Finite Group Databasebeta

← Group #98795

Character table — Group #98795

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size11111111111111112222222222222222222222224444444444444444888888888888888888888888888888888888888888888888
order12222222222222224444444444444444444444444444444444444444444444444444444488888888888888888888888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111
χ5111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−i
χ6111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii
χ7111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−i−i−i−i−iiiiiiiii
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111−i−i−i−i−i−i−i−iiiiiiiiiiiiiiiii−i−i−i−i−i−i−i−i
χ91111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ101111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111
χ111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ121111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ131111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiii
χ141111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−i
χ151111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111111111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i
χ161111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111111111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii
χ171111-1-1-111-1-1-11-11-1iiii−i−i−i−iii−i−iii−i−iii−i−iii−i−i11-1-1ii−i−i11-1-111-1-111-1-1ii−i−iii−i−i11-1-1ζζ−ζ−ζζ3ζ3−ζ3−ζ3ζ3ζ3−ζ3−ζ3ζζ−ζ−ζζζ−ζ−ζζ3ζ3−ζ3−ζ3ζ3ζ3−ζ3−ζ3ζζ−ζ−ζ
χ181111-1-1-111-1-1-11-11-1iiii−i−i−i−iii−i−iii−i−iii−i−iii−i−i11-1-1ii−i−i11-1-111-1-111-1-1ii−i−iii−i−i11-1-1−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ3−ζ3ζ3ζ3−ζ−ζζζ
χ191111-1-1-111-1-1-11-11-1iiii−i−i−i−iii−i−iii−i−iii−i−iii−i−i11-1-1ii−i−i11-1-111-1-1-1-111−i−iii−i−iii-1-111ζζ−ζ−ζζ3ζ3−ζ3−ζ3ζ3ζ3−ζ3−ζ3ζζ−ζ−ζ−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ3−ζ3ζ3ζ3−ζ−ζζζ
χ201111-1-1-111-1-1-11-11-1iiii−i−i−i−iii−i−iii−i−iii−i−iii−i−i11-1-1ii−i−i11-1-111-1-1-1-111−i−iii−i−iii-1-111−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ3−ζ3ζ3ζ3−ζ−ζζζζζ−ζ−ζζ3ζ3−ζ3−ζ3ζ3ζ3−ζ3−ζ3ζζ−ζ−ζ
χ211111-1-1-111-1-1-11-11-1iiii−i−i−i−i−i−iii−i−iii−i−iii−i−iii11-1-1ii−i−i-1-111-1-11111-1-1ii−i−i−i−iii-1-111ζ3ζ3−ζ3−ζ3−ζ−ζζζζζ−ζ−ζ−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ3−ζ3−ζ−ζζζζζ−ζ−ζ−ζ3−ζ3ζ3ζ3
χ221111-1-1-111-1-1-11-11-1iiii−i−i−i−i−i−iii−i−iii−i−iii−i−iii11-1-1ii−i−i-1-111-1-11111-1-1ii−i−i−i−iii-1-111−ζ3−ζ3ζ3ζ3ζζ−ζ−ζ−ζ−ζζζζ3ζ3−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζζ−ζ−ζ−ζ−ζζζζ3ζ3−ζ3−ζ3
χ231111-1-1-111-1-1-11-11-1iiii−i−i−i−i−i−iii−i−iii−i−iii−i−iii11-1-1ii−i−i-1-111-1-111-1-111−i−iiiii−i−i11-1-1ζ3ζ3−ζ3−ζ3−ζ−ζζζζζ−ζ−ζ−ζ3−ζ3ζ3ζ3−ζ3−ζ3ζ3ζ3ζζ−ζ−ζ−ζ−ζζζζ3ζ3−ζ3−ζ3
χ241111-1-1-111-1-1-11-11-1iiii−i−i−i−i−i−iii−i−iii−i−iii−i−iii11-1-1ii−i−i-1-111-1-111-1-111−i−iiiii−i−i11-1-1−ζ3−ζ3ζ3ζ3ζζ−ζ−ζ−ζ−ζζζζ3ζ3−ζ3−ζ3ζ3ζ3−ζ3−ζ3−ζ−ζζζζζ−ζ−ζ−ζ3−ζ3ζ3ζ3
χ251111-1-1-111-1-1-11-11-1−i−i−i−iiiiiii−i−iii−i−iii−i−iii−i−i11-1-1−i−iii-1-111-1-11111-1-1−i−iiiii−i−i-1-111ζζ−ζ−ζ−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ3−ζ3−ζ−ζζζζζ−ζ−ζ−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ3−ζ3−ζ−ζζζ
