Finite Group Databasebeta

← Group #96822

Character table — Group #96822

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116
size1111111111111111222222222222222222222222222222224444444444444444444444444444444444444444444488888888888888881616161616161616
order12222222444444442222444444444444888888888888888844448888888888888888888888888888888888888888444444448888888824448888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ4111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ511111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ611111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ811111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ91111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i1-1-1111-1-1
χ101111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiii−i−i−i−iiiii-111-1-1-111
χ111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−iiiii−i−i−i−i-111-1-1-111
χ121111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−iiiii1-1-1111-1-1
χ131111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i−i−i−i−iiiii1-1-11-1-111
χ141111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−iiiiiiiii−i−i−i−i-111-111-1-1
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii-111-111-1-1
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i1-1-11-1-111
χ1711111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-1ii−i−iii−i−i1111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-111-1-1ii−i−iii−i−i11-1-1i−ii−i
χ1811111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-1ii−i−iii−i−i1111-1-1-1-11111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-111-1-111−i−iii−i−iii-1-111−ii−ii
χ1911111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-1ii−i−iii−i−i-1-1-1-11111-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-1ii−i−iii−i−i-1-111−ii−ii
χ2011111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-1ii−i−iii−i−i-1-1-1-11111-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii-1-111-1-111−i−iii−i−iii11-1-1i−ii−i
χ2111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-1−i−iii−i−iii1111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-1−i−iii−i−iii11-1-1−ii−ii
χ2211111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-1−i−iii−i−iii1111-1-1-1-11111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-111-1-111ii−i−iii−i−i-1-111i−ii−i
χ2311111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-1−i−iii−i−iii-1-1-1-11111-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i11-1-111-1-1−i−iii−i−iii-1-111i−ii−i
χ2411111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-1−i−iii−i−iii-1-1-1-11111-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i-1-111-1-111ii−i−iii−i−i11-1-1−ii−ii
χ2511111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111iiii−i−i−i−i−i−i−i−iiiii11-1-1−i−iiiii−i−iiiii−i−i−i−i−i−i−i−iiiii-1-1-1-111111111-1-1-1-1ii−i−i−i−iii-1-11111-1-11-11-1i−i−ii
χ2611111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111iiii−i−i−i−i−i−i−i−iiiii11-1-1−i−iiiii−i−iiiii−i−i−i−i−i−i−i−iiiii-1-1-1-111111111-1-1-1-1−i−iiiii−i−i11-1-1-1-111-11-11−iii−i
χ2711111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111iiii−i−i−i−i−i−i−i−iiiii11-1-1−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1-1-1-1-11111ii−i−i−i−iii-1-11111-1-1-11-11−iii−i
χ2811111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111iiii−i−i−i−i−i−i−i−iiiii11-1-1−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i1111-1-1-1-1-1-1-1-11111−i−iiiii−i−i11-1-1-1-1111-11-1i−i−ii
χ2911111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111−i−i−i−iiiiiiiii−i−i−i−i11-1-1ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1-1-1-1-11111ii−i−i−i−iii11-1-1-1-1111-11-1−iii−i
χ3011111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111−i−i−i−iiiiiiiii−i−i−i−i11-1-1ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii1111-1-1-1-1-1-1-1-11111−i−iiiii−i−i-1-11111-1-1-11-11i−i−ii
χ3111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111−i−i−i−iiiiiiiii−i−i−i−i11-1-1ii−i−i−i−iii−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-111111111-1-1-1-1ii−i−i−i−iii11-1-1-1-111-11-11i−i−ii
χ3211111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111−i−i−i−iiiiiiiii−i−i−i−i11-1-1ii−i−i−i−iii−i−i−i−iiiiiiiii−i−i−i−i-1-1-1-111111111-1-1-1-1−i−iiiii−i−i-1-11111-1-11-11-1−iii−i
χ332222222222222222222222-2-2-2-2-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-200000000000000000000000000000000000000000000000000000000
