Finite Group Databasebeta

← Group #13157486

Character table — Group #13157486

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155C156C157C158C159C160C161C162C163C164C165C166C167C168C169C170C171C172C173C174C175C176C177C178C179C180
size111122222222224444444466666666888888888881212121212121212181818182424242424247211112222222222444444446666666688888888888121212121212121218181818242424242424721111222222222244444444666666668888888888812121212121212121818181824242424242472
order122233446666663666121212122244888841212121212121212121266121224242424888824661212436663312126666663666121212126612122424242412121212121212121212126612122424242424242424612661212123666331212666666366612121212661212242424241212121212121212121212661212242424242424242461266121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1111111111111111111111111111111-1-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1111111111111111111111111111111-1-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1111111111111111-1-1-1-1-1-1-1-11-111-1-1-111111111111111111111111111-1-1-1-1111111111111111-1-1-1-1-1-1-1-11-111-1-1-111111111111111111111111111-1-1-1-1111111111111111-1-1-1-1-1-1-1-11-111-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-11-1-111111111111111111111111111111-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-11-1-111111111111111111111111111111-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-11-1-1111
χ51111111111111111111111-1-1-1-1111111111111111-1-1-1-11111-1-1-1-1-11-1-111-11111111111111111111111-1-1-1-1111111111111111-1-1-1-11111-1-1-1-1-11-1-111-11111111111111111111111-1-1-1-1111111111111111-1-1-1-11111-1-1-1-1-11-1-111-1
χ61111111111111111111111-1-1-1-11111-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11-111-1-111111111111111111111111-1-1-1-11111-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11-111-1-111111111111111111111111-1-1-1-11111-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11-111-1-11
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
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-11111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1
χ9222222-2-22222222222-2-2-2-222-2-2000000000-2-2000022-2-2000000000000000222222-2-22222222222-2-2-2-222-2-2000000000-2-2000022-2-2000000000000000222222-2-22222222222-2-2-2-222-2-2000000000-2-2000022-2-2000000000000000
χ10222222-2-22222222222-2-2-2-2-2-222000000000-2-20000-2-222000000000000000222222-2-22222222222-2-2-2-2-2-222000000000-2-20000-2-222000000000000000222222-2-22222222222-2-2-2-2-2-222000000000-2-20000-2-222000000000000000
χ1122222-1222-12-1-12-1-1-1-1-1-12222220000222-1-1-1-1-1-1-1-1-1-1-1-10000000020-1-100022222-1222-12-1-12-1-1-1-1-1-12222220000222-1-1-1-1-1-1-1-1-1-1-1-10000000020-1-100022222-1222-12-1-12-1-1-1-1-1-12222220000222-1-1-1-1-1-1-1-1-1-1-1-10000000020-1-1000
