Finite Group Databasebeta

← Group #13173205

Character table — Group #13173205

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155C156C157C158C159C160C161C162C163C164C165C166C167C168C169C170C171C172C173C174C175C176C177C178C179C180C181C182C183C184C185C186C187C188C189C190C191C192C193C194C195C196C197C198C199C200C201C202C203C204C205C206C207C208C209C210C211C212C213C214C215C216
size112444444449918181818181124444444499181818181811244444444991818181818112444444449918181818181124444444499181818181811244444444991818181818112444444449918181818181124444444499181818181811244444444991818181818112444444449918181818181124444444499181818181811244444444991818181818
order1243366121212122244444444121212121212121244444442246666121212122244444444121212121212121244444443612336612121212661212121212121212121212121212121212121212121212661266661212121266121212121212121212121212121212121212121212121236123366121212126612121212121212121212121212121212121212121212126612666612121212661212121212121212121212121212121212121212121212
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χ211111111111111-1-1-1-111111111111111-1-1-1-111111111111111-1-1-1-111111111111111-1-1-1-111111111111111-1-1-1-111111111111111-1-1-1-111111111111111-1-1-1-111111111111111-1-1-1-111111111111111-1-1-1-111111111111111-1-1-1-111111111111111-1-1-1-111111111111111-1-1-1-1
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χ102-2022-2-20000-22000002-2022-2-20000-22000002-2022-2-20000-22000002-2022-2-20000-22000002-2022-2-20000-22000002-2022-2-20000-22000002-2022-2-20000-22000002-2022-2-20000-22000002-2022-2-20000-22000002-2022-2-20000-22000002-2022-2-20000-22000002-2022-2-20000-2200000
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χ2011111111111111-1-1-1-1iiiiiiiiiiiiii−i−i−i−i-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiii11111111111111-1-1-1-1iiiiiiiiiiiiii−i−i−i−i-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiii11111111111111-1-1-1-1iiiiiiiiiiiiii−i−i−i−i-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiii
χ2111111111111-1-1-1ii−i−iiiiiiiiiiii−i−i−i-1-111-1-1-1-1-1-1-1-1-1-1-1111−i−iii−i−i−i−i−i−i−i−i−i−i−iiii11-1-111111111111-1-1-1ii−i−iiiiiiiiiiii−i−i−i-1-111-1-1-1-1-1-1-1-1-1-1-1111−i−iii−i−i−i−i−i−i−i−i−i−i−iiii11-1-111111111111-1-1-1ii−i−iiiiiiiiiiii−i−i−i-1-111-1-1-1-1-1-1-1-1-1-1-1111−i−iii−i−i−i−i−i−i−i−i−i−i−iiii11-1-1
