Finite Group Databasebeta

← Group #13172996

Character table — Group #13172996

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126C127C128C129C130C131C132C133C134C135C136C137C138C139C140C141C142C143C144C145C146C147C148C149C150C151C152C153C154C155C156C157C158C159C160C161C162
size111122222222226666888888888888888888888888121212123636363636363636111122222222226666888888888888888888888888121212123636363636363636111122222222226666888888888888888888888888121212123636363636363636
order122234466612121212444433366666666612121212121212121212121212121212224488883666312126661212121212121212333666666666121212121212121212121212121212126612122424242436663121266612121212121212123336666666661212121212121212121212121212121266121224242424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ311111-1-1111-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-111111-1-1111-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-111111-1-1111-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1
χ411111-1-1111-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-11111111-1-1111-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-11111111-1-1111-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-111
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χ61-11-11i−i-11-1ii−i−ii−i1-1111111-1-1-1-1-1-1iiiiii−i−i−i−i−i−i1-1i−i-11−ii-11−ii1-11-11i−i-11-1ii−i−ii−i1-1111111-1-1-1-1-1-1iiiiii−i−i−i−i−i−i1-1i−i-11−ii-11−ii1-11-11i−i-11-1ii−i−ii−i1-1111111-1-1-1-1-1-1iiiiii−i−i−i−i−i−i1-1i−i-11−ii-11−ii
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χ1022222-2-2222-2-2-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1-111111111111122-2-20000000022222-2-2222-2-2-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1-111111111111122-2-20000000022222-2-2222-2-2-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1-111111111111122-2-200000000
χ112222-122-1-1-1-1-1-1-122222-1-12-1-12-1-12-1-122-1-1-1-122-1-1-1-1-1-1-1-1000000002222-122-1-1-1-1-1-1-122222-1-12-1-12-1-12-1-122-1-1-1-122-1-1-1-1-1-1-1-1000000002222-122-1-1-1-1-1-1-122222-1-12-1-12-1-12-1-122-1-1-1-122-1-1-1-1-1-1-1-100000000
χ122222-122-1-1-1-1-1-1-12222-12-1-12-1-12-1-12-1-1-122-1-1-1-122-1-1-1-1-1-1000000002222-122-1-1-1-1-1-1-12222-12-1-12-1-12-1-12-1-1-122-1-1-1-122-1-1-1-1-1-1000000002222-122-1-1-1-1-1-1-12222-12-1-12-1-12-1-12-1-1-122-1-1-1-122-1-1-1-1-1-100000000
χ132222-122-1-1-1-1-1-1-12222-1-12-1-12-1-12-1-12-1-1-1-122-1-1-1-122-1-1-1-1000000002222-122-1-1-1-1-1-1-12222-1-12-1-12-1-12-1-12-1-1-1-122-1-1-1-122-1-1-1-1000000002222-122-1-1-1-1-1-1-12222-1-12-1-12-1-12-1-12-1-1-1-122-1-1-1-122-1-1-1-100000000