χ261111-1-1-111-1-1-11-11-1−i−i−i−iiiiiii−i−iii−i−iii−i−iii−i−i11-1-1−i−iii-1-111-1-11111-1-1−i−iiiii−i−i-1-111−ζ−ζζζζ3ζ3−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζζ−ζ−ζ−ζ−ζζζζ3ζ3−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζζ−ζ−ζ
χ271111-1-1-111-1-1-11-11-1−i−i−i−iiiiiii−i−iii−i−iii−i−iii−i−i11-1-1−i−iii-1-111-1-111-1-111ii−i−i−i−iii11-1-1ζζ−ζ−ζ−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ3−ζ3−ζ−ζζζ−ζ−ζζζζ3ζ3−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζζ−ζ−ζ
χ281111-1-1-111-1-1-11-11-1−i−i−i−iiiiiii−i−iii−i−iii−i−iii−i−i11-1-1−i−iii-1-111-1-111-1-111ii−i−i−i−iii11-1-1−ζ−ζζζζ3ζ3−ζ3−ζ3−ζ3−ζ3ζ3ζ3ζζ−ζ−ζζζ−ζ−ζ−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ3−ζ3−ζ−ζζζ
χ291111-1-1-111-1-1-11-11-1−i−i−i−iiiii−i−iii−i−iii−i−iii−i−iii11-1-1−i−iii11-1-111-1-111-1-1−i−iii−i−iii11-1-1ζ3ζ3−ζ3−ζ3ζζ−ζ−ζζζ−ζ−ζζ3ζ3−ζ3−ζ3ζ3ζ3−ζ3−ζ3ζζ−ζ−ζζζ−ζ−ζζ3ζ3−ζ3−ζ3
χ301111-1-1-111-1-1-11-11-1−i−i−i−iiiii−i−iii−i−iii−i−iii−i−iii11-1-1−i−iii11-1-111-1-111-1-1−i−iii−i−iii11-1-1−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ−ζζζ−ζ3−ζ3ζ3ζ3−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ−ζζζ−ζ3−ζ3ζ3ζ3
χ311111-1-1-111-1-1-11-11-1−i−i−i−iiiii−i−iii−i−iii−i−iii−i−iii11-1-1−i−iii11-1-111-1-1-1-111ii−i−iii−i−i-1-111ζ3ζ3−ζ3−ζ3ζζ−ζ−ζζζ−ζ−ζζ3ζ3−ζ3−ζ3−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ−ζζζ−ζ3−ζ3ζ3ζ3
χ321111-1-1-111-1-1-11-11-1−i−i−i−iiiii−i−iii−i−iii−i−iii−i−iii11-1-1−i−iii11-1-111-1-1-1-111ii−i−iii−i−i-1-111−ζ3−ζ3ζ3ζ3−ζ−ζζζ−ζ−ζζζ−ζ3−ζ3ζ3ζ3ζ3ζ3−ζ3−ζ3ζζ−ζ−ζζζ−ζ−ζζ3ζ3−ζ3−ζ3
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χ34222222222222222222222222-2-2-2-22222-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-22222000000000000000000000000000000000000000000000000
χ352222222222222222-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2-2-2-2-2-2-22222-2-2-2-22222000000000000000000000000000000000000000000000000
χ362222222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-22222-2-2-2-222222222-2-2-2-2000000000000000000000000000000000000000000000000
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χ382222-2-2-222-2-2-22-22-22i2i2i2i−2i−2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i-2-222−2i−2i2i2i-2-22222-2-2000000000000000000000000000000000000000000000000
χ392222-2-2-222-2-2-22-22-2−2i−2i−2i−2i2i2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i-2-2222i2i−2i−2i-2-22222-2-2000000000000000000000000000000000000000000000000
χ402222-2-2-222-2-2-22-22-2−2i−2i−2i−2i2i2i2i2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i-2-2222i2i−2i−2i22-2-2-2-222000000000000000000000000000000000000000000000000
χ41222-222-2-2-22-2-2-2-22222-2-222-2-22i−2i2i−2i00002i−2i2i−2i0000000000002i−2i2i−2i0000000000000000000000000000000000001−i−1+i1−i−1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i1+i−1−i1+i−1−i
χ42222-222-2-2-22-2-2-2-22222-2-222-2-22i−2i2i−2i00002i−2i2i−2i0000000000002i−2i2i−2i000000000000000000000000000000000000−1+i1−i−1+i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i−1−i1+i−1−i1+i
