Finite Group Databasebeta

← Group #13157793

Character table — Group #13157793

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155C156C157C158C159C160C161C162C163C164C165C166C167C168C169C170C171C172C173C174C175C176C177C178C179C180C181C182C183C184C185C186C187C188C189
size111122222222224444444444444444444444444444441212121218182424242424242424242436363611112222222222444444444444444444444444444444121212121818242424242424242424243636361111222222222244444444444444444444444444444412121212181824242424242424242424363636
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χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1111-1-1-1-111-1-1-11111111111111111111111111111111111111111111111-1-1-1-1-1111-1-1-1-111-1-1-11111111111111111111111111111111111111111111111-1-1-1-1-1111-1-1-1-111-1-1-1
χ311111111111111111111111111111111111111111111-1-111-1-11-1-1-11111-1-1-1-1-111111111111111111111111111111111111111111111-1-111-1-11-1-1-11111-1-1-1-1-111111111111111111111111111111111111111111111-1-111-1-11-1-1-11111-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1111
χ5111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1111-1-1111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1111-1-1111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1111-1-1
χ6111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11-1-1-1-1-11111-111111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11-1-1-1-1-11111-111111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11-1-1-1-1-11111-111
χ7111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111111-1-1-1-1-111111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111111-1-1-1-1-111111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111111-1-1-1-1-111
χ8111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-11-1-1111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-11-1-1111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-11-1-1
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χ1122222-1222-12-1-12-1-1-1-122-12-1-1-12-1-12222-1-1-1-1-1-1-1-1-1-1-1-10022002000-1-1-1-10000022222-1222-12-1-12-1-1-1-122-12-1-1-12-1-12222-1-1-1-1-1-1-1-1-1-1-1-10022002000-1-1-1-10000022222-1222-12-1-12-1-1-1-122-12-1-1-12-1-12222-1-1-1-1-1-1-1-1-1-1-1-10022002000-1-1-1-100000
χ1222222-1222-12-1-12-1-1-1-122-12-1-1-12-1-12222-1-1-1-1-1-1-1-1-1-1-1-100-2-200-200011110000022222-1222-12-1-12-1-1-1-122-12-1-1-12-1-12222-1-1-1-1-1-1-1-1-1-1-1-100-2-200-200011110000022222-1222-12-1-12-1-1-1-122-12-1-1-12-1-12222-1-1-1-1-1-1-1-1-1-1-1-100-2-200-2000111100000
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χ1422222-1222-12-1-12-1-1-1-1-2-2-12-1-1-12-1-1-2-2-2-211111111111100-2-200200011-1-10000022222-1222-12-1-12-1-1-1-1-2-2-12-1-1-12-1-1-2-2-2-211111111111100-2-200200011-1-10000022222-1222-12-1-12-1-1-1-1-2-2-12-1-1-12-1-1-2-2-2-211111111111100-2-200200011-1-100000
χ152222-1222-12-122-1-1-1-1-1222-1-1-12-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122000002-1-10000-1-10002222-1222-12-122-1-1-1-1-1222-1-1-12-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122000002-1-10000-1-10002222-1222-12-122-1-1-1-1-1222-1-1-12-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122000002-1-10000-1-1000
χ162222-1222-12-122-1-1-1-1-1222-1-1-12-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-200000-2110000110002222-1222-12-122-1-1-1-1-1222-1-1-12-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-200000-2110000110002222-1222-12-122-1-1-1-1-1222-1-1-12-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-200000-211000011000
χ172222-1222-12-122-1-1-1-1-1-2-22-1-1-12-1-1-11111-2-2-2-2111111112200000-2110000-1-10002222-1222-12-122-1-1-1-1-1-2-22-1-1-12-1-1-11111-2-2-2-2111111112200000-2110000-1-10002222-1222-12-122-1-1-1-1-1-2-22-1-1-12-1-1-11111-2-2-2-2111111112200000-2110000-1-1000
χ182222-1222-12-122-1-1-1-1-1-2-22-1-1-12-1-1-11111-2-2-2-211111111-2-2000002-1-10000110002222-1222-12-122-1-1-1-1-1-2-22-1-1-12-1-1-11111-2-2-2-211111111-2-2000002-1-10000110002222-1222-12-122-1-1-1-1-1-2-22-1-1-12-1-1-11111-2-2-2-211111111-2-2000002-1-1000011000
