2-21111111111111111-2-2-2-2111111111111000000000000000000000000-2211-1-1
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χ4622-2-2-122-2200-1112-22-2-2-2−33-2-222−33-1-12-1-10-111-1112-2-2-1-11111001-1-223−3000000−3−333−3−3330000−3−3−3−3333311-1-111-1-1-2-2221111-1-1-1-133−3−333−3−300003333−3−3−3−30000−222−200000000−ζ13+ζ23ζ13−ζ23−ζ5+ζ7ζ5−ζ7ζ13−ζ23−ζ13+ζ23ζ5−ζ7−ζ5+ζ7000000
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χ1464-4-44-2-2-2000022-22222-2-223−2323−23−2323−2323111−1−3i32−1+3i320-1-11-1-11-1-111+3i321−3i321+3i321−3i32−1−3i32−1+3i32000000000000−2i32i3−333−3−333−33i−3i−3i3iζ14+2ζ22−2ζ14−ζ22−ζ14−2ζ222ζ14+ζ22−ζ14−2ζ222ζ14+ζ22ζ14+2ζ22−2ζ14−ζ223i−3i−3i3i−333−3−333−3ζ14+2ζ22−2ζ14−ζ22−ζ14−2ζ222ζ14+ζ22−ζ14−2ζ222ζ14+ζ22ζ14+2ζ22−2ζ14−ζ22i3−i3−i3i33-3-33i3−i3−i3i3−3−i32−3+i323+i323−i323+i323−i32−3−i32−3+i32000000000000000000000000000000
χ1474-4-44-2-2-2000022-22222-2-223−2323−23−2323−2323111−1+3i32−1−3i320-1-11-1-11-1-111−3i321+3i321−3i321+3i32−1+3i32−1−3i320000000000002i3−2i3−333−3−333−3−3i3i3i−3i−2ζ14−ζ22ζ14+2ζ222ζ14+ζ22−ζ14−2ζ222ζ14+ζ22−ζ14−2ζ22−2ζ14−ζ22ζ14+2ζ22−3i3i3i−3i−333−3−333−3−2ζ14−ζ22ζ14+2ζ222ζ14+ζ22−ζ14−2ζ222ζ14+ζ22−ζ14−2ζ22−2ζ14−ζ22ζ14+2ζ22−i3i3i3−i33-3-33−i3i3i3−i3−3+i32−3−i323−i323+i323−i323+i32−3+i32−3−i32000000000000000000000000000000
χ1484-4-44-2-2-2000022-22222-2-223−23−232323−23−2323111−1−3i32−1+3i320-1-11-1-11-1-111+3i321−3i321+3i321−3i32−1−3i32−1+3i320000000000002i3−2i3−333−3−333−33i−3i−3i3iζ14+2ζ22−2ζ14−ζ22−ζ14−2ζ222ζ14+ζ22−ζ14−2ζ222ζ14+ζ22ζ14+2ζ22−2ζ14−ζ22−3i3i3i−3i3−3−333−3−33−ζ14−2ζ222ζ14+ζ22ζ14+2ζ22−2ζ14−ζ22ζ14+2ζ22−2ζ14−ζ22−ζ14−2ζ222ζ14+ζ22−i3i3i3−i3-333-3−i3i3i3−i33+i323−i32−3−i32−3+i32−3−i32−3+i323+i323−i32000000000000000000000000000000
χ1494-4-44-2-2-2000022-22222-2-223−23−232323−23−2323111−1+3i32−1−3i320-1-11-1-11-1-111−3i321+3i321−3i321+3i32−1+3i32−1−3i32000000000000−2i32i3−333−3−333−3−3i3i3i−3i−2ζ14−ζ22ζ14+2ζ222ζ14+ζ22−ζ14−2ζ222ζ14+ζ22−ζ14−2ζ22−2ζ14−ζ22ζ14+2ζ223i−3i−3i3i3−3−333−3−332ζ14+ζ22−ζ14−2ζ22−2ζ14−ζ22ζ14+2ζ22−2ζ14−ζ22ζ14+2ζ222ζ14+ζ22−ζ14−2ζ22i3−i3−i3i3-333-3i3−i3−i3i33−i323+i32−3+i32−3−i32−3+i32−3−i323−i323+i32000000000000000000000000000000
