Finite Group Databasebeta

← Group #11784439

Character table — Group #11784439

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120
size1122244444444444444449918181836363636112224444444444444444991818183636363611222444444444444444499181818363636361122244444444444444449918181836363636
order12488336612121212242424242424242422488444444488121212121212121224242424242424244448844442248866661212121224242424242424242248844444448812121212121212122424242424242424444884444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111-1-1-1-111111111111111111111111111-1-1-1-111111111111111111111111111-1-1-1-111111111111111111111111111-1-1-1-1
χ3111111111111111111111-1-1-1-1-1ii−i−i111111111111111111111-1-1-1-1-1ii−i−i111111111111111111111-1-1-1-1-1ii−i−i111111111111111111111-1-1-1-1-1ii−i−i
χ4111111111111111111111-1-1-1-1-1−i−iii111111111111111111111-1-1-1-1-1−i−iii111111111111111111111-1-1-1-1-1−i−iii111111111111111111111-1-1-1-1-1−i−iii
χ5111-1-111111111-1-1-1-1-1-1-1-1111-1-11-11-1111-1-111111111-1-1-1-1-1-1-1-1111-1-11-11-1111-1-111111111-1-1-1-1-1-1-1-1111-1-11-11-1111-1-111111111-1-1-1-1-1-1-1-1111-1-11-11-1
χ6111-1-111111111-1-1-1-1-1-1-1-1111-1-1-11-11111-1-111111111-1-1-1-1-1-1-1-1111-1-1-11-11111-1-111111111-1-1-1-1-1-1-1-1111-1-1-11-11111-1-111111111-1-1-1-1-1-1-1-1111-1-1-11-11
χ7111-1-111111111-1-1-1-1-1-1-1-1-1-1-111i−i−ii111-1-111111111-1-1-1-1-1-1-1-1-1-1-111i−i−ii111-1-111111111-1-1-1-1-1-1-1-1-1-1-111i−i−ii111-1-111111111-1-1-1-1-1-1-1-1-1-1-111i−i−ii
χ8111-1-111111111-1-1-1-1-1-1-1-1-1-1-111−iii−i111-1-111111111-1-1-1-1-1-1-1-1-1-1-111−iii−i111-1-111111111-1-1-1-1-1-1-1-1-1-1-111−iii−i111-1-111111111-1-1-1-1-1-1-1-1-1-1-111−iii−i
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χ1022-2002222-2-2-2-200000000-2-2200000022-2002222-2-2-2-200000000-2-2200000022-2002222-2-2-2-200000000-2-2200000022-2002222-2-2-2-200000000-2-22000000
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χ18444-4-4-21-21-2-21122-1-122-1-1000000000444-4-4-21-21-2-21122-1-122-1-1000000000444-4-4-21-21-2-21122-1-122-1-1000000000444-4-4-21-21-2-21122-1-122-1-1000000000
