Finite Group Databasebeta

← Group #11776809

Character table — Group #11776809

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120
size1111111122222222222244444444444444444444444444444444444444444444444444444444444444449999999918181818181818181818181836363636363636363636363636363636
order12224444444488888888336666661212121212121212121212121212121212121212121212122424242424242424242424242424242424242424242424242424242424242424444444442244888888888888888888888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i
χ4111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii
χ5111111111111-1-1-1-1-1-1-1-111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ6111111111111-1-1-1-1-1-1-1-111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ7111111111111-1-1-1-1-1-1-1-111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111iiii−i−i−i−i−i−i−i−iiiii
χ8111111111111-1-1-1-1-1-1-1-111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111−i−i−i−iiiiiiiii−i−i−i−i
χ91111-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1ii−i−iii−i−iii−i−iii−i−i
χ101111-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-1-1-1−i−iii−i−iii−i−iii−i−iii
χ111111-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1111111-1-111-1-1-1-111-1-111
χ121111-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-11111-1-111-1-11111-1-111-1-1
χ131111-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-111-1-1-1-1-1-11111ii−i−i−i−iiiii−i−i−i−iii
χ141111-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-111-1-1-1-1-1-11111−i−iiiii−i−i−i−iiiii−i−i
χ151111-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1111111-1-1-1-111-1-1-1-111-1-11111-1-1
χ161111-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1111111-1-1-1-1-1-11111-1-111-1-1-1-111
χ1711-1-1ii−i−ii−i1-111-1-1ii−i−i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-111111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-1ii−i−i1-1i−i11-1-1ii−i−iζ−ζζ3−ζ3ζ−ζζ3−ζ3ζ−ζζ3−ζ3ζ−ζζ3−ζ3
χ1811-1-1ii−i−ii−i1-111-1-1ii−i−i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-111111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-1ii−i−i1-1i−i11-1-1ii−i−i−ζζ−ζ3ζ3−ζζ−ζ3ζ3−ζζ−ζ3ζ3−ζζ−ζ3ζ3
χ1911-1-1ii−i−ii−i1-111-1-1ii−i−i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-111111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-111−i−iii-11−ii-1-111−i−iiiζ3−ζ3−ζζζ3−ζ3−ζζ−ζ3ζ3ζ−ζ−ζ3ζ3ζ−ζ
χ2011-1-1ii−i−ii−i1-111-1-1ii−i−i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-111111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-111−i−iii-11−ii-1-111−i−iii−ζ3ζ3ζ−ζ−ζ3ζ3ζ−ζζ3−ζ3−ζζζ3−ζ3−ζζ
