Finite Group Databasebeta

← Group #13178509

Character table — Group #13178509

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155C156C157C158C159C160C161C162C163C164C165C166C167C168C169C170C171C172C173C174C175C176C177C178C179C180C181C182C183C184C185C186C187C188C189C190C191C192C193C194C195C196C197C198C199C200C201C202C203C204C205C206C207C208C209C210C211C212C213C214C215C216
size111122222222222244444444444444444444181818181818181818181818181818181818111122222222222244444444444444444444181818181818181818181818181818181818111122222222222244444444444444444444181818181818181818181818181818181818111122222222222244444444444444444444181818181818181818181818181818181818
order12443336661212121212123333366666121212121212121212122466888812122424242424242424224466666612121212121266666666661212121212121212121224668888121224242424242424242244666666121212121212666666666612121212121212121212246688881212242424242424242422446666661212121212126666666666121212121212121212122466888812122424242424242424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1111111111111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1111111111111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1111111111111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-11111111111111111111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-11111111111111111111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-11111111111111111111111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-11111
χ511-1-1111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11-111i−ii−i-1-1ii−i−iii−i−i11-1-1111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11-111i−ii−i-1-1ii−i−iii−i−i11-1-1111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11-111i−ii−i-1-1ii−i−iii−i−i11-1-1111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11-111i−ii−i-1-1ii−i−iii−i−i
χ611-1-1111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11-111−ii−ii-1-1−i−iii−i−iii11-1-1111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11-111−ii−ii-1-1−i−iii−i−iii11-1-1111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11-111−ii−ii-1-1−i−iii−i−iii11-1-1111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11-111−ii−ii-1-1−i−iii−i−iii
χ711-1-1111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-11-1-1i−i−ii11ii−i−i−i−iii11-1-1111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-11-1-1i−i−ii11ii−i−i−i−iii11-1-1111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-11-1-1i−i−ii11ii−i−i−i−iii11-1-1111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-11-1-1i−i−ii11ii−i−i−i−iii
χ811-1-1111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-11-1-1−iii−i11−i−iiiii−i−i11-1-1111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-11-1-1−iii−i11−i−iiiii−i−i11-1-1111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-11-1-1−iii−i11−i−iiiii−i−i11-1-1111111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-11-1-1−iii−i11−i−iiiii−i−i