χ1222222-1222-12-1-12-1-1-1-1-1-12222220000-2-2-211-1-11111-1-1-1-100000000-201100022222-1222-12-1-12-1-1-1-1-1-12222220000-2-2-211-1-11111-1-1-1-100000000-201100022222-1222-12-1-12-1-1-1-1-1-12222220000-2-2-211-1-11111-1-1-1-100000000-2011000
χ1322222-1222-12-1-12-1-1-1-1-1-122-2-2-2-20000222-1-1-1-1-1-1-1-1111100000000-201100022222-1222-12-1-12-1-1-1-1-1-122-2-2-2-20000222-1-1-1-1-1-1-1-1111100000000-201100022222-1222-12-1-12-1-1-1-1-1-122-2-2-2-20000222-1-1-1-1-1-1-1-1111100000000-2011000
χ1422222-1222-12-1-12-1-1-1-1-1-122-2-2-2-20000-2-2-211-1-1111111110000000020-1-100022222-1222-12-1-12-1-1-1-1-1-122-2-2-2-20000-2-2-211-1-1111111110000000020-1-100022222-1222-12-1-12-1-1-1-1-1-122-2-2-2-20000-2-2-211-1-1111111110000000020-1-1000
χ1522222-1-2-22-12-1-12-1-1-1-111-2-222-2-20000000−i3i311−i3−i3i3i3-1-1110000000000−i3i300022222-1-2-22-12-1-12-1-1-1-111-2-222-2-20000000−i3i311−i3−i3i3i3-1-1110000000000−i3i300022222-1-2-22-12-1-12-1-1-1-111-2-222-2-20000000−i3i311−i3−i3i3i3-1-1110000000000−i3i3000
χ1622222-1-2-22-12-1-12-1-1-1-111-2-222-2-20000000i3−i311i3i3−i3−i3-1-1110000000000i3−i300022222-1-2-22-12-1-12-1-1-1-111-2-222-2-20000000i3−i311i3i3−i3−i3-1-1110000000000i3−i300022222-1-2-22-12-1-12-1-1-1-111-2-222-2-20000000i3−i311i3i3−i3−i3-1-1110000000000i3−i3000
χ1722222-1-2-22-12-1-12-1-1-1-111-2-2-2-2220000000−i3i311−i3−i3i3i311-1-10000000000i3−i300022222-1-2-22-12-1-12-1-1-1-111-2-2-2-2220000000−i3i311−i3−i3i3i311-1-10000000000i3−i300022222-1-2-22-12-1-12-1-1-1-111-2-2-2-2220000000−i3i311−i3−i3i3i311-1-10000000000i3−i3000
χ1822222-1-2-22-12-1-12-1-1-1-111-2-2-2-2220000000i3−i311i3i3−i3−i311-1-10000000000−i3i300022222-1-2-22-12-1-12-1-1-1-111-2-2-2-2220000000i3−i311i3i3−i3−i311-1-10000000000−i3i300022222-1-2-22-12-1-12-1-1-1-111-2-2-2-2220000000i3−i311i3i3−i3−i311-1-10000000000−i3i3000
χ192222-1222-12-122-1-1-1-1-122-1-1000022222-1-122-1-1-1-1-1-10000-1-1-1-100000200-1-102222-1222-12-122-1-1-1-1-122-1-1000022222-1-122-1-1-1-1-1-10000-1-1-1-100000200-1-102222-1222-12-122-1-1-1-1-122-1-1000022222-1-122-1-1-1-1-1-10000-1-1-1-100000200-1-10
χ202222-1222-12-122-1-1-1-1-122-1-100002222-211-2-2-1-111110000-1-1-1-100000-2001102222-1222-12-122-1-1-1-1-122-1-100002222-211-2-2-1-111110000-1-1-1-100000-2001102222-1222-12-122-1-1-1-1-122-1-100002222-211-2-2-1-111110000-1-1-1-100000-200110
χ212222-1222-12-122-1-1-1-1-122-1-10000-2-2-2-22-1-122-1-1-1-1-1-10000111100000-2001102222-1222-12-122-1-1-1-1-122-1-10000-2-2-2-22-1-122-1-1-1-1-1-10000111100000-2001102222-1222-12-122-1-1-1-1-122-1-10000-2-2-2-22-1-122-1-1-1-1-1-10000111100000-200110