χ342222222222222222222222-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2222200000000000000000000000000000000000000000000000000000000
χ352222222222222222-2-2-2-2-2-222222222-2-22222222222222222-2-2-2-2-2-2-2-2-2-2-2-200000000000000000000000000000000000000000000000000000000
χ362222222222222222-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-22222222200000000000000000000000000000000000000000000000000000000
χ3722222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-22222-2-22i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i-2-2222i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000000000000000000000000000
χ3822222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-22222-2-2−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i-2-222−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000000000000000000000000000
χ3922222222-2-2-2-2-2-2-2-2-2-2-2-2222222-2-2-2-2222i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i-2-222−2i−2i2i2i−2i−2i2i2i00000000000000000000000000000000000000000000000000000000
χ4022222222-2-2-2-2-2-2-2-2-2-2-2-2222222-2-2-2-222−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i-2-2222i2i−2i−2i2i2i−2i−2i00000000000000000000000000000000000000000000000000000000
χ41222-2-2-2-2222-2-2-2-2220000002i2i−2i−2i2i2i−2i−2i002i2i−2i−2i2i2i−2i−2i22-2-222-2-2000000000000000000000000000000000000000000001+i−1−i1+i−1−i1−i−1+i1−i−1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i00000000
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χ46222-2-2-2-2222-2-2-2-222000000−2i−2i2i2i−2i−2i2i2i002i2i−2i−2i2i2i−2i−2i-2-222-2-22200000000000000000000000000000000000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i1+i−1−i1+i−1−i1−i−1+i1−i−1+i00000000
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χ48222-2-2-2-2222-2-2-2-222000000−2i−2i2i2i−2i−2i2i2i00−2i−2i2i2i−2i−2i2i2i22-2-222-2-200000000000000000000000000000000000000000000−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i00000000
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χ50222-2-2-2-22-2-22222-2-20000002i2i−2i−2i−2i−2i2i2i0022-2-2-2-222−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000000000000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i1+i−1−i−1−i1+i−1+i1−i1−i−1+i00000000
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χ52222-2-2-2-22-2-22222-2-20000002i2i−2i−2i−2i−2i2i2i00-2-22222-2-22i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000000000000000−1−i1+i1+i−1−i−1+i1−i1−i−1+i−1−i1+i1+i−1−i1−i−1+i−1+i1−i00000000
χ53222-2-2-2-22-2-22222-2-2000000−2i−2i2i2i2i2i−2i−2i0022-2-2-2-2222i2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000000000001−i−1+i−1+i1−i1+i−1−i−1−i1+i−1+i1−i1−i−1+i1+i−1−i−1−i1+i00000000
χ54222-2-2-2-22-2-22222-2-2000000−2i−2i2i2i2i2i−2i−2i0022-2-2-2-2222i2i−2i−2i−2i−2i2i2i00000000000000000000000000000000000000000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i1−i−1+i−1+i1−i−1−i1+i1+i−1−i00000000
χ55222-2-2-2-22-2-22222-2-2000000−2i−2i2i2i2i2i−2i−2i00-2-22222-2-2−2i−2i2i2i2i2i−2i−2i000000000000000000000000000000000000000000001−i−1+i−1+i1−i1+i−1−i−1−i1+i1−i−1+i−1+i1−i−1−i1+i1+i−1−i00000000
χ56222-2-2-2-22-2-22222-2-2000000−2i−2i2i2i2i2i−2i−2i00-2-22222-2-2−2i−2i2i2i2i2i−2i−2i00000000000000000000000000000000000000000000−1+i1−i1−i−1+i−1−i1+i1+i−1−i−1+i1−i1−i−1+i1+i−1−i−1−i1+i00000000
χ5722-222-2-2-22i−2i2i2i−2i−2i2i−2i2-22-22i−2i000000002i−2i2ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ30000000000002ζ−2ζ2ζ3−2ζ30000i2i2−i2−i222−2−2i2i2−i2−i222−2−21−i1−i−1+i−1+i1+i1+i−1−i−1−i1−i1−i−1+i−1+i1+i1+i−1−i−1−i000000000000000000000000
χ5822-222-2-2-22i−2i2i2i−2i−2i2i−2i2-22-22i−2i000000002i−2i2ζ−2ζ2ζ−2ζ2ζ3−2ζ32ζ3−2ζ30000000000002ζ−2ζ2ζ3−2ζ30000−i2−i2i2i2−2−222−i2−i2i2i2−2−222−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1−i−1−i1+i1+i000000000000000000000000
χ5922-222-2-2-22i−2i2i2i−2i−2i2i−2i2-22-22i−2i000000002i−2i−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ3000000000000−2ζ2ζ−2ζ32ζ30000i2i2−i2−i222−2−2i2i2−i2−i222−2−2−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1−i−1−i1+i1+i000000000000000000000000
χ6022-222-2-2-22i−2i2i2i−2i−2i2i−2i2-22-22i−2i000000002i−2i−2ζ2ζ−2ζ2ζ−2ζ32ζ3−2ζ32ζ3000000000000−2ζ2ζ−2ζ32ζ30000−i2−i2i2i2−2−222−i2−i2i2i2−2−2221−i1−i−1+i−1+i1+i1+i−1−i−1−i1−i1−i−1+i−1+i1+i1+i−1−i−1−i000000000000000000000000
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Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.