χ9222222-122-1-1-122222-1-1-1-12-1-1-1-122-1-1-1-1-1-1-1-122-1-10000-1-100000000222222-122-1-1-122222-1-1-1-12-1-1-1-122-1-1-1-1-1-1-1-122-1-10000-1-100000000222222-122-1-1-122222-1-1-1-12-1-1-1-122-1-1-1-1-1-1-1-122-1-10000-1-100000000222222-122-1-1-122222-1-1-1-12-1-1-1-122-1-1-1-1-1-1-1-122-1-10000-1-100000000
χ10222222-122-1-1-122222-1-1-1-12-1-1-1-122-1-1-1-1-1-1-1-1-2-21100001100000000222222-122-1-1-122222-1-1-1-12-1-1-1-122-1-1-1-1-1-1-1-1-2-21100001100000000222222-122-1-1-122222-1-1-1-12-1-1-1-122-1-1-1-1-1-1-1-1-2-21100001100000000222222-122-1-1-122222-1-1-1-12-1-1-1-122-1-1-1-1-1-1-1-1-2-21100001100000000
χ1122222-122-122222-1-1-12-1-1-1-12-1-1-1-1-122-1-1-1-1-1-100000022000000-1-1-1-122222-122-122222-1-1-12-1-1-1-12-1-1-1-1-122-1-1-1-1-1-100000022000000-1-1-1-122222-122-122222-1-1-12-1-1-1-12-1-1-1-1-122-1-1-1-1-1-100000022000000-1-1-1-122222-122-122222-1-1-12-1-1-1-12-1-1-1-1-122-1-1-1-1-1-100000022000000-1-1-1-1
χ1222222-122-122222-1-1-12-1-1-1-12-1-1-1-1-122-1-1-1-1-1-1000000-2-2000000111122222-122-122222-1-1-12-1-1-1-12-1-1-1-1-122-1-1-1-1-1-1000000-2-2000000111122222-122-122222-1-1-12-1-1-1-12-1-1-1-1-122-1-1-1-1-1-1000000-2-2000000111122222-122-122222-1-1-12-1-1-1-12-1-1-1-1-122-1-1-1-1-1-1000000-2-20000001111
χ132222-122-12222-1-122-1-12-1-1-1-12-1-1-1-1-1-122-1-1-1-10000220000-1-1-1-100002222-122-12222-1-122-1-12-1-1-1-12-1-1-1-1-1-122-1-1-1-10000220000-1-1-1-100002222-122-12222-1-122-1-12-1-1-1-12-1-1-1-1-1-122-1-1-1-10000220000-1-1-1-100002222-122-12222-1-122-1-12-1-1-1-12-1-1-1-1-1-122-1-1-1-10000220000-1-1-1-10000
χ142222-122-12222-1-122-1-12-1-1-1-12-1-1-1-1-1-122-1-1-1-10000-2-20000111100002222-122-12222-1-122-1-12-1-1-1-12-1-1-1-1-1-122-1-1-1-10000-2-20000111100002222-122-12222-1-122-1-12-1-1-1-12-1-1-1-1-1-122-1-1-1-10000-2-20000111100002222-122-12222-1-122-1-12-1-1-1-12-1-1-1-1-1-122-1-1-1-10000-2-2000011110000
χ1522-2-222-122-111-2-2-2-22-1-1-1-12-1-1-1-1-2-2111111112-2-1-10000110000000022-2-222-122-111-2-2-2-22-1-1-1-12-1-1-1-1-2-2111111112-2-1-10000110000000022-2-222-122-111-2-2-2-22-1-1-1-12-1-1-1-1-2-2111111112-2-1-10000110000000022-2-222-122-111-2-2-2-22-1-1-1-12-1-1-1-1-2-2111111112-2-1-100001100000000
χ1622-2-222-122-111-2-2-2-22-1-1-1-12-1-1-1-1-2-211111111-22110000-1-10000000022-2-222-122-111-2-2-2-22-1-1-1-12-1-1-1-1-2-211111111-22110000-1-10000000022-2-222-122-111-2-2-2-22-1-1-1-12-1-1-1-1-2-211111111-22110000-1-10000000022-2-222-122-111-2-2-2-22-1-1-1-12-1-1-1-1-2-211111111-22110000-1-100000000
χ1722-2-22-122-12-2-2-2-211-12-1-1-1-12-1-1-111-2-21111110000002i−2i000000−i−iii22-2-22-122-12-2-2-2-211-12-1-1-1-12-1-1-111-2-21111110000002i−2i000000−i−iii22-2-22-122-12-2-2-2-211-12-1-1-1-12-1-1-111-2-21111110000002i−2i000000−i−iii22-2-22-122-12-2-2-2-211-12-1-1-1-12-1-1-111-2-21111110000002i−2i000000−i−iii