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χ2044-4001-21-2-1-122−3i3i00−3i3i0000000000044-4001-21-2-1-122−3i3i00−3i3i0000000000044-4001-21-2-1-122−3i3i00−3i3i0000000000044-4001-21-2-1-122−3i3i00−3i3i00000000000
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χ244-402i2−2i21-2-12−3i3i00−ζ+2ζ32ζ−ζ3−i2−i2ζ−2ζ3−2ζ+ζ3i2i20000000004-402i2−2i21-2-12−3i3i00−ζ+2ζ32ζ−ζ3−i2−i2ζ−2ζ3−2ζ+ζ3i2i20000000004-402i2−2i21-2-12−3i3i00−ζ+2ζ32ζ−ζ3−i2−i2ζ−2ζ3−2ζ+ζ3i2i20000000004-402i2−2i21-2-12−3i3i00−ζ+2ζ32ζ−ζ3−i2−i2ζ−2ζ3−2ζ+ζ3i2i2000000000
χ254-402i2−2i2-212-1003i−3i−i2−i22ζ−ζ3−ζ+2ζ3i2i2−2ζ+ζ3ζ−2ζ30000000004-402i2−2i2-212-1003i−3i−i2−i22ζ−ζ3−ζ+2ζ3i2i2−2ζ+ζ3ζ−2ζ30000000004-402i2−2i2-212-1003i−3i−i2−i22ζ−ζ3−ζ+2ζ3i2i2−2ζ+ζ3ζ−2ζ30000000004-402i2−2i2-212-1003i−3i−i2−i22ζ−ζ3−ζ+2ζ3i2i2−2ζ+ζ3ζ−2ζ3000000000
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χ274-40−2i22i21-2-123i−3i00−2ζ+ζ3ζ−2ζ3i2i22ζ−ζ3−ζ+2ζ3−i2−i20000000004-40−2i22i21-2-123i−3i00−2ζ+ζ3ζ−2ζ3i2i22ζ−ζ3−ζ+2ζ3−i2−i20000000004-40−2i22i21-2-123i−3i00−2ζ+ζ3ζ−2ζ3i2i22ζ−ζ3−ζ+2ζ3−i2−i20000000004-40−2i22i21-2-123i−3i00−2ζ+ζ3ζ−2ζ3i2i22ζ−ζ3−ζ+2ζ3−i2−i2000000000
χ284-40−2i22i21-2-12−3i3i00ζ−2ζ3−2ζ+ζ3i2i2−ζ+2ζ32ζ−ζ3−i2−i20000000004-40−2i22i21-2-12−3i3i00ζ−2ζ3−2ζ+ζ3i2i2−ζ+2ζ32ζ−ζ3−i2−i20000000004-40−2i22i21-2-12−3i3i00ζ−2ζ3−2ζ+ζ3i2i2−ζ+2ζ32ζ−ζ3−i2−i20000000004-40−2i22i21-2-12−3i3i00ζ−2ζ3−2ζ+ζ3i2i2−ζ+2ζ32ζ−ζ3−i2−i2000000000
χ294-40−2i22i2-212-1003i−3ii2i2−2ζ+ζ3ζ−2ζ3−i2−i22ζ−ζ3−ζ+2ζ30000000004-40−2i22i2-212-1003i−3ii2i2−2ζ+ζ3ζ−2ζ3−i2−i22ζ−ζ3−ζ+2ζ30000000004-40−2i22i2-212-1003i−3ii2i2−2ζ+ζ3ζ−2ζ3−i2−i22ζ−ζ3−ζ+2ζ30000000004-40−2i22i2-212-1003i−3ii2i2−2ζ+ζ3ζ−2ζ3−i2−i22ζ−ζ3−ζ+2ζ3000000000
χ304-40−2i22i2-212-100−3i3ii2i2ζ−2ζ3−2ζ+ζ3−i2−i2−ζ+2ζ32ζ−ζ30000000004-40−2i22i2-212-100−3i3ii2i2ζ−2ζ3−2ζ+ζ3−i2−i2−ζ+2ζ32ζ−ζ30000000004-40−2i22i2-212-100−3i3ii2i2ζ−2ζ3−2ζ+ζ3−i2−i2−ζ+2ζ32ζ−ζ30000000004-40−2i22i2-212-100−3i3ii2i2ζ−2ζ3−2ζ+ζ3−i2−i2−ζ+2ζ32ζ−ζ3000000000
χ31111111111111111111111111111111iiiiiiiiiiiiiiiiiiiiiiiiiiiiii-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i
χ3211111111111111111111111111-1-1-1-1iiiiiiiiiiiiiiiiiiiiiiiiii−i−i−i−i-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiii
χ33111111111111111111111-1-1-1-1-1ii−i−iiiiiiiiiiiiiiiiiiiiii−i−i−i−i−i-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111−i−iii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiii11-1-1
χ34111111111111111111111-1-1-1-1-1−i−iiiiiiiiiiiiiiiiiiiiiiii−i−i−i−i−i11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111ii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiii-1-111
χ35111-1-111111111-1-1-1-1-1-1-1-1111-1-11-11-1iii−i−iiiiiiiii−i−i−i−i−i−i−i−iiii−i−ii−ii−i-1-1-111-1-1-1-1-1-1-1-111111111-1-1-111-11-11−i−i−iii−i−i−i−i−i−i−i−iiiiiiiii−i−i−iii−ii−ii
χ36111-1-111111111-1-1-1-1-1-1-1-1111-1-1-11-11iii−i−iiiiiiiii−i−i−i−i−i−i−i−iiii−i−i−ii−ii-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1111-11-1−i−i−iii−i−i−i−i−i−i−i−iiiiiiiii−i−i−iiii−ii−i
χ37111-1-111111111-1-1-1-1-1-1-1-1-1-1-111i−i−iiiii−i−iiiiiiiii−i−i−i−i−i−i−i−i−i−i−iii-111-1-1-1-111-1-1-1-1-1-1-1-111111111111-1-1−iii−i−i−i−iii−i−i−i−i−i−i−i−iiiiiiiiiiii−i−i1-1-11
χ38111-1-111111111-1-1-1-1-1-1-1-1-1-1-111−iii−iiii−i−iiiiiiiii−i−i−i−i−i−i−i−i−i−i−iii1-1-11-1-1-111-1-1-1-1-1-1-1-111111111111-1-1i−i−ii−i−i−iii−i−i−i−i−i−i−i−iiiiiiiiiiii−i−i-111-1
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χ544-402i2−2i21-2-12−3i3i00−ζ+2ζ32ζ−ζ3−i2−i2ζ−2ζ3−2ζ+ζ3i2i20000000004i−4i0−2222i−2i−i2i3-300−2ζ−ζ3ζ+2ζ3222ζ+ζ3−ζ−2ζ3−2−2000000000-440−2i22i2-121-23i−3i00ζ−2ζ3−2ζ+ζ3i2i2−ζ+2ζ32ζ−ζ3−i2−i2000000000−4i4i022−22−i2ii−2i-33002ζ+ζ3−ζ−2ζ3−2−2−2ζ−ζ3ζ+2ζ322000000000
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χ11044-4001-21-2-1-122−3i3i00−3i3i00000000000−4i−4i4i00−i2i−i2iii−2i−2i-3300-3300000000000-4-4400-12-1211-2-23i−3i003i−3i000000000004i4i−4i00i−2ii−2i−i−i2i2i3-3003-300000000000
χ11144-400-21-2122-1-1003i−3i003i−3i000000000−4i−4i4i002i−i2i−i−2i−2iii003-3003-3000000000-4-44002-12-1-2-21100−3i3i00−3i3i0000000004i4i−4i00−2ii−2ii2i2i−i−i00-3300-33000000000
χ11244-400-21-2122-1-100−3i3i00−3i3i000000000−4i−4i4i002i−i2i−i−2i−2iii00-3300-33000000000-4-44002-12-1-2-211003i−3i003i−3i0000000004i4i−4i00−2ii−2ii2i2i−i−i003-3003-3000000000