χ2211111111111-1-1-1−i−iiiiiiiiiiiiii−i−i−i11-1-1-1-1-1-1-1-1-1-1-1-1-1111ii−i−i−i−i−i−i−i−i−i−i−i−i−iiii-1-11111111111111-1-1-1−i−iiiiiiiiiiiiii−i−i−i11-1-1-1-1-1-1-1-1-1-1-1-1-1111ii−i−i−i−i−i−i−i−i−i−i−i−i−iiii-1-11111111111111-1-1-1−i−iiiiiiiiiiiiii−i−i−i11-1-1-1-1-1-1-1-1-1-1-1-1-1111ii−i−i−i−i−i−i−i−i−i−i−i−i−iiii-1-111
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χ20511-11111-1-1-1-1-1-11i−i−ii−i−ii−i−i−i−iiiiiii−i1-1-11-1-11-1-1-1-1111111-1−iii−iii−iiiii−i−i−i−i−i−ii-111-1−1−i32−1−i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i32ζ11−ζ11−ζ11ζ11−ζ11−ζ11ζ11−ζ11−ζ11−ζ11−ζ11ζ11ζ11ζ11ζ11ζ11ζ11−ζ11−1−i321+i321+i32−1−i321+i321+i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i32−ζ11ζ11ζ11−ζ11ζ11ζ11−ζ11ζ11ζ11ζ11ζ11−ζ11−ζ11−ζ11−ζ11−ζ11−ζ11ζ111+i32−1−i32−1−i321+i32−1+i32−1+i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1+i32ζ7−ζ7−ζ7ζ7−ζ7−ζ7ζ7−ζ7−ζ7−ζ7−ζ7ζ7ζ7ζ7ζ7ζ7ζ7−ζ7−1+i321−i321−i32−1+i321−i321−i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i32−ζ7ζ7ζ7−ζ7ζ7ζ7−ζ7ζ7ζ7ζ7ζ7−ζ7−ζ7−ζ7−ζ7−ζ7−ζ7ζ71−i32−1+i32−1+i321−i32
χ20611-11111-1-1-1-1-1-11−iii−i−i−ii−i−i−i−iiiiiii−i-111-1-1-11-1-1-1-1111111-1i−i−iiii−iiiii−i−i−i−i−i−ii1-1-11−1−i32−1−i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i32−ζ11ζ11ζ11−ζ11−ζ11−ζ11ζ11−ζ11−ζ11−ζ11−ζ11ζ11ζ11ζ11ζ11ζ11ζ11−ζ111+i32−1−i32−1−i321+i321+i321+i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i32ζ11−ζ11−ζ11ζ11ζ11ζ11−ζ11ζ11ζ11ζ11ζ11−ζ11−ζ11−ζ11−ζ11−ζ11−ζ11ζ11−1−i321+i321+i32−1−i32−1+i32−1+i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1+i32−ζ7ζ7ζ7−ζ7−ζ7−ζ7ζ7−ζ7−ζ7−ζ7−ζ7ζ7ζ7ζ7ζ7ζ7ζ7−ζ71−i32−1+i32−1+i321−i321−i321−i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i32ζ7−ζ7−ζ7ζ7ζ7ζ7−ζ7ζ7ζ7ζ7ζ7−ζ7−ζ7−ζ7−ζ7−ζ7−ζ7ζ7−1+i321−i321−i32−1+i32
χ2072-2022-2-200002-200000−2i2i0−2i−2i2i2i0000−2i2i00000-220-2-2220000-22000002i−2i02i2i−2i−2i00002i−2i00000−1−i31+i30−1−i3−1−i31+i31+i30000−1−i31+i300000−2ζ112ζ110−2ζ11−2ζ112ζ112ζ110000−2ζ112ζ11000001+i3−1−i301+i31+i3−1−i3−1−i300001+i3−1−i3000002ζ11−2ζ1102ζ112ζ11−2ζ11−2ζ1100002ζ11−2ζ1100000−1+i31−i30−1+i3−1+i31−i31−i30000−1+i31−i300000−2ζ72ζ70−2ζ7−2ζ72ζ72ζ70000−2ζ72ζ7000001−i3−1+i301−i31−i3−1+i3−1+i300001−i3−1+i3000002ζ7−2ζ702ζ72ζ7−2ζ7−2ζ700002ζ7−2ζ700000