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χ162222-1-2-2-1-1-11111-2-222-1-12-1-12-1-12-1-121111-2-21111-2-2-1-111000000002222-1-2-2-1-1-11111-2-222-1-12-1-12-1-12-1-121111-2-21111-2-2-1-111000000002222-1-2-2-1-1-11111-2-222-1-12-1-12-1-12-1-121111-2-21111-2-2-1-11100000000
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χ182-22-22−2i2i-22-2−2i−2i2i2i−2i2i2-2-1-1-1-1-1-1111111iiiiii−i−i−i−i−i−i2-2−2i2i000000002-22-22−2i2i-22-2−2i−2i2i2i−2i2i2-2-1-1-1-1-1-1111111iiiiii−i−i−i−i−i−i2-2−2i2i000000002-22-22−2i2i-22-2−2i−2i2i2i−2i2i2-2-1-1-1-1-1-1111111iiiiii−i−i−i−i−i−i2-2−2i2i00000000
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χ222-22-2-1−2i2i1-11ii−i−i−2i2i2-22-1-12-1-1-211-211−2i−2iiiii2i2i−i−i−i−i-11i−i000000002-22-2-1−2i2i1-11ii−i−i−2i2i2-22-1-12-1-1-211-211−2i−2iiiii2i2i−i−i−i−i-11i−i000000002-22-2-1−2i2i1-11ii−i−i−2i2i2-22-1-12-1-1-211-211−2i−2iiiii2i2i−i−i−i−i-11i−i00000000
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χ2533333333333333-1-1-1-1000000000000000000000000-1-1-1-11111-1-1-1-133333333333333-1-1-1-1000000000000000000000000-1-1-1-11111-1-1-1-133333333333333-1-1-1-1000000000000000000000000-1-1-1-11111-1-1-1-1
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χ2733333-3-3333-3-3-3-311-1-1000000000000000000000000-1-11111-1-1-1-11133333-3-3333-3-3-3-311-1-1000000000000000000000000-1-11111-1-1-1-11133333-3-3333-3-3-3-311-1-1000000000000000000000000-1-11111-1-1-1-111
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χ117222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222200000000−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i31+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i32−1−i3−1−i3−1−i3−1−i300000000−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i31−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i32−1+i3−1+i3−1+i3−1+i300000000
χ11822222-2-2222-2-2-2-2-2-222-1-1-1-1-1-1-1-1-1-1-1-111111111111122-2-200000000−1−i3−1−i3−1−i3−1−i3−1−i31+i31+i3−1−i3−1−i3−1−i31+i31+i31+i31+i31+i31+i3−1−i3−1−i31+i321+i321+i321+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−i32−1−i32−1−i32−1−i3−1−i31+i31+i300000000−1+i3−1+i3−1+i3−1+i3−1+i31−i31−i3−1+i3−1+i3−1+i31−i31−i31−i31−i31−i31−i3−1+i3−1+i31−i321−i321−i321−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+i32−1+i32−1+i32−1+i3−1+i31−i31−i300000000