χ222222-1222-12-122-1-1-1-1-122-1-10000-2-2-2-2-211-2-2-1-111110000111100000200-1-102222-1222-12-122-1-1-1-1-122-1-10000-2-2-2-2-211-2-2-1-111110000111100000200-1-102222-1222-12-122-1-1-1-1-122-1-10000-2-2-2-2-211-2-2-1-111110000111100000200-1-10
χ2322-2-22200-2-222-2-22-2-2200002-200−i2−i2i2i2000000000002-200−i2−i2i2i2−i2−i2i2i2000000022-2-22200-2-222-2-22-2-2200002-200−i2−i2i2i2000000000002-200−i2−i2i2i2−i2−i2i2i2000000022-2-22200-2-222-2-22-2-2200002-200−i2−i2i2i2000000000002-200−i2−i2i2i2−i2−i2i2i20000000
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χ2522-2-22200-2-222-2-22-2-220000-2200−i2−i2i2i200000000000-2200−i2−i2i2i2i2i2−i2−i2000000022-2-22200-2-222-2-22-2-220000-2200−i2−i2i2i200000000000-2200−i2−i2i2i2i2i2−i2−i2000000022-2-22200-2-222-2-22-2-220000-2200−i2−i2i2i200000000000-2200−i2−i2i2i2i2i2−i2−i20000000
χ2622-2-22200-2-222-2-22-2-220000-2200i2i2−i2−i200000000000-2200i2i2−i2−i2−i2−i2i2i2000000022-2-22200-2-222-2-22-2-220000-2200i2i2−i2−i200000000000-2200i2i2−i2−i2−i2−i2i2i2000000022-2-22200-2-222-2-22-2-220000-2200i2i2−i2−i200000000000-2200i2i2−i2−i2−i2−i2i2i20000000
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χ282-22-2222-2-2-2-2-2222-22-22-22-20000−2i2i−2i2i000002-200000000−2i2i−2i2i000000000002-22-2222-2-2-2-2-2222-22-22-22-20000−2i2i−2i2i000002-200000000−2i2i−2i2i000000000002-22-2222-2-2-2-2-2222-22-22-22-20000−2i2i−2i2i000002-200000000−2i2i−2i2i00000000000
χ292-22-222-22-2-2-2-2222-22-2-22-220000000000000-220000000000002-22-200000002-22-222-22-2-2-2-2222-22-2-22-220000000000000-220000000000002-22-200000002-22-222-22-2-2-2-2222-22-2-22-220000000000000-220000000000002-22-20000000
χ302-22-222-22-2-2-2-2222-22-2-22-220000000000000-22000000000000-22-2200000002-22-222-22-2-2-2-2222-22-2-22-220000000000000-22000000000000-22-2200000002-22-222-22-2-2-2-2222-22-2-22-220000000000000-22000000000000-22-220000000
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χ322-22-2-122-21-21-22-1-11-112-2-1100002i−2i2i−2i0−3300-11−33−330000−ii−ii00000000i3−i302-22-2-122-21-21-22-1-11-112-2-1100002i−2i2i−2i0−3300-11−33−330000−ii−ii00000000i3−i302-22-2-122-21-21-22-1-11-112-2-1100002i−2i2i−2i0−3300-11−33−330000−ii−ii00000000i3−i30
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χ7122222-1222-12-1-12-1-1-1-1-1-12222220000222-1-1-1-1-1-1-1-1-1-1-1-10000000020-1-1000−1+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−i321−i32−1+i3−1+i3−1+i3−1+i3−1+i3−1+i30000−1+i3−1+i3−1+i31−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i3200000000−1+i301−i321−i32000−1−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+i321+i32−1−i3−1−i3−1−i3−1−i3−1−i3−1−i30000−1−i3−1−i3−1−i31+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i3200000000−1−i301+i321+i32000