χ1504-4-44-2-2-2000022-22222-2-2−232323−23−232323−23111−1−3i32−1+3i320-1-11-1-11-1-111+3i321−3i321+3i321−3i32−1−3i32−1+3i320000000000002i3−2i33−3−333−3−33−3i3i3i−3i−ζ14−2ζ222ζ14+ζ22ζ14+2ζ22−2ζ14−ζ22ζ14+2ζ22−2ζ14−ζ22−ζ14−2ζ222ζ14+ζ223i−3i−3i3i−333−3−333−3ζ14+2ζ22−2ζ14−ζ22−ζ14−2ζ222ζ14+ζ22−ζ14−2ζ222ζ14+ζ22ζ14+2ζ22−2ζ14−ζ22−i3i3i3−i3-333-3−i3i3i3−i33+i323−i32−3−i32−3+i32−3−i32−3+i323+i323−i32000000000000000000000000000000
χ1514-4-44-2-2-2000022-22222-2-2−232323−23−232323−23111−1+3i32−1−3i320-1-11-1-11-1-111−3i321+3i321−3i321+3i32−1+3i32−1−3i32000000000000−2i32i33−3−333−3−333i−3i−3i3i2ζ14+ζ22−ζ14−2ζ22−2ζ14−ζ22ζ14+2ζ22−2ζ14−ζ22ζ14+2ζ222ζ14+ζ22−ζ14−2ζ22−3i3i3i−3i−333−3−333−3−2ζ14−ζ22ζ14+2ζ222ζ14+ζ22−ζ14−2ζ222ζ14+ζ22−ζ14−2ζ22−2ζ14−ζ22ζ14+2ζ22i3−i3−i3i3-333-3i3−i3−i3i33−i323+i32−3+i32−3−i32−3+i32−3−i323−i323+i32000000000000000000000000000000
χ1524-4-44-2-2-2000022-22222-2-2−2323−232323−2323−23111−1−3i32−1+3i320-1-11-1-11-1-111+3i321−3i321+3i321−3i32−1−3i32−1+3i32000000000000−2i32i33−3−333−3−33−3i3i3i−3i−ζ14−2ζ222ζ14+ζ22ζ14+2ζ22−2ζ14−ζ22ζ14+2ζ22−2ζ14−ζ22−ζ14−2ζ222ζ14+ζ22−3i3i3i−3i3−3−333−3−33−ζ14−2ζ222ζ14+ζ22ζ14+2ζ22−2ζ14−ζ22ζ14+2ζ22−2ζ14−ζ22−ζ14−2ζ222ζ14+ζ22i3−i3−i3i33-3-33i3−i3−i3i3−3−i32−3+i323+i323−i323+i323−i32−3−i32−3+i32000000000000000000000000000000
χ1534-4-44-2-2-2000022-22222-2-2−2323−232323−2323−23111−1+3i32−1−3i320-1-11-1-11-1-111−3i321+3i321−3i321+3i32−1+3i32−1−3i320000000000002i3−2i33−3−333−3−333i−3i−3i3i2ζ14+ζ22−ζ14−2ζ22−2ζ14−ζ22ζ14+2ζ22−2ζ14−ζ22ζ14+2ζ222ζ14+ζ22−ζ14−2ζ223i−3i−3i3i3−3−333−3−332ζ14+ζ22−ζ14−2ζ22−2ζ14−ζ22ζ14+2ζ22−2ζ14−ζ22ζ14+2ζ222ζ14+ζ22−ζ14−2ζ22−i3i3i3−i33-3-33−i3i3i3−i3−3+i32−3−i323−i323+i323−i323+i32−3+i32−3−i32000000000000000000000000000000

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