Finite Group Databasebeta

← Group #13158458

Character table — Group #13158458

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155C156C157C158C159C160C161C162C163C164C165C166C167C168C169C170C171C172C173C174C175C176C177C178C179C180
size111122222222224444444466666666888888888881212121212121212181818182424242424247211112222222222444444446666666688888888888121212121212121218181818242424242424721111222222222244444444666666668888888888812121212121212121818181824242424242472
order1222334466666636661212121222448888266666666121266121224242424888824661212436663312126666663666121212126612122424242466666666612126612122424242424242424612661212123666331212666666366612121212661212242424246666666661212661212242424242424242461266121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1111111111111111111111111111111-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1111111111111111111111111111111-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-11-1-111-111111111111111111111111111-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-11-1-111-111111111111111111111111111-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-11-1-111-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11-111-1-1111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11-111-1-1111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11-111-1-11
χ51111111111111111111111-1-1-1-1111111111111111-1-1-1-11111-1-1-1-11-111-1-1-11111111111111111111111-1-1-1-1111111111111111-1-1-1-11111-1-1-1-11-111-1-1-11111111111111111111111-1-1-1-1111111111111111-1-1-1-11111-1-1-1-11-111-1-1-1
χ61111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-11-1-11111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-11-1-11111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-11-1-1111
χ71111111111111111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111111111111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111111111111111111-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1
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χ152222-1222-1222-1-1-1-1-1-12-1-12222200002-1-122-1-1-1-1-1-1-1-1-1-1000000000200-1-102222-1222-1222-1-1-1-1-1-12-1-12222200002-1-122-1-1-1-1-1-1-1-1-1-1000000000200-1-102222-1222-1222-1-1-1-1-1-12-1-12222200002-1-122-1-1-1-1-1-1-1-1-1-1000000000200-1-10
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χ222222-12-2-2-1222-1-1-1-1-1-1-211-2-2-22200000i3−i300i3i3−i3−i31111-1-1000000000000−i3i302222-12-2-2-1222-1-1-1-1-1-1-211-2-2-22200000i3−i300i3i3−i3−i31111-1-1000000000000−i3i302222-12-2-2-1222-1-1-1-1-1-1-211-2-2-22200000i3−i300i3i3−i3−i31111-1-1000000000000−i3i30
χ2322-2-2220022-2-2-2-222-2-20000002i−2i22−2−200000000000002i−2i22−2−2−i2−i2i2i2000000022-2-2220022-2-2-2-222-2-20000002i−2i22−2−200000000000002i−2i22−2−2−i2−i2i2i2000000022-2-2220022-2-2-2-222-2-20000002i−2i22−2−200000000000002i−2i22−2−2−i2−i2i2i20000000
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χ681111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1−1+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+i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−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+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−i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+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−i321+i32
χ69222222-2-22222222222-2-2-2-222-2-20000000000000-2-222-2-2000000000000000−1+i3−1+i3−1+i3−1+i3−1+i3−1+i31−i31−i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i31−i31−i31−i31−i3−1+i3−1+i31−i31−i300000000000001−i31−i3−1+i3−1+i31−i31−i3000000000000000−1−i3−1−i3−1−i3−1−i3−1−i3−1−i31+i31+i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i31+i31+i31+i31+i3−1−i3−1−i31+i31+i300000000000001+i31+i3−1−i3−1−i31+i31+i3000000000000000
χ70222222-2-22222222222-2-2-2-2-2-2220000000000000-2-2-2-222000000000000000−1+i3−1+i3−1+i3−1+i3−1+i3−1+i31−i31−i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i31−i31−i31−i31−i31−i31−i3−1+i3−1+i300000000000001−i31−i31−i31−i3−1+i3−1+i3000000000000000−1−i3−1−i3−1−i3−1−i3−1−i3−1−i31+i31+i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i31+i31+i31+i31+i31+i31+i3−1−i3−1−i300000000000001+i31+i31+i31+i3−1−i3−1−i3000000000000000
χ7122222-1222-1-1-122-1-1-1-1-122-100002222222-1-1-1-1-1-1-1-10000-1-1-1-1000020-1-1000−1+i3−1+i3−1+i3−1+i3−1+i31−i32−1+i3−1+i3−1+i31−i321−i321−i32−1+i3−1+i31−i321−i321−i321−i321−i32−1+i3−1+i31−i320000−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i31−i321−i321−i321−i321−i321−i321−i321−i3200001−i321−i321−i321−i320000−1+i301−i321−i32000−1−i3−1−i3−1−i3−1−i3−1−i31+i32−1−i3−1−i3−1−i31+i321+i321+i32−1−i3−1−i31+i321+i321+i321+i321+i32−1−i3−1−i31+i320000−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i31+i321+i321+i321+i321+i321+i321+i321+i3200001+i321+i321+i321+i320000−1−i301+i321+i32000
χ7222222-1222-1-1-122-1-1-1-1-122-100002222-2-2-2111111-1-10000-1-1-1-10000-2011000−1+i3−1+i3−1+i3−1+i3−1+i31−i32−1+i3−1+i3−1+i31−i321−i321−i32−1+i3−1+i31−i321−i321−i321−i321−i32−1+i3−1+i31−i320000−1+i3−1+i3−1+i3−1+i31−i31−i31−i3−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i3200001−i321−i321−i321−i3200001−i30−1+i32−1+i32000−1−i3−1−i3−1−i3−1−i3−1−i31+i32−1−i3−1−i3−1−i31+i321+i321+i32−1−i3−1−i31+i321+i321+i321+i321+i32−1−i3−1−i31+i320000−1−i3−1−i3−1−i3−1−i31+i31+i31+i3−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i3200001+i321+i321+i321+i3200001+i30−1−i32−1−i32000
χ7322222-1222-1-1-122-1-1-1-1-122-10000-2-2-2-2222-1-1-1-1-1-1-1-1000011110000-2011000−1+i3−1+i3−1+i3−1+i3−1+i31−i32−1+i3−1+i3−1+i31−i321−i321−i32−1+i3−1+i31−i321−i321−i321−i321−i32−1+i3−1+i31−i3200001−i31−i31−i31−i3−1+i3−1+i3−1+i31−i321−i321−i321−i321−i321−i321−i321−i320000−1+i32−1+i32−1+i32−1+i3200001−i30−1+i32−1+i32000−1−i3−1−i3−1−i3−1−i3−1−i31+i32−1−i3−1−i3−1−i31+i321+i321+i32−1−i3−1−i31+i321+i321+i321+i321+i32−1−i3−1−i31+i3200001+i31+i31+i31+i3−1−i3−1−i3−1−i31+i321+i321+i321+i321+i321+i321+i321+i320000−1−i32−1−i32−1−i32−1−i3200001+i30−1−i32−1−i32000
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χ13122222-1222-1-1-122-1-1-1-1-122-100002222222-1-1-1-1-1-1-1-10000-1-1-1-1000020-1-1000−1−i3−1−i3−1−i3−1−i3−1−i31+i32−1−i3−1−i3−1−i31+i321+i321+i32−1−i3−1−i31+i321+i321+i321+i321+i32−1−i3−1−i31+i320000−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i31+i321+i321+i321+i321+i321+i321+i321+i3200001+i321+i321+i321+i320000−1−i301+i321+i32000−1+i3−1+i3−1+i3−1+i3−1+i31−i32−1+i3−1+i3−1+i31−i321−i321−i32−1+i3−1+i31−i321−i321−i321−i321−i32−1+i3−1+i31−i320000−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i31−i321−i321−i321−i321−i321−i321−i321−i3200001−i321−i321−i321−i320000−1+i301−i321−i32000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.