χ1192222-122-1-1-1-1-1-1-122222-1-12-1-12-1-12-1-122-1-1-1-122-1-1-1-1-1-1-1-100000000−1−i3−1−i3−1−i3−1−i31+i32−1−i3−1−i31+i321+i321+i321+i321+i321+i321+i32−1−i3−1−i3−1−i3−1−i3−1−i31+i321+i32−1−i31+i321+i32−1−i31+i321+i32−1−i31+i321+i32−1−i3−1−i31+i321+i321+i321+i32−1−i3−1−i31+i321+i321+i321+i321+i321+i321+i321+i3200000000−1+i3−1+i3−1+i3−1+i31−i32−1+i3−1+i31−i321−i321−i321−i321−i321−i321−i32−1+i3−1+i3−1+i3−1+i3−1+i31−i321−i32−1+i31−i321−i32−1+i31−i321−i32−1+i31−i321−i32−1+i3−1+i31−i321−i321−i321−i32−1+i3−1+i31−i321−i321−i321−i321−i321−i321−i321−i3200000000
χ1202222-122-1-1-1-1-1-1-12222-12-1-12-1-12-1-12-1-1-122-1-1-1-122-1-1-1-1-1-100000000−1−i3−1−i3−1−i3−1−i31+i32−1−i3−1−i31+i321+i321+i321+i321+i321+i321+i32−1−i3−1−i3−1−i3−1−i31+i32−1−i31+i321+i32−1−i31+i321+i32−1−i31+i321+i32−1−i31+i321+i321+i32−1−i3−1−i31+i321+i321+i321+i32−1−i3−1−i31+i321+i321+i321+i321+i321+i3200000000−1+i3−1+i3−1+i3−1+i31−i32−1+i3−1+i31−i321−i321−i321−i321−i321−i321−i32−1+i3−1+i3−1+i3−1+i31−i32−1+i31−i321−i32−1+i31−i321−i32−1+i31−i321−i32−1+i31−i321−i321−i32−1+i3−1+i31−i321−i321−i321−i32−1+i3−1+i31−i321−i321−i321−i321−i321−i3200000000
χ1212222-122-1-1-1-1-1-1-12222-1-12-1-12-1-12-1-12-1-1-1-122-1-1-1-122-1-1-1-100000000−1−i3−1−i3−1−i3−1−i31+i32−1−i3−1−i31+i321+i321+i321+i321+i321+i321+i32−1−i3−1−i3−1−i3−1−i31+i321+i32−1−i31+i321+i32−1−i31+i321+i32−1−i31+i321+i32−1−i31+i321+i321+i321+i32−1−i3−1−i31+i321+i321+i321+i32−1−i3−1−i31+i321+i321+i321+i3200000000−1+i3−1+i3−1+i3−1+i31−i32−1+i3−1+i31−i321−i321−i321−i321−i321−i321−i32−1+i3−1+i3−1+i3−1+i31−i321−i32−1+i31−i321−i32−1+i31−i321−i32−1+i31−i321−i32−1+i31−i321−i321−i321−i32−1+i3−1+i31−i321−i321−i321−i32−1+i3−1+i31−i321−i321−i321−i3200000000
χ1222222-1-2-2-1-1-11111-2-2222-1-12-1-12-1-12-1-1-2-21111-2-21111-1-11100000000−1−i3−1−i3−1−i3−1−i31+i321+i31+i31+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i31+i3−1−i3−1−i3−1−i31+i321+i32−1−i31+i321+i32−1−i31+i321+i32−1−i31+i321+i321+i31+i3−1−i32−1−i32−1−i32−1−i321+i31+i3−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i3200000000−1+i3−1+i3−1+i3−1+i31−i321−i31−i31−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i31−i3−1+i3−1+i3−1+i31−i321−i32−1+i31−i321−i32−1+i31−i321−i32−1+i31−i321−i321−i31−i3−1+i32−1+i32−1+i32−1+i321−i31−i3−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i3200000000
χ1232222-1-2-2-1-1-11111-2-222-12-1-12-1-12-1-12-111-2-21111-2-211-1-11100000000−1−i3−1−i3−1−i3−1−i31+i321+i31+i31+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i31+i3−1−i3−1−i31+i32−1−i31+i321+i32−1−i31+i321+i32−1−i31+i321+i32−1−i31+i32−1−i32−1−i321+i31+i3−1−i32−1−i32−1−i32−1−i321+i31+i3−1−i32−1−i321+i321+i32−1−i32−1−i3200000000−1+i3−1+i3−1+i3−1+i31−i321−i31−i31−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i31−i3−1+i3−1+i31−i32−1+i31−i321−i32−1+i31−i321−i32−1+i31−i321−i32−1+i31−i32−1+i32−1+i321−i31−i3−1+i32−1+i32−1+i32−1+i321−i31−i3−1+i32−1+i321−i321−i32−1+i32−1+i3200000000