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χ13822222-1-2-22-12-1-12-1-1-1-111-2-2-2-2220000000i3−i311i3i3−i3−i311-1-10000000000−i3i3000−1−i3−1−i3−1−i3−1−i3−1−i31+i321+i31+i3−1−i31+i32−1−i31+i321+i32−1−i31+i321+i321+i321+i32−1−i32−1−i321+i31+i31+i31+i3−1−i3−1−i300000003−i32−3+i32−1−i32−1−i323−i323−i32−3+i32−3+i32−1−i32−1−i321+i321+i320000000000−3+i323−i32000−1+i3−1+i3−1+i3−1+i3−1+i31−i321−i31−i3−1+i31−i32−1+i31−i321−i32−1+i31−i321−i321−i321−i32−1+i32−1+i321−i31−i31−i31−i3−1+i3−1+i30000000−3−i323+i32−1+i32−1+i32−3−i32−3−i323+i323+i32−1+i32−1+i321−i321−i3200000000003+i32−3−i32000
χ1392222-1222-12-122-1-1-1-1-122-1-1000022222-1-122-1-1-1-1-1-10000-1-1-1-100000200-1-10−1−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−i31+i321+i320000−1−i3−1−i3−1−i3−1−i3−1−i31+i321+i32−1−i3−1−i31+i321+i321+i321+i321+i321+i3200001+i321+i321+i321+i3200000−1−i3001+i321+i320−1+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+i31−i321−i320000−1+i3−1+i3−1+i3−1+i3−1+i31−i321−i32−1+i3−1+i31−i321−i321−i321−i321−i321−i3200001−i321−i321−i321−i3200000−1+i3001−i321−i320
χ1402222-1222-12-122-1-1-1-1-122-1-100002222-211-2-2-1-111110000-1-1-1-100000-200110−1−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−i31+i321+i320000−1−i3−1−i3−1−i3−1−i31+i3−1−i32−1−i321+i31+i31+i321+i32−1−i32−1−i32−1−i32−1−i3200001+i321+i321+i321+i32000001+i300−1−i32−1−i320−1+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+i31−i321−i320000−1+i3−1+i3−1+i3−1+i31−i3−1+i32−1+i321−i31−i31−i321−i32−1+i32−1+i32−1+i32−1+i3200001−i321−i321−i321−i32000001−i300−1+i32−1+i320
χ1412222-1222-12-122-1-1-1-1-122-1-10000-2-2-2-22-1-122-1-1-1-1-1-10000111100000-200110−1−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−i31+i321+i3200001+i31+i31+i31+i3−1−i31+i321+i32−1−i3−1−i31+i321+i321+i321+i321+i321+i320000−1−i32−1−i32−1−i32−1−i32000001+i300−1−i32−1−i320−1+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+i31−i321−i3200001−i31−i31−i31−i3−1+i31−i321−i32−1+i3−1+i31−i321−i321−i321−i321−i321−i320000−1+i32−1+i32−1+i32−1+i32000001−i300−1+i32−1+i320
χ1422222-1222-12-122-1-1-1-1-122-1-10000-2-2-2-2-211-2-2-1-111110000111100000200-1-10−1−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−i31+i321+i3200001+i31+i31+i31+i31+i3−1−i32−1−i321+i31+i31+i321+i32−1−i32−1−i32−1−i32−1−i320000−1−i32−1−i32−1−i32−1−i3200000−1−i3001+i321+i320−1+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+i31−i321−i3200001−i31−i31−i31−i31−i3−1+i32−1+i321−i31−i31−i321−i32−1+i32−1+i32−1+i32−1+i320000−1+i32−1+i32−1+i32−1+i3200000−1+i3001−i321−i320
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χ14422-2-22200-2-222-2-22-2-2200002-200i2i2−i2−i2000000000002-200i2i2−i2−i2i2i2−i2−i20000000−1−i3−1−i31+i31+i3−1−i3−1−i3001+i31+i3−1−i3−1−i31+i31+i3−1−i31+i31+i3−1−i30000−1−i31+i300−ζ7−ζ13−ζ7−ζ13ζ7+ζ13ζ7+ζ1300000000000−1−i31+i300−ζ7−ζ13−ζ7−ζ13ζ7+ζ13ζ7+ζ13−ζ7−ζ13−ζ7−ζ13ζ7+ζ13ζ7+ζ130000000−1+i3−1+i31−i31−i3−1+i3−1+i3001−i31−i3−1+i3−1+i31−i31−i3−1+i31−i31−i3−1+i30000−1+i31−i300−ζ5−ζ23−ζ5−ζ23ζ5+ζ23ζ5+ζ2300000000000−1+i31−i300−ζ5−ζ23−ζ5−ζ23ζ5+ζ23ζ5+ζ23−ζ5−ζ23−ζ5−ζ23ζ5+ζ23ζ5+ζ230000000