χ2082-2022-2-20000-2200000−2i2i0−2i−2i2i2i00002i−2i00000-220-2-22200002-2000002i−2i02i2i−2i−2i0000−2i2i00000−1−i31+i30−1−i3−1−i31+i31+i300001+i3−1−i300000−2ζ112ζ110−2ζ11−2ζ112ζ112ζ1100002ζ11−2ζ11000001+i3−1−i301+i31+i3−1−i3−1−i30000−1−i31+i3000002ζ11−2ζ1102ζ112ζ11−2ζ11−2ζ110000−2ζ112ζ1100000−1+i31−i30−1+i3−1+i31−i31−i300001−i3−1+i300000−2ζ72ζ70−2ζ7−2ζ72ζ72ζ700002ζ7−2ζ7000001−i3−1+i301−i31−i3−1+i3−1+i30000−1+i31−i3000002ζ7−2ζ702ζ72ζ7−2ζ7−2ζ70000−2ζ72ζ700000
χ2094441-21-211-2-20000000−4i−4i−4i−i2i−i2i−i−i2i2i0000000-4-4-4-12-12-1-12200000004i4i4ii−2ii−2iii−2i−2i0000000−2−2i3−2−2i3−2−2i3−1−i321+i3−1−i321+i3−1−i32−1−i321+i31+i30000000−4ζ11−4ζ11−4ζ11−ζ112ζ11−ζ112ζ11−ζ11−ζ112ζ112ζ1100000002+2i32+2i32+2i31+i32−1−i31+i32−1−i31+i321+i32−1−i3−1−i300000004ζ114ζ114ζ11ζ11−2ζ11ζ11−2ζ11ζ11ζ11−2ζ11−2ζ110000000−2+2i3−2+2i3−2+2i3−1+i321−i3−1+i321−i3−1+i32−1+i321−i31−i30000000−4ζ7−4ζ7−4ζ7−ζ72ζ7−ζ72ζ7−ζ7−ζ72ζ72ζ700000002−2i32−2i32−2i31−i32−1+i31−i32−1+i31−i321−i32−1+i3−1+i300000004ζ74ζ74ζ7ζ7−2ζ7ζ7−2ζ7ζ7ζ7−2ζ7−2ζ70000000
χ210444-21-21-2-2110000000−4i−4i−4i2i−i2i−i2i2i−i−i0000000-4-4-42-12-122-1-100000004i4i4i−2ii−2ii−2i−2iii0000000−2−2i3−2−2i3−2−2i31+i3−1−i321+i3−1−i321+i31+i3−1−i32−1−i320000000−4ζ11−4ζ11−4ζ112ζ11−ζ112ζ11−ζ112ζ112ζ11−ζ11−ζ1100000002+2i32+2i32+2i3−1−i31+i32−1−i31+i32−1−i3−1−i31+i321+i3200000004ζ114ζ114ζ11−2ζ11ζ11−2ζ11ζ11−2ζ11−2ζ11ζ11ζ110000000−2+2i3−2+2i3−2+2i31−i3−1+i321−i3−1+i321−i31−i3−1+i32−1+i320000000−4ζ7−4ζ7−4ζ72ζ7−ζ72ζ7−ζ72ζ72ζ7−ζ7−ζ700000002−2i32−2i32−2i3−1+i31−i32−1+i31−i32−1+i3−1+i31−i321−i3200000004ζ74ζ74ζ7−2ζ7ζ7−2ζ7ζ7−2ζ7−2ζ7ζ7ζ70000000
χ21144-41-21-2-1-1220000000−4i−4i4i−i2i−i2iii−2i−2i0000000-4-44-12-1211-2-200000004i4i−4ii−2ii−2i−i−i2i2i0000000−2−2i3−2−2i32+2i3−1−i321+i3−1−i321+i31+i321+i32−1−i3−1−i30000000−4ζ11−4ζ114ζ11−ζ112ζ11−ζ112ζ11ζ11ζ11−2ζ11−2ζ1100000002+2i32+2i3−2−2i31+i32−1−i31+i32−1−i3−1−i32−1−i321+i31+i300000004ζ114ζ11−4ζ11ζ11−2ζ11ζ11−2ζ11−ζ11−ζ112ζ112ζ110000000−2+2i3−2+2i32−2i3−1+i321−i3−1+i321−i31−i321−i32−1+i3−1+i30000000−4ζ7−4ζ74ζ7−ζ72ζ7−ζ72ζ7ζ7ζ7−2ζ7−2ζ700000002−2i32−2i3−2+2i31−i32−1+i31−i32−1+i3−1+i32−1+i321−i31−i300000004ζ74ζ7−4ζ7ζ7−2ζ7ζ7−2ζ7−ζ7−ζ72ζ72ζ70000000