χ1822-2-22-122-12-2-2-2-211-12-1-1-1-12-1-1-111-2-2111111000000−2i2i000000ii−i−i22-2-22-122-12-2-2-2-211-12-1-1-1-12-1-1-111-2-2111111000000−2i2i000000ii−i−i22-2-22-122-12-2-2-2-211-12-1-1-1-12-1-1-111-2-2111111000000−2i2i000000ii−i−i22-2-22-122-12-2-2-2-211-12-1-1-1-12-1-1-111-2-2111111000000−2i2i000000ii−i−i
χ1922-2-2-122-122-2-211-2-2-1-12-1-1-1-12-1-11111-2-2111100002i−2i0000−i−iii000022-2-2-122-122-2-211-2-2-1-12-1-1-1-12-1-11111-2-2111100002i−2i0000−i−iii000022-2-2-122-122-2-211-2-2-1-12-1-1-1-12-1-11111-2-2111100002i−2i0000−i−iii000022-2-2-122-122-2-211-2-2-1-12-1-1-1-12-1-11111-2-2111100002i−2i0000−i−iii0000
χ2022-2-2-122-122-2-211-2-2-1-12-1-1-1-12-1-11111-2-211110000−2i2i0000ii−i−i000022-2-2-122-122-2-211-2-2-1-12-1-1-1-12-1-11111-2-211110000−2i2i0000ii−i−i000022-2-2-122-122-2-211-2-2-1-12-1-1-1-12-1-11111-2-211110000−2i2i0000ii−i−i000022-2-2-122-122-2-211-2-2-1-12-1-1-1-12-1-11111-2-211110000−2i2i0000ii−i−i0000
χ212-22i−2i222-2-2-22i−2i2i−2i2i−2i22222-2-2-2-2-22i−2i2i−2i2i−2i2i2i−2i−2i0000000000000000002-22i−2i222-2-2-22i−2i2i−2i2i−2i22222-2-2-2-2-22i−2i2i−2i2i−2i2i2i−2i−2i0000000000000000002-22i−2i222-2-2-22i−2i2i−2i2i−2i22222-2-2-2-2-22i−2i2i−2i2i−2i2i2i−2i−2i0000000000000000002-22i−2i222-2-2-22i−2i2i−2i2i−2i22222-2-2-2-2-22i−2i2i−2i2i−2i2i2i−2i−2i000000000000000000
χ222-22i−2i22-1-2-21−ii2i−2i2i−2i2-1-1-1-1-211112i−2i−ii−ii−i−iii00−i3i300003−3000000002-22i−2i22-1-2-21−ii2i−2i2i−2i2-1-1-1-1-211112i−2i−ii−ii−i−iii00−i3i300003−3000000002-22i−2i22-1-2-21−ii2i−2i2i−2i2-1-1-1-1-211112i−2i−ii−ii−i−iii00−i3i300003−3000000002-22i−2i22-1-2-21−ii2i−2i2i−2i2-1-1-1-1-211112i−2i−ii−ii−i−iii00−i3i300003−300000000
χ232-22i−2i22-1-2-21−ii2i−2i2i−2i2-1-1-1-1-211112i−2i−ii−ii−i−iii00i3−i30000−33000000002-22i−2i22-1-2-21−ii2i−2i2i−2i2-1-1-1-1-211112i−2i−ii−ii−i−iii00i3−i30000−33000000002-22i−2i22-1-2-21−ii2i−2i2i−2i2-1-1-1-1-211112i−2i−ii−ii−i−iii00i3−i30000−33000000002-22i−2i22-1-2-21−ii2i−2i2i−2i2-1-1-1-1-211112i−2i−ii−ii−i−iii00i3−i30000−3300000000
χ242-22i−2i2-12-21-22i−2i2i−2i−ii-12-1-1-11-2111−ii2i−2i−ii−i−iii00000000000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ232-22i−2i2-12-21-22i−2i2i−2i−ii-12-1-1-11-2111−ii2i−2i−ii−i−iii00000000000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ232-22i−2i2-12-21-22i−2i2i−2i−ii-12-1-1-11-2111−ii2i−2i−ii−i−iii00000000000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ232-22i−2i2-12-21-22i−2i2i−2i−ii-12-1-1-11-2111−ii2i−2i−ii−i−iii00000000000000ζ5−ζ13−ζ5+ζ13−ζ7+ζ23ζ7−ζ23
χ252-22i−2i2-12-21-22i−2i2i−2i−ii-12-1-1-11-2111−ii2i−2i−ii−i−iii00000000000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ232-22i−2i2-12-21-22i−2i2i−2i−ii-12-1-1-11-2111−ii2i−2i−ii−i−iii00000000000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ232-22i−2i2-12-21-22i−2i2i−2i−ii-12-1-1-11-2111−ii2i−2i−ii−i−iii00000000000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ232-22i−2i2-12-21-22i−2i2i−2i−ii-12-1-1-11-2111−ii2i−2i−ii−i−iii00000000000000−ζ5+ζ13ζ5−ζ13ζ7−ζ23−ζ7+ζ23