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χ44222-222-2-2-22-2-2-2-22222-2-222-2-2−2i2i−2i2i0000−2i2i−2i2i000000000000−2i2i−2i2i000000000000000000000000000000000000−1−i1+i−1−i1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i−1+i1−i−1+i1−i
χ45222-222-2-2-22-2-2-2-222-2-222-2-2222i−2i2i−2i00002i−2i2i−2i000000000000−2i2i−2i2i0000000000000000000000000000000000001−i−1+i1−i−1+i−1+i1−i−1+i1−i1+i−1−i1+i−1−i−1−i1+i−1−i1+i
χ46222-222-2-2-22-2-2-2-222-2-222-2-2222i−2i2i−2i00002i−2i2i−2i000000000000−2i2i−2i2i000000000000000000000000000000000000−1+i1−i−1+i1−i1−i−1+i1−i−1+i−1−i1+i−1−i1+i1+i−1−i1+i−1−i
χ47222-222-2-2-22-2-2-2-222-2-222-2-222−2i2i−2i2i0000−2i2i−2i2i0000000000002i−2i2i−2i0000000000000000000000000000000000001+i−1−i1+i−1−i−1−i1+i−1−i1+i1−i−1+i1−i−1+i−1+i1−i−1+i1−i
χ48222-222-2-2-22-2-2-2-222-2-222-2-222−2i2i−2i2i0000−2i2i−2i2i0000000000002i−2i2i−2i000000000000000000000000000000000000−1−i1+i−1−i1+i1+i−1−i1+i−1−i−1+i1−i−1+i1−i1−i−1+i1−i−1+i
χ49222-2-2-22-2-2-222-222-22i2i−2i−2i−2i−2i2i2i2-2-2200002-2-22000000000000−2i2i2i−2i000000000000000000000000000000000000i2−i2−i2i2−222−2i2−i2−i2i22−2−22
χ50222-2-2-22-2-2-222-222-22i2i−2i−2i−2i−2i2i2i2-2-2200002-2-22000000000000−2i2i2i−2i000000000000000000000000000000000000−i2i2i2−i22−2−22−i2i2i2−i2−222−2
χ51222-2-2-22-2-2-222-222-22i2i−2i−2i−2i−2i2i2i-222-20000-222-20000000000002i−2i−2i2i0000000000000000000000000000000000002−2−22i2−i2−i2i2−222−2i2−i2−i2i2
χ52222-2-2-22-2-2-222-222-22i2i−2i−2i−2i−2i2i2i-222-20000-222-20000000000002i−2i−2i2i000000000000000000000000000000000000−222−2−i2i2i2−i22−2−22−i2i2i2−i2
χ53222-2-2-22-2-2-222-222-2−2i−2i2i2i2i2i−2i−2i2-2-2200002-2-220000000000002i−2i−2i2i000000000000000000000000000000000000i2−i2−i2i22−2−22i2−i2−i2i2−222−2
χ54222-2-2-22-2-2-222-222-2−2i−2i2i2i2i2i−2i−2i2-2-2200002-2-220000000000002i−2i−2i2i000000000000000000000000000000000000−i2i2i2−i2−222−2−i2i2i2−i22−2−22
χ55222-2-2-22-2-2-222-222-2−2i−2i2i2i2i2i−2i−2i-222-20000-222-2000000000000−2i2i2i−2i0000000000000000000000000000000000002−2−22−i2i2i2−i2−222−2−i2i2i2−i2
χ56222-2-2-22-2-2-222-222-2−2i−2i2i2i2i2i−2i−2i-222-20000-222-2000000000000−2i2i2i−2i000000000000000000000000000000000000−222−2i2−i2−i2i22−2−22i2−i2−i2i2
χ5722-2-22-222-2-22-22-2-220000000022222222-2-2-2-2-2-2-2-22-22-20000000000002-22-200002-22-2000000000000000000000000000000000000
χ5822-2-22-222-2-22-22-2-220000000022222222-2-2-2-2-2-2-2-22-22-2000000000000-22-220000-22-22000000000000000000000000000000000000
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χ6022-2-22-222-2-22-22-2-22000000002222-2-2-2-2-2-2-2-22222-22-220000000000000000−2i2i−2i2i0000−2i2i−2i2i00000000000000000000000000000000
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χ6222-2-22-222-2-22-22-2-2200000000-2-2-2-222222222-2-2-2-2-22-220000000000000000−2i2i−2i2i00002i−2i2i−2i00000000000000000000000000000000
χ6322-2-22-222-2-22-22-2-2200000000-2-2-2-2-2-2-2-2222222222-22-20000000000002-22-20000-22-22000000000000000000000000000000000000
χ6422-2-22-222-2-22-22-2-2200000000-2-2-2-2-2-2-2-2222222222-22-2000000000000-22-2200002-22-2000000000000000000000000000000000000