χ1242222-1-2-2-1-1-11111-2-222-1-12-1-12-1-12-1-121111-2-21111-2-2-1-11100000000−1−i3−1−i3−1−i3−1−i31+i321+i31+i31+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i31+i3−1−i3−1−i31+i321+i32−1−i31+i321+i32−1−i31+i321+i32−1−i31+i321+i32−1−i3−1−i32−1−i32−1−i32−1−i321+i31+i3−1−i32−1−i32−1−i32−1−i321+i31+i31+i321+i32−1−i32−1−i3200000000−1+i3−1+i3−1+i3−1+i31−i321−i31−i31−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i31−i3−1+i3−1+i31−i321−i32−1+i31−i321−i32−1+i31−i321−i32−1+i31−i321−i32−1+i3−1+i32−1+i32−1+i32−1+i321−i31−i3−1+i32−1+i32−1+i32−1+i321−i31−i31−i321−i32−1+i32−1+i3200000000
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χ1544-4-44-20022-223−23−232300001-21-12-11-21-12-1−33003−33−300−33000000000000−2−2i32+2i32+2i3−2−2i31+i300−1−i3−1−i31+i34ζ7+2ζ11−4ζ7−2ζ11−4ζ7−2ζ114ζ7+2ζ110000−1−i321+i3−1−i321+i32−1−i31+i32−1−i321+i3−1−i321+i32−1−i31+i32−2ζ7−ζ112ζ7+ζ11002ζ7+ζ11−2ζ7−ζ112ζ7+ζ11−2ζ7−ζ1100−2ζ7−ζ112ζ7+ζ11000000000000−2+2i32−2i32−2i3−2+2i31−i300−1+i3−1+i31−i3−2ζ7−4ζ112ζ7+4ζ112ζ7+4ζ11−2ζ7−4ζ110000−1+i321−i3−1+i321−i32−1+i31−i32−1+i321−i3−1+i321−i32−1+i31−i32ζ7+2ζ11−ζ7−2ζ1100−ζ7−2ζ11ζ7+2ζ11−ζ7−2ζ11ζ7+2ζ1100ζ7+2ζ11−ζ7−2ζ11000000000000
χ1554-4-44-20022-223−23−23230000-2112-1-1-2112-1-1003−3−3300−333−3000000000000−2−2i32+2i32+2i3−2−2i31+i300−1−i3−1−i31+i34ζ7+2ζ11−4ζ7−2ζ11−4ζ7−2ζ114ζ7+2ζ1100001+i3−1−i32−1−i32−1−i31+i321+i321+i3−1−i32−1−i32−1−i31+i321+i32002ζ7+ζ11−2ζ7−ζ11−2ζ7−ζ112ζ7+ζ1100−2ζ7−ζ112ζ7+ζ112ζ7+ζ11−2ζ7−ζ11000000000000−2+2i32−2i32−2i3−2+2i31−i300−1+i3−1+i31−i3−2ζ7−4ζ112ζ7+4ζ112ζ7+4ζ11−2ζ7−4ζ1100001−i3−1+i32−1+i32−1+i31−i321−i321−i3−1+i32−1+i32−1+i31−i321−i3200−ζ7−2ζ11ζ7+2ζ11ζ7+2ζ11−ζ7−2ζ1100ζ7+2ζ11−ζ7−2ζ11−ζ7−2ζ11ζ7+2ζ11000000000000
χ1564-4-44-20022-2−232323−23000011-2-1-1211-2-1-12−333−3003−3−3300000000000000−2−2i32+2i32+2i3−2−2i31+i300−1−i3−1−i31+i3−4ζ7−2ζ114ζ7+2ζ114ζ7+2ζ11−4ζ7−2ζ110000−1−i32−1−i321+i31+i321+i32−1−i3−1−i32−1−i321+i31+i321+i32−1−i3−2ζ7−ζ112ζ7+ζ112ζ7+ζ11−2ζ7−ζ11002ζ7+ζ11−2ζ7−ζ11−2ζ7−ζ112ζ7+ζ1100000000000000−2+2i32−2i32−2i3−2+2i31−i300−1+i3−1+i31−i32ζ7+4ζ11−2ζ7−4ζ11−2ζ7−4ζ112ζ7+4ζ110000−1+i32−1+i321−i31−i321−i32−1+i3−1+i32−1+i321−i31−i321−i32−1+i3ζ7+2ζ11−ζ7−2ζ11−ζ7−2ζ11ζ7+2ζ1100−ζ7−2ζ11ζ7+2ζ11ζ7+2ζ11−ζ7−2ζ1100000000000000