χ262-22i−2i-1221-2-22i−2i−ii2i−2i-1-12-1-111-211−ii−ii2i−2i−i−iii0000000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ1300002-22i−2i-1221-2-22i−2i−ii2i−2i-1-12-1-111-211−ii−ii2i−2i−i−iii0000000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ1300002-22i−2i-1221-2-22i−2i−ii2i−2i-1-12-1-111-211−ii−ii2i−2i−i−iii0000000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ1300002-22i−2i-1221-2-22i−2i−ii2i−2i-1-12-1-111-211−ii−ii2i−2i−i−iii0000000000−ζ7+ζ23ζ7−ζ23ζ5−ζ13−ζ5+ζ130000
χ272-22i−2i-1221-2-22i−2i−ii2i−2i-1-12-1-111-211−ii−ii2i−2i−i−iii0000000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ1300002-22i−2i-1221-2-22i−2i−ii2i−2i-1-12-1-111-211−ii−ii2i−2i−i−iii0000000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ1300002-22i−2i-1221-2-22i−2i−ii2i−2i-1-12-1-111-211−ii−ii2i−2i−i−iii0000000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ1300002-22i−2i-1221-2-22i−2i−ii2i−2i-1-12-1-111-211−ii−ii2i−2i−i−iii0000000000ζ7−ζ23−ζ7+ζ23−ζ5+ζ13ζ5−ζ130000
χ282-2−2i2i222-2-2-2−2i2i−2i2i−2i2i22222-2-2-2-2-2−2i2i−2i2i−2i2i−2i−2i2i2i0000000000000000002-2−2i2i222-2-2-2−2i2i−2i2i−2i2i22222-2-2-2-2-2−2i2i−2i2i−2i2i−2i−2i2i2i0000000000000000002-2−2i2i222-2-2-2−2i2i−2i2i−2i2i22222-2-2-2-2-2−2i2i−2i2i−2i2i−2i−2i2i2i0000000000000000002-2−2i2i222-2-2-2−2i2i−2i2i−2i2i22222-2-2-2-2-2−2i2i−2i2i−2i2i−2i−2i2i2i000000000000000000
χ292-2−2i2i22-1-2-21i−i−2i2i−2i2i2-1-1-1-1-21111−2i2ii−ii−iii−i−i00−i3i30000−33000000002-2−2i2i22-1-2-21i−i−2i2i−2i2i2-1-1-1-1-21111−2i2ii−ii−iii−i−i00−i3i30000−33000000002-2−2i2i22-1-2-21i−i−2i2i−2i2i2-1-1-1-1-21111−2i2ii−ii−iii−i−i00−i3i30000−33000000002-2−2i2i22-1-2-21i−i−2i2i−2i2i2-1-1-1-1-21111−2i2ii−ii−iii−i−i00−i3i30000−3300000000
χ302-2−2i2i22-1-2-21i−i−2i2i−2i2i2-1-1-1-1-21111−2i2ii−ii−iii−i−i00i3−i300003−3000000002-2−2i2i22-1-2-21i−i−2i2i−2i2i2-1-1-1-1-21111−2i2ii−ii−iii−i−i00i3−i300003−3000000002-2−2i2i22-1-2-21i−i−2i2i−2i2i2-1-1-1-1-21111−2i2ii−ii−iii−i−i00i3−i300003−3000000002-2−2i2i22-1-2-21i−i−2i2i−2i2i2-1-1-1-1-21111−2i2ii−ii−iii−i−i00i3−i300003−300000000
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χ2164-4−4i4i-2-2-22222i−2i2i−2i2i−2i111−1+3i32−1−3i32-1-1-11−3i321+3i32−ii−ii−ii−2ζ14+ζ22ζ14−2ζ222ζ14−ζ22−ζ14+2ζ22000000000000000000-444i−4i222-2-2-2−2i2i−2i2i−2i2i-1-1-11−3i321+3i32111−1+3i32−1−3i32i−ii−ii−i2ζ14−ζ22−ζ14+2ζ22−2ζ14+ζ22ζ14−2ζ22000000000000000000-444i−4i222-2-2-2−2i2i−2i2i−2i2i-1-1-11−3i321+3i32111−1+3i32−1−3i32i−ii−ii−i2ζ14−ζ22−ζ14+2ζ22−2ζ14+ζ22ζ14−2ζ220000000000000000004-4−4i4i-2-2-22222i−2i2i−2i2i−2i111−1+3i32−1−3i32-1-1-11−3i321+3i32−ii−ii−ii−2ζ14+ζ22ζ14−2ζ222ζ14−ζ22−ζ14+2ζ22000000000000000000

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