χ2111-1-1ii−i−ii−i1-1-1-111−i−iii1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-1-1-1-1-1-1-1-1-111111111−i−i−i−i−i−i−i−iiiiiiiii11-1-1ii−i−i1-1i−i-1-111−i−iiiζ−ζζ3−ζ3−ζζ−ζ3ζ3ζ−ζζ3−ζ3−ζζ−ζ3ζ3
χ2211-1-1ii−i−ii−i1-1-1-111−i−iii1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-1-1-1-1-1-1-1-1-111111111−i−i−i−i−i−i−i−iiiiiiiii11-1-1ii−i−i1-1i−i-1-111−i−iii−ζζ−ζ3ζ3ζ−ζζ3−ζ3−ζζ−ζ3ζ3ζ−ζζ3−ζ3
χ2311-1-1ii−i−ii−i1-1-1-111−i−iii1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-1-1-1-1-1-1-1-1-111111111−i−i−i−i−i−i−i−iiiiiiiii-1-111−i−iii-11−ii11-1-1ii−i−iζ3−ζ3−ζζ−ζ3ζ3ζ−ζ−ζ3ζ3ζ−ζζ3−ζ3−ζζ
χ2411-1-1ii−i−ii−i1-1-1-111−i−iii1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i1111-1-1-1-1-1-1-1-1-1-1-1-111111111−i−i−i−i−i−i−i−iiiiiiiii-1-111−i−iii-11−ii11-1-1ii−i−i−ζ3ζ3ζ−ζζ3−ζ3−ζζζ3−ζ3−ζζ−ζ3ζ3ζ−ζ
χ2511-1-1−i−iii−ii1-111-1-1−i−iii1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-111111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-1−i−iii1-1−ii11-1-1−i−iiiζ3−ζ3ζ−ζζ3−ζ3ζ−ζζ3−ζ3ζ−ζζ3−ζ3ζ−ζ
χ2611-1-1−i−iii−ii1-111-1-1−i−iii1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-111111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-1−i−iii1-1−ii11-1-1−i−iii−ζ3ζ3−ζζ−ζ3ζ3−ζζ−ζ3ζ3−ζζ−ζ3ζ3−ζζ
χ2711-1-1−i−iii−ii1-111-1-1−i−iii1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-111111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-111ii−i−i-11i−i-1-111ii−i−iζ−ζ−ζ3ζ3ζ−ζ−ζ3ζ3−ζζζ3−ζ3−ζζζ3−ζ3
χ2811-1-1−i−iii−ii1-111-1-1−i−iii1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-111111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-111ii−i−i-11i−i-1-111ii−i−i−ζζζ3−ζ3−ζζζ3−ζ3ζ−ζ−ζ3ζ3ζ−ζ−ζ3ζ3
χ2911-1-1−i−iii−ii1-1-1-111ii−i−i1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-1-1-1-1-1-1-1-1-111111111iiiiiiii−i−i−i−i−i−i−i−i11-1-1−i−iii1-1−ii-1-111ii−i−iζ3−ζ3ζ−ζ−ζ3ζ3−ζζζ3−ζ3ζ−ζ−ζ3ζ3−ζζ
χ3011-1-1−i−iii−ii1-1-1-111ii−i−i1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-1-1-1-1-1-1-1-1-111111111iiiiiiii−i−i−i−i−i−i−i−i11-1-1−i−iii1-1−ii-1-111ii−i−i−ζ3ζ3−ζζζ3−ζ3ζ−ζ−ζ3ζ3−ζζζ3−ζ3ζ−ζ
χ3111-1-1−i−iii−ii1-1-1-111ii−i−i1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-1-1-1-1-1-1-1-1-111111111iiiiiiii−i−i−i−i−i−i−i−i-1-111ii−i−i-11i−i11-1-1−i−iiiζ−ζ−ζ3ζ3−ζζζ3−ζ3−ζζζ3−ζ3ζ−ζ−ζ3ζ3
χ3211-1-1−i−iii−ii1-1-1-111ii−i−i1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii1111-1-1-1-1-1-1-1-1-1-1-1-111111111iiiiiiii−i−i−i−i−i−i−i−i-1-111ii−i−i-11i−i11-1-1−i−iii−ζζζ3−ζ3ζ−ζ−ζ3ζ3ζ−ζ−ζ3ζ3−ζζζ3−ζ3