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χ2422-2-22-1-22-2-1-2112-111-1001-211-12-1-10000−i3−i3i3i3−i3−i3−i3−i3i3i3i3i300−2i2i000000i−i−330000022-2-22-1-22-2-1-2112-111-1001-211-12-1-10000−i3−i3i3i3−i3−i3−i3−i3i3i3i3i300−2i2i000000i−i−330000022-2-22-1-22-2-1-2112-111-1001-211-12-1-10000−i3−i3i3i3−i3−i3−i3−i3i3i3i3i300−2i2i000000i−i−3300000
χ2522-2-22-1-22-2-1-2112-111-1001-211-12-1-10000i3i3−i3−i3i3i3i3i3−i3−i3−i3−i3002i−2i000000−ii−330000022-2-22-1-22-2-1-2112-111-1001-211-12-1-10000i3i3−i3−i3i3i3i3i3−i3−i3−i3−i3002i−2i000000−ii−330000022-2-22-1-22-2-1-2112-111-1001-211-12-1-10000i3i3−i3−i3i3i3i3i3−i3−i3−i3−i3002i−2i000000−ii−3300000
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χ132111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11-1-1-1-1-11111-111−1−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+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−i321+i321+i321+i321+i32−1−i321+i321+i321+i321+i321+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+i321−i321−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+i321−i321−i321−i321−i32−1+i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i32−1+i32−1+i32
χ133111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111111-1-1-1-1-111−1−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+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+i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−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+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+i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i32−1+i32−1+i32
χ134111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-11-1-1−1−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−i321+i321+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−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+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+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+i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i321−i321−i32
χ135222222-2-2222222222200-2-2-2-2-2-2-2-200000000000000000000220000000000-200−1−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−i3001+i31+i31+i31+i31+i31+i31+i31+i300000000000000000000−1−i3−1−i300000000001+i300−1+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+i3001−i31−i31−i31−i31−i31−i31−i31−i300000000000000000000−1+i3−1+i300000000001−i300
χ136222222-2-2222222222200-2-2-2-2-2-2-2-200000000000000000000-2-20000000000200−1−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−i3001+i31+i31+i31+i31+i31+i31+i31+i3000000000000000000001+i31+i30000000000−1−i300−1+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+i3001−i31−i31−i31−i31−i31−i31−i31−i3000000000000000000001−i31−i30000000000−1+i300
χ13722222-1222-12-1-12-1-1-1-122-12-1-1-12-1-12222-1-1-1-1-1-1-1-1-1-1-1-10022002000-1-1-1-100000−1−i3−1−i3−1−i3−1−i3−1−i31+i32−1−i3−1−i3−1−i31+i32−1−i31+i321+i32−1−i31+i321+i321+i321+i32−1−i3−1−i31+i32−1−i31+i321+i321+i32−1−i31+i321+i32−1−i3−1−i3−1−i3−1−i31+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i3200−1−i3−1−i300−1−i30001+i321+i321+i321+i3200000−1+i3−1+i3−1+i3−1+i3−1+i31−i32−1+i3−1+i3−1+i31−i32−1+i31−i321−i32−1+i31−i321−i321−i321−i32−1+i3−1+i31−i32−1+i31−i321−i321−i32−1+i31−i321−i32−1+i3−1+i3−1+i3−1+i31−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i3200−1+i3−1+i300−1+i30001−i321−i321−i321−i3200000
χ13822222-1222-12-1-12-1-1-1-122-12-1-1-12-1-12222-1-1-1-1-1-1-1-1-1-1-1-100-2-200-2000111100000−1−i3−1−i3−1−i3−1−i3−1−i31+i32−1−i3−1−i3−1−i31+i32−1−i31+i321+i32−1−i31+i321+i321+i321+i32−1−i3−1−i31+i32−1−i31+i321+i321+i32−1−i31+i321+i32−1−i3−1−i3−1−i3−1−i31+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i32001+i31+i3001+i3000−1−i32−1−i32−1−i32−1−i3200000−1+i3−1+i3−1+i3−1+i3−1+i31−i32−1+i3−1+i3−1+i31−i32−1+i31−i321−i32−1+i31−i321−i321−i321−i32−1+i3−1+i31−i32−1+i31−i321−i321−i32−1+i31−i321−i32−1+i3−1+i3−1+i3−1+i31−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i32001−i31−i3001−i3000−1+i32−1+i32−1+i32−1+i3200000