χ1134-402i2−2i21-2-123i−3i002ζ−ζ3−ζ+2ζ3−i2−i2−2ζ+ζ3ζ−2ζ3i2i2000000000−4i4i022−22−i2ii−2i3-300−ζ−2ζ32ζ+ζ3−2−2ζ+2ζ3−2ζ−ζ322000000000-440−2i22i2-121-2−3i3i00−2ζ+ζ3ζ−2ζ3i2i22ζ−ζ3−ζ+2ζ3−i2−i20000000004i−4i0−2222i−2i−i2i-3300ζ+2ζ3−2ζ−ζ322−ζ−2ζ32ζ+ζ3−2−2000000000
χ1144-402i2−2i21-2-12−3i3i00−ζ+2ζ32ζ−ζ3−i2−i2ζ−2ζ3−2ζ+ζ3i2i2000000000−4i4i022−22−i2ii−2i-33002ζ+ζ3−ζ−2ζ3−2−2−2ζ−ζ3ζ+2ζ322000000000-440−2i22i2-121-23i−3i00ζ−2ζ3−2ζ+ζ3i2i2−ζ+2ζ32ζ−ζ3−i2−i20000000004i−4i0−2222i−2i−i2i3-300−2ζ−ζ3ζ+2ζ3222ζ+ζ3−ζ−2ζ3−2−2000000000
χ1154-402i2−2i2-212-1003i−3i−i2−i22ζ−ζ3−ζ+2ζ3i2i2−2ζ+ζ3ζ−2ζ3000000000−4i4i022−222i−i−2ii003-3−2−2−ζ−2ζ32ζ+ζ322ζ+2ζ3−2ζ−ζ3000000000-440−2i22i22-1-2100−3i3ii2i2−2ζ+ζ3ζ−2ζ3−i2−i22ζ−ζ3−ζ+2ζ30000000004i−4i0−2222−2ii2i−i00-3322ζ+2ζ3−2ζ−ζ3−2−2−ζ−2ζ32ζ+ζ3000000000
χ1164-402i2−2i2-212-100−3i3i−i2−i2−ζ+2ζ32ζ−ζ3i2i2ζ−2ζ3−2ζ+ζ3000000000−4i4i022−222i−i−2ii00-33−2−22ζ+ζ3−ζ−2ζ322−2ζ−ζ3ζ+2ζ3000000000-440−2i22i22-1-21003i−3ii2i2ζ−2ζ3−2ζ+ζ3−i2−i2−ζ+2ζ32ζ−ζ30000000004i−4i0−2222−2ii2i−i003-322−2ζ−ζ3ζ+2ζ3−2−22ζ+ζ3−ζ−2ζ3000000000
χ1174-40−2i22i21-2-123i−3i00−2ζ+ζ3ζ−2ζ3i2i22ζ−ζ3−ζ+2ζ3−i2−i2000000000−4i4i0−2222−i2ii−2i3-300ζ+2ζ3−2ζ−ζ322−ζ−2ζ32ζ+ζ3−2−2000000000-4402i2−2i2-121-2−3i3i002ζ−ζ3−ζ+2ζ3−i2−i2−2ζ+ζ3ζ−2ζ3i2i20000000004i−4i022−22i−2i−i2i-3300−ζ−2ζ32ζ+ζ3−2−2ζ+2ζ3−2ζ−ζ322000000000
χ1184-40−2i22i21-2-12−3i3i00ζ−2ζ3−2ζ+ζ3i2i2−ζ+2ζ32ζ−ζ3−i2−i2000000000−4i4i0−2222−i2ii−2i-3300−2ζ−ζ3ζ+2ζ3222ζ+ζ3−ζ−2ζ3−2−2000000000-4402i2−2i2-121-23i−3i00−ζ+2ζ32ζ−ζ3−i2−i2ζ−2ζ3−2ζ+ζ3i2i20000000004i−4i022−22i−2i−i2i3-3002ζ+ζ3−ζ−2ζ3−2−2−2ζ−ζ3ζ+2ζ322000000000
χ1194-40−2i22i2-212-1003i−3ii2i2−2ζ+ζ3ζ−2ζ3−i2−i22ζ−ζ3−ζ+2ζ3000000000−4i4i0−22222i−i−2ii003-322ζ+2ζ3−2ζ−ζ3−2−2−ζ−2ζ32ζ+ζ3000000000-4402i2−2i22-1-2100−3i3i−i2−i22ζ−ζ3−ζ+2ζ3i2i2−2ζ+ζ3ζ−2ζ30000000004i−4i022−22−2ii2i−i00-33−2−2−ζ−2ζ32ζ+ζ322ζ+2ζ3−2ζ−ζ3000000000
χ1204-40−2i22i2-212-100−3i3ii2i2ζ−2ζ3−2ζ+ζ3−i2−i2−ζ+2ζ32ζ−ζ3000000000−4i4i0−22222i−i−2ii00-3322−2ζ−ζ3ζ+2ζ3−2−22ζ+ζ3−ζ−2ζ3000000000-4402i2−2i22-1-21003i−3i−i2−i2−ζ+2ζ32ζ−ζ3i2i2ζ−2ζ3−2ζ+ζ30000000004i−4i022−22−2ii2i−i003-3−2−22ζ+ζ3−ζ−2ζ322−2ζ−ζ3ζ+2ζ3000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.