χ3322222222-2-2-2-200000000222222222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000000000022222222-2-2-2-2000000000000000000000000
χ3422222222-2-2-2-200000000222222222222-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000-2-2-2-2-2-2-2-22222000000000000000000000000
χ352222-2-2-2-222-2-20000000022222222-2-2-2-22222-2-2-2-22222-2-2-2-2-2-2-2-2000000000000000000000000000000002222-2-2-2-2-2-222000000000000000000000000
χ362222-2-2-2-222-2-20000000022222222-2-2-2-22222-2-2-2-22222-2-2-2-2-2-2-2-200000000000000000000000000000000-2-2-2-2222222-2-2000000000000000000000000
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χ3922-2-2−2i−2i2i2i2i−2i-22000000002222-2-2-2-2−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i-2-2-2-222220000000000000000000000000000000022-2-2−2i−2i2i2i-222i−2i000000000000000000000000
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χ432-22-22-22-20000−i2i2−i2i2−i2i2−i2i222-2-222-2-222-2-2000022-2-2000000000000−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i22i−2i2i−2i2i−2i2i−2i0000−22−22−22−220000000000000000
χ442-22-22-22-20000−i2i2−i2i2−i2i2−i2i222-2-222-2-222-2-2000022-2-2000000000000−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−2i2i−2i2i−2i2i−2i2i00002−22−22−22−20000000000000000
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χ462-22-2-22-220000i2−i2i2−i2−i2i2−i2i222-2-222-2-2-2-2220000-2-222000000000000i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−2i2i−2i2i2i−2i2i−2i0000−22−222−22−20000000000000000
χ472-22-2-22-220000−i2i2−i2i2i2−i2i2−i222-2-222-2-2-2-2220000-2-222000000000000−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i22i−2i2i−2i−2i2i−2i2i0000−22−222−22−20000000000000000
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χ502-2-222i−2i−2i2i0000i2−i2−i2i2−222−222-2-2-2-2222i2i−2i−2i0000−2i−2i2i2i000000000000i2i2i2i2−i2−i2−i2−i2−i2−i2−i2−i2i2i2i2i2−2−2−2−222222222−2−2−2−2−2i2i2i−2i2-2-220000−222−2−i2i2i2−i20000000000000000
χ512-2-222i−2i−2i2i0000−i2i2i2−i22−2−2222-2-2-2-2222i2i−2i−2i0000−2i−2i2i2i000000000000−i2−i2−i2−i2i2i2i2i2i2i2i2i2−i2−i2−i2−i22222−2−2−2−2−2−2−2−222222i−2i−2i2i-222-20000−222−2−i2i2i2−i20000000000000000
χ522-2-222i−2i−2i2i0000−i2i2i2−i22−2−2222-2-2-2-2222i2i−2i−2i0000−2i−2i2i2i000000000000−i2−i2−i2−i2i2i2i2i2i2i2i2i2−i2−i2−i2−i22222−2−2−2−2−2−2−2−22222−2i2i2i−2i2-2-2200002−2−22i2−i2−i2i20000000000000000