χ1574-4-44-20022-2−232323−2300001-21-12-11-21-12-13−300−33−33003−3000000000000−2−2i32+2i32+2i3−2−2i31+i300−1−i3−1−i31+i3−4ζ7−2ζ114ζ7+2ζ114ζ7+2ζ11−4ζ7−2ζ110000−1−i321+i3−1−i321+i32−1−i31+i32−1−i321+i3−1−i321+i32−1−i31+i322ζ7+ζ11−2ζ7−ζ1100−2ζ7−ζ112ζ7+ζ11−2ζ7−ζ112ζ7+ζ11002ζ7+ζ11−2ζ7−ζ11000000000000−2+2i32−2i32−2i3−2+2i31−i300−1+i3−1+i31−i32ζ7+4ζ11−2ζ7−4ζ11−2ζ7−4ζ112ζ7+4ζ110000−1+i321−i3−1+i321−i32−1+i31−i32−1+i321−i3−1+i321−i32−1+i31−i32−ζ7−2ζ11ζ7+2ζ1100ζ7+2ζ11−ζ7−2ζ11ζ7+2ζ11−ζ7−2ζ1100−ζ7−2ζ11ζ7+2ζ11000000000000
χ1584-4-44-20022-2−232323−230000-2112-1-1-2112-1-100−333−3003−3−33000000000000−2−2i32+2i32+2i3−2−2i31+i300−1−i3−1−i31+i3−4ζ7−2ζ114ζ7+2ζ114ζ7+2ζ11−4ζ7−2ζ1100001+i3−1−i32−1−i32−1−i31+i321+i321+i3−1−i32−1−i32−1−i31+i321+i3200−2ζ7−ζ112ζ7+ζ112ζ7+ζ11−2ζ7−ζ11002ζ7+ζ11−2ζ7−ζ11−2ζ7−ζ112ζ7+ζ11000000000000−2+2i32−2i32−2i3−2+2i31−i300−1+i3−1+i31−i32ζ7+4ζ11−2ζ7−4ζ11−2ζ7−4ζ112ζ7+4ζ1100001−i3−1+i32−1+i32−1+i31−i321−i321−i3−1+i32−1+i32−1+i31−i321−i3200ζ7+2ζ11−ζ7−2ζ11−ζ7−2ζ11ζ7+2ζ1100−ζ7−2ζ11ζ7+2ζ11ζ7+2ζ11−ζ7−2ζ11000000000000
χ1596666-366-3-3-3-3-3-3-3-2-2-2-2000000000000000000000000111100000000−3−3i3−3−3i3−3−3i3−3−3i33+3i32−3−3i3−3−3i33+3i323+3i323+3i323+3i323+3i323+3i323+3i321+i31+i31+i31+i3000000000000000000000000−1−i32−1−i32−1−i32−1−i3200000000−3+3i3−3+3i3−3+3i3−3+3i33−3i32−3+3i3−3+3i33−3i323−3i323−3i323−3i323−3i323−3i323−3i321−i31−i31−i31−i3000000000000000000000000−1+i32−1+i32−1+i32−1+i3200000000
χ1606666-3-6-6-3-3-3333322-2-200000000000000000000000011-1-100000000−3−3i3−3−3i3−3−3i3−3−3i33+3i323+3i33+3i33+3i323+3i323+3i32−3−3i32−3−3i32−3−3i32−3−3i32−1−i3−1−i31+i31+i3000000000000000000000000−1−i32−1−i321+i321+i3200000000−3+3i3−3+3i3−3+3i3−3+3i33−3i323−3i33−3i33−3i323−3i323−3i32−3+3i32−3+3i32−3+3i32−3+3i32−1+i3−1+i31−i31−i3000000000000000000000000−1+i32−1+i321−i321−i3200000000
χ1616-66-6-36i−6i3-33−3i−3i3i3i−2i2i-220000000000000000000000001-1i−i00000000−3−3i33+3i3−3−3i33+3i33+3i326ζ11−6ζ11−3−3i323+3i32−3−3i32−3ζ11−3ζ113ζ113ζ11−2ζ112ζ111+i3−1−i3000000000000000000000000−1−i321+i32ζ11−ζ1100000000−3+3i33−3i3−3+3i33−3i33−3i326ζ7−6ζ7−3+3i323−3i32−3+3i32−3ζ7−3ζ73ζ73ζ7−2ζ72ζ71−i3−1+i3000000000000000000000000−1+i321−i32ζ7−ζ700000000
χ1626-66-6-3−6i6i3-333i3i−3i−3i2i−2i-220000000000000000000000001-1−ii00000000−3−3i33+3i3−3−3i33+3i33+3i32−6ζ116ζ11−3−3i323+3i32−3−3i323ζ113ζ11−3ζ11−3ζ112ζ11−2ζ111+i3−1−i3000000000000000000000000−1−i321+i32−ζ11ζ1100000000−3+3i33−3i3−3+3i33−3i33−3i32−6ζ76ζ7−3+3i323−3i32−3+3i323ζ73ζ7−3ζ7−3ζ72ζ7−2ζ71−i3−1+i3000000000000000000000000−1+i321−i32−ζ7ζ700000000

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