χ21244-4-21-2122-1-10000000−4i−4i4i2i−i2i−i−2i−2iii0000000-4-442-12-1-2-21100000004i4i−4i−2ii−2ii2i2i−i−i0000000−2−2i3−2−2i32+2i31+i3−1−i321+i3−1−i32−1−i3−1−i31+i321+i320000000−4ζ11−4ζ114ζ112ζ11−ζ112ζ11−ζ11−2ζ11−2ζ11ζ11ζ1100000002+2i32+2i3−2−2i3−1−i31+i32−1−i31+i321+i31+i3−1−i32−1−i3200000004ζ114ζ11−4ζ11−2ζ11ζ11−2ζ11ζ112ζ112ζ11−ζ11−ζ110000000−2+2i3−2+2i32−2i31−i3−1+i321−i3−1+i32−1+i3−1+i31−i321−i320000000−4ζ7−4ζ74ζ72ζ7−ζ72ζ7−ζ7−2ζ7−2ζ7ζ7ζ700000002−2i32−2i3−2+2i3−1+i31−i32−1+i31−i321−i31−i3−1+i32−1+i3200000004ζ74ζ7−4ζ7−2ζ7ζ7−2ζ7ζ72ζ72ζ7−ζ7−ζ70000000
χ2134-401-2-123i−3i000000000−4i4i0−i2ii−2i3-3000000000-440-121-2−3i3i0000000004i−4i0i−2i−i2i-33000000000−2−2i32+2i30−1−i321+i31+i32−1−i33ζ11−3ζ11000000000−4ζ114ζ110−ζ112ζ11ζ11−2ζ11−3−3i323+3i320000000002+2i3−2−2i301+i32−1−i3−1−i321+i3−3ζ113ζ110000000004ζ11−4ζ110ζ11−2ζ11−ζ112ζ113+3i32−3−3i32000000000−2+2i32−2i30−1+i321−i31−i32−1+i33ζ7−3ζ7000000000−4ζ74ζ70−ζ72ζ7ζ7−2ζ7−3+3i323−3i320000000002−2i3−2+2i301−i32−1+i3−1+i321−i3−3ζ73ζ70000000004ζ7−4ζ70ζ7−2ζ7−ζ72ζ73−3i32−3+3i32000000000
χ2144-401-2-12−3i3i000000000−4i4i0−i2ii−2i-33000000000-440-121-23i−3i0000000004i−4i0i−2i−i2i3-3000000000−2−2i32+2i30−1−i321+i31+i32−1−i3−3ζ113ζ11000000000−4ζ114ζ110−ζ112ζ11ζ11−2ζ113+3i32−3−3i320000000002+2i3−2−2i301+i32−1−i3−1−i321+i33ζ11−3ζ110000000004ζ11−4ζ110ζ11−2ζ11−ζ112ζ11−3−3i323+3i32000000000−2+2i32−2i30−1+i321−i31−i32−1+i3−3ζ73ζ7000000000−4ζ74ζ70−ζ72ζ7ζ7−2ζ73−3i32−3+3i320000000002−2i3−2+2i301−i32−1+i3−1+i321−i33ζ7−3ζ70000000004ζ7−4ζ70ζ7−2ζ7−ζ72ζ7−3+3i323−3i32000000000
χ2154-40-212-1003i−3i0000000−4i4i02i−i−2ii003-30000000-4402-1-2100−3i3i00000004i−4i0−2ii2i−i00-330000000−2−2i32+2i301+i3−1−i32−1−i31+i32003ζ11−3ζ110000000−4ζ114ζ1102ζ11−ζ11−2ζ11ζ1100−3−3i323+3i3200000002+2i3−2−2i30−1−i31+i321+i3−1−i3200−3ζ113ζ1100000004ζ11−4ζ110−2ζ11ζ112ζ11−ζ11003+3i32−3−3i320000000−2+2i32−2i301−i3−1+i32−1+i31−i32003ζ7−3ζ70000000−4ζ74ζ702ζ7−ζ7−2ζ7ζ700−3+3i323−3i3200000002−2i3−2+2i30−1+i31−i321−i3−1+i3200−3ζ73ζ700000004ζ7−4ζ70−2ζ7ζ72ζ7−ζ7003−3i32−3+3i320000000
χ2164-40-212-100−3i3i0000000−4i4i02i−i−2ii00-330000000-4402-1-21003i−3i00000004i−4i0−2ii2i−i003-30000000−2−2i32+2i301+i3−1−i32−1−i31+i3200−3ζ113ζ110000000−4ζ114ζ1102ζ11−ζ11−2ζ11ζ11003+3i32−3−3i3200000002+2i3−2−2i30−1−i31+i321+i3−1−i32003ζ11−3ζ1100000004ζ11−4ζ110−2ζ11ζ112ζ11−ζ1100−3−3i323+3i320000000−2+2i32−2i301−i3−1+i32−1+i31−i3200−3ζ73ζ70000000−4ζ74ζ702ζ7−ζ7−2ζ7ζ7003−3i32−3+3i3200000002−2i3−2+2i30−1+i31−i321−i3−1+i32003ζ7−3ζ700000004ζ7−4ζ70−2ζ7ζ72ζ7−ζ700−3+3i323−3i320000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.