χ532-2-22−2i2i2i−2i0000i2−i2−i2i22−2−2222-2-2-2-222−2i−2i2i2i00002i2i−2i−2i000000000000i2i2i2i2−i2−i2−i2−i2−i2−i2−i2−i2i2i2i2i22222−2−2−2−2−2−2−2−222222i−2i−2i2i2-2-2200002−2−22−i2i2i2−i20000000000000000
χ542-2-22−2i2i2i−2i0000i2−i2−i2i22−2−2222-2-2-2-222−2i−2i2i2i00002i2i−2i−2i000000000000i2i2i2i2−i2−i2−i2−i2−i2−i2−i2−i2i2i2i2i22222−2−2−2−2−2−2−2−22222−2i2i2i−2i-222-20000−222−2i2−i2−i2i20000000000000000
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χ1134-4-44−4i4i4i−4i00002i2−2i2−2i22i222−22−22221-2-12-121-2−i2ii−2i3-300i−2i−i2i-33003i−3i00−3i3i002ζ−ζ3−ζ+2ζ3−i2−i2−2ζ+ζ3ζ−2ζ3i2i2−2ζ+ζ3ζ−2ζ3i2i22ζ−ζ3−ζ+2ζ3−i2−i2−ζ−2ζ32ζ+ζ3−2−2ζ+2ζ3−2ζ−ζ322ζ+2ζ3−2ζ−ζ322−ζ−2ζ32ζ+ζ3−2−2000000000000000000000000000000000000
χ1144-4-44−4i4i4i−4i00002i2−2i2−2i22i222−22−22221-2-12-121-2−i2ii−2i-3300i−2i−i2i3-300−3i3i003i−3i00−ζ+2ζ32ζ−ζ3−i2−i2ζ−2ζ3−2ζ+ζ3i2i2ζ−2ζ3−2ζ+ζ3i2i2−ζ+2ζ32ζ−ζ3−i2−i22ζ+ζ3−ζ−2ζ3−2−2−2ζ−ζ3ζ+2ζ322−2ζ−ζ3ζ+2ζ3222ζ+ζ3−ζ−2ζ3−2−2000000000000000000000000000000000000
χ1154-4-44−4i4i4i−4i00002i2−2i2−2i22i222−22−2222-212-12-1-212i−i−2ii003-3−2ii2i−i00-33003i−3i00−3i3i−i2−i22ζ−ζ3−ζ+2ζ3i2i2−2ζ+ζ3ζ−2ζ3i2i2−2ζ+ζ3ζ−2ζ3−i2−i22ζ−ζ3−ζ+2ζ3−2−2−ζ−2ζ32ζ+ζ322ζ+2ζ3−2ζ−ζ322ζ+2ζ3−2ζ−ζ3−2−2−ζ−2ζ32ζ+ζ3000000000000000000000000000000000000
χ1164-4-44−4i4i4i−4i00002i2−2i2−2i22i222−22−2222-212-12-1-212i−i−2ii00-33−2ii2i−i003-300−3i3i003i−3i−i2−i2−ζ+2ζ32ζ−ζ3i2i2ζ−2ζ3−2ζ+ζ3i2i2ζ−2ζ3−2ζ+ζ3−i2−i2−ζ+2ζ32ζ−ζ3−2−22ζ+ζ3−ζ−2ζ322−2ζ−ζ3ζ+2ζ322−2ζ−ζ3ζ+2ζ3−2−22ζ+ζ3−ζ−2ζ3000000000000000000000000000000000000
χ1174-4-44−4i4i4i−4i0000−2i22i22i2−2i2−222222−221-2-12-121-2−i2ii−2i3-300i−2i−i2i-33003i−3i00−3i3i00−2ζ+ζ3ζ−2ζ3i2i22ζ−ζ3−ζ+2ζ3−i2−i22ζ−ζ3−ζ+2ζ3−i2−i2−2ζ+ζ3ζ−2ζ3i2i2ζ+2ζ3−2ζ−ζ322−ζ−2ζ32ζ+ζ3−2−2−ζ−2ζ32ζ+ζ3−2−2ζ+2ζ3−2ζ−ζ322000000000000000000000000000000000000
χ1184-4-44−4i4i4i−4i0000−2i22i22i2−2i2−222222−221-2-12-121-2−i2ii−2i-3300i−2i−i2i3-300−3i3i003i−3i00ζ−2ζ3−2ζ+ζ3i2i2−ζ+2ζ32ζ−ζ3−i2−i2−ζ+2ζ32ζ−ζ3−i2−i2ζ−2ζ3−2ζ+ζ3i2i2−2ζ−ζ3ζ+2ζ3222ζ+ζ3−ζ−2ζ3−2−22ζ+ζ3−ζ−2ζ3−2−2−2ζ−ζ3ζ+2ζ322000000000000000000000000000000000000
χ1194-4-44−4i4i4i−4i0000−2i22i22i2−2i2−222222−22-212-12-1-212i−i−2ii003-3−2ii2i−i00-33003i−3i00−3i3ii2i2−2ζ+ζ3ζ−2ζ3−i2−i22ζ−ζ3−ζ+2ζ3−i2−i22ζ−ζ3−ζ+2ζ3i2i2−2ζ+ζ3ζ−2ζ322ζ+2ζ3−2ζ−ζ3−2−2−ζ−2ζ32ζ+ζ3−2−2−ζ−2ζ32ζ+ζ322ζ+2ζ3−2ζ−ζ3000000000000000000000000000000000000
χ1204-4-44−4i4i4i−4i0000−2i22i22i2−2i2−222222−22-212-12-1-212i−i−2ii00-33−2ii2i−i003-300−3i3i003i−3ii2i2ζ−2ζ3−2ζ+ζ3−i2−i2−ζ+2ζ32ζ−ζ3−i2−i2−ζ+2ζ32ζ−ζ3i2i2ζ−2ζ3−2ζ+ζ322−2ζ−ζ3ζ+2ζ3−2−22ζ+ζ3−ζ−2ζ3−2−22ζ+ζ3−ζ−2ζ322−2ζ−ζ3ζ+2ζ3000000000000000000000000000000000000

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