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χ14622-2-22200-2-222-2-22-2-220000-2200i2i2−i2−i200000000000-2200i2i2−i2−i2−i2−i2i2i20000000−1−i3−1−i31+i31+i3−1−i3−1−i3001+i31+i3−1−i3−1−i31+i31+i3−1−i31+i31+i3−1−i300001+i3−1−i300−ζ7−ζ13−ζ7−ζ13ζ7+ζ13ζ7+ζ13000000000001+i3−1−i300−ζ7−ζ13−ζ7−ζ13ζ7+ζ13ζ7+ζ13ζ7+ζ13ζ7+ζ13−ζ7−ζ13−ζ7−ζ130000000−1+i3−1+i31−i31−i3−1+i3−1+i3001−i31−i3−1+i3−1+i31−i31−i3−1+i31−i31−i3−1+i300001−i3−1+i300−ζ5−ζ23−ζ5−ζ23ζ5+ζ23ζ5+ζ23000000000001−i3−1+i300−ζ5−ζ23−ζ5−ζ23ζ5+ζ23ζ5+ζ23ζ5+ζ23ζ5+ζ23−ζ5−ζ23−ζ5−ζ230000000
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χ1492-22-222-22-2-2-2-2222-22-2-22-220000000000000-220000000000002-22-20000000−1−i31+i3−1−i31+i3−1−i3−1−i31+i3−1−i31+i31+i31+i31+i3−1−i3−1−i3−1−i31+i3−1−i31+i31+i3−1−i31+i3−1−i300000000000001+i3−1−i3000000000000−1−i31+i3−1−i31+i30000000−1+i31−i3−1+i31−i3−1+i3−1+i31−i3−1+i31−i31−i31−i31−i3−1+i3−1+i3−1+i31−i3−1+i31−i31−i3−1+i31−i3−1+i300000000000001−i3−1+i3000000000000−1+i31−i3−1+i31−i30000000
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χ1542-22-2-122-21-21-22-1-11-112-2-110000−2i2i−2i2i0−3300-11−33−330000i−ii−i00000000−i3i30−1−i31+i3−1−i31+i31+i32−1−i3−1−i31+i3−1−i321+i3−1−i321+i3−1−i31+i321+i32−1−i321+i32−1−i32−1−i31+i31+i32−1−i320000−2ζ222ζ22−2ζ222ζ220−2ζ14−ζ222ζ14+ζ22001+i32−1−i32−2ζ14−ζ222ζ14+ζ22−2ζ14−ζ222ζ14+ζ220000ζ22−ζ22ζ22−ζ2200000000−3+i323−i320−1+i31−i3−1+i31−i31−i32−1+i3−1+i31−i3−1+i321−i3−1+i321−i3−1+i31−i321−i32−1+i321−i32−1+i32−1+i31−i31−i32−1+i320000−2ζ142ζ14−2ζ142ζ140ζ14+2ζ22−ζ14−2ζ22001−i32−1+i32ζ14+2ζ22−ζ14−2ζ22ζ14+2ζ22−ζ14−2ζ220000ζ14−ζ14ζ14−ζ14000000003+i32−3−i320
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χ1774-4-44-2400-242-4-42-2-2220000000022−22−2222000000000000000−222−200000000000−2−2i32+2i32+2i3−2−2i31+i3−2−2i3001+i3−2−2i3−1−i32+2i32+2i3−1−i31+i31+i3−1−i3−1−i300000000−2ζ7+2ζ132ζ7−2ζ132ζ7−2ζ13−2ζ7+2ζ13000000000000000ζ7−ζ13−ζ7+ζ13−ζ7+ζ13ζ7−ζ1300000000000−2+2i32−2i32−2i3−2+2i31−i3−2+2i3001−i3−2+2i3−1+i32−2i32−2i3−1+i31−i31−i3−1+i3−1+i3000000002ζ5−2ζ23−2ζ5+2ζ23−2ζ5+2ζ232ζ5−2ζ23000000000000000−ζ5+ζ23ζ5−ζ23ζ5−ζ23−ζ5+ζ2300000000000
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χ1808-8-88-4-400-4-4444422-2-2000000000000000000000000000000000000000000−4−4i34+4i34+4i3−4−4i32+2i32+2i3002+2i32+2i3−2−2i3−2−2i3−2−2i3−2−2i3−1−i3−1−i31+i31+i3000000000000000000000000000000000000000000−4+4i34−4i34−4i3−4+4i32−2i32−2i3002−2i32−2i3−2+2i3−2+2i3−2+2i3−2+2i3−1+i3−1+i31−i31−i3000000000000000000000000000000000000000000

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