χ13922222-1222-12-1-12-1-1-1-1-2-2-12-1-1-12-1-1-2-2-2-2111111111111002200-2000-1-11100000−1−i3−1−i3−1−i3−1−i3−1−i31+i32−1−i3−1−i3−1−i31+i32−1−i31+i321+i32−1−i31+i321+i321+i321+i321+i31+i31+i32−1−i31+i321+i321+i32−1−i31+i321+i321+i31+i31+i31+i3−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i3200−1−i3−1−i3001+i30001+i321+i32−1−i32−1−i3200000−1+i3−1+i3−1+i3−1+i3−1+i31−i32−1+i3−1+i3−1+i31−i32−1+i31−i321−i32−1+i31−i321−i321−i321−i321−i31−i31−i32−1+i31−i321−i321−i32−1+i31−i321−i321−i31−i31−i31−i3−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i3200−1+i3−1+i3001−i30001−i321−i32−1+i32−1+i3200000
χ14022222-1222-12-1-12-1-1-1-1-2-2-12-1-1-12-1-1-2-2-2-211111111111100-2-200200011-1-100000−1−i3−1−i3−1−i3−1−i3−1−i31+i32−1−i3−1−i3−1−i31+i32−1−i31+i321+i32−1−i31+i321+i321+i321+i321+i31+i31+i32−1−i31+i321+i321+i32−1−i31+i321+i321+i31+i31+i31+i3−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32001+i31+i300−1−i3000−1−i32−1−i321+i321+i3200000−1+i3−1+i3−1+i3−1+i3−1+i31−i32−1+i3−1+i3−1+i31−i32−1+i31−i321−i32−1+i31−i321−i321−i321−i321−i31−i31−i32−1+i31−i321−i321−i32−1+i31−i321−i321−i31−i31−i31−i3−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32001−i31−i300−1+i3000−1+i32−1+i321−i321−i3200000
χ1412222-1222-12-122-1-1-1-1-1222-1-1-12-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-122000002-1-10000-1-1000−1−i3−1−i3−1−i3−1−i31+i32−1−i3−1−i3−1−i31+i32−1−i31+i32−1−i3−1−i31+i321+i321+i321+i321+i32−1−i3−1−i3−1−i31+i321+i321+i32−1−i31+i321+i321+i321+i321+i321+i321+i32−1−i3−1−i3−1−i3−1−i31+i321+i321+i321+i321+i321+i321+i321+i32−1−i3−1−i300000−1−i31+i321+i3200001+i321+i32000−1+i3−1+i3−1+i3−1+i31−i32−1+i3−1+i3−1+i31−i32−1+i31−i32−1+i3−1+i31−i321−i321−i321−i321−i32−1+i3−1+i3−1+i31−i321−i321−i32−1+i31−i321−i321−i321−i321−i321−i321−i32−1+i3−1+i3−1+i3−1+i31−i321−i321−i321−i321−i321−i321−i321−i32−1+i3−1+i300000−1+i31−i321−i3200001−i321−i32000
χ1422222-1222-12-122-1-1-1-1-1222-1-1-12-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-2-200000-211000011000−1−i3−1−i3−1−i3−1−i31+i32−1−i3−1−i3−1−i31+i32−1−i31+i32−1−i3−1−i31+i321+i321+i321+i321+i32−1−i3−1−i3−1−i31+i321+i321+i32−1−i31+i321+i321+i321+i321+i321+i321+i32−1−i3−1−i3−1−i3−1−i31+i321+i321+i321+i321+i321+i321+i321+i321+i31+i3000001+i3−1−i32−1−i320000−1−i32−1−i32000−1+i3−1+i3−1+i3−1+i31−i32−1+i3−1+i3−1+i31−i32−1+i31−i32−1+i3−1+i31−i321−i321−i321−i321−i32−1+i3−1+i3−1+i31−i321−i321−i32−1+i31−i321−i321−i321−i321−i321−i321−i32−1+i3−1+i3−1+i3−1+i31−i321−i321−i321−i321−i321−i321−i321−i321−i31−i3000001−i3−1+i32−1+i320000−1+i32−1+i32000
χ1432222-1222-12-122-1-1-1-1-1-2-22-1-1-12-1-1-11111-2-2-2-2111111112200000-2110000-1-1000−1−i3−1−i3−1−i3−1−i31+i32−1−i3−1−i3−1−i31+i32−1−i31+i32−1−i3−1−i31+i321+i321+i321+i321+i321+i31+i3−1−i31+i321+i321+i32−1−i31+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i31+i31+i31+i3−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i3−1−i3000001+i3−1−i32−1−i3200001+i321+i32000−1+i3−1+i3−1+i3−1+i31−i32−1+i3−1+i3−1+i31−i32−1+i31−i32−1+i3−1+i31−i321−i321−i321−i321−i321−i31−i3−1+i31−i321−i321−i32−1+i31−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i31−i31−i31−i3−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i3−1+i3000001−i3−1+i32−1+i3200001−i321−i32000
χ1442222-1222-12-122-1-1-1-1-1-2-22-1-1-12-1-1-11111-2-2-2-211111111-2-2000002-1-1000011000−1−i3−1−i3−1−i3−1−i31+i32−1−i3−1−i3−1−i31+i32−1−i31+i32−1−i3−1−i31+i321+i321+i321+i321+i321+i31+i3−1−i31+i321+i321+i32−1−i31+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i31+i31+i31+i3−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i31+i300000−1−i31+i321+i320000−1−i32−1−i32000−1+i3−1+i3−1+i3−1+i31−i32−1+i3−1+i3−1+i31−i32−1+i31−i32−1+i3−1+i31−i321−i321−i321−i321−i321−i31−i3−1+i31−i321−i321−i32−1+i31−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i31−i31−i31−i3−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i31−i300000−1+i31−i321−i320000−1+i32−1+i32000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.