χ6522-2-2-22-22-22-2222-2-2000000002i2i−2i−2i2i2i−2i−2i−2i−2i2i2i−2i−2i2i2i2-2-220000000000002-2-2200002i−2i−2i2i000000000000000000000000000000000000
χ6622-2-2-22-22-22-2222-2-2000000002i2i−2i−2i2i2i−2i−2i−2i−2i2i2i−2i−2i2i2i2-2-22000000000000-222-20000−2i2i2i−2i000000000000000000000000000000000000
χ6722-2-2-22-22-22-2222-2-2000000002i2i−2i−2i−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i-222-200000000000000002-2-220000−2i2i2i−2i00000000000000000000000000000000
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χ7222-2-2-22-22-22-2222-2-200000000−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i2-2-22000000000000-222-200002i−2i−2i2i000000000000000000000000000000000000
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χ832-22-2-222-22-2-222-2-222i−2i2i−2i−2i2i−2i2i0000-222-20000-222-20000000000002i−2i−2i2i0000000000000000i2−i2−i2i2−222−2i2−i2−i2i22−2−220000000000000000
χ842-22-2-222-22-2-222-2-222i−2i2i−2i−2i2i−2i2i0000-222-20000-222-20000000000002i−2i−2i2i0000000000000000−i2i2i2−i22−2−22−i2i2i2−i2−222−20000000000000000
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χ8944-444-4-4-44-4-44-44-44000000004i−4i4i−4i0000−4i4i−4i4i00000000000000000000000000000000000000000000000000000000000000000000
χ9044-444-4-4-44-4-44-44-4400000000−4i4i−4i4i00004i−4i4i−4i00000000000000000000000000000000000000000000000000000000000000000000
χ9144-44-444-4444-4-4-4-4-4000000004-4-440000-444-400000000000000000000000000000000000000000000000000000000000000000000
χ9244-44-444-4444-4-4-4-4-400000000-444-400004-4-4400000000000000000000000000000000000000000000000000000000000000000000
χ934-4444-444-44-44-4-4-4-44-4-444-4-4400000000000000000000000000000000000000000000000000000000000000000000000000000000
χ944-4444-444-44-44-4-4-4-4-444-4-444-400000000000000000000000000000000000000000000000000000000000000000000000000000000
χ954-444-44-44-4-44-4-44-444i−4i−4i4i−4i4i4i−4i00000000000000000000000000000000000000000000000000000000000000000000000000000000
χ964-444-44-44-4-44-4-44-44−4i4i4i−4i4i−4i−4i4i00000000000000000000000000000000000000000000000000000000000000000000000000000000
χ974-4-4444-4-4-4-4444-44-40000000000004i−4i4i−4i0000−4i4i−4i4i0000000000000000000000000000000000000000000000000000000000000000
χ984-4-4444-4-4-4-4444-44-4000000000000−4i4i−4i4i00004i−4i4i−4i0000000000000000000000000000000000000000000000000000000000000000
χ994-4-44-4-44-4-44-4-444440000000000004-4-440000-444-40000000000000000000000000000000000000000000000000000000000000000
χ1004-4-44-4-44-4-44-4-44444000000000000-444-400004-4-440000000000000000000000000000000000000000000000000000000000000000
χ1014-4-4-444444-4-4-4-444-400000000000000000000000000004i−4i4i−4i00000000000000000000000000000000000000000000000000000000
χ1024-4-4-444444-4-4-4-444-40000000000000000000000000000−4i4i−4i4i00000000000000000000000000000000000000000000000000000000
χ1034-4-4-4-4-4-444444-4-44400000000000000000000000000004-4-4400000000000000000000000000000000000000000000000000000000
χ1044-4-4-4-4-4-444444-4-4440000000000000000000000000000-444-400000000000000000000000000000000000000000000000000000000

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