Finite Group Databasebeta

← Group #10703031

Character table — Group #10703031

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size1111111122222222222222222222222222224444444444444444444444444444444488888888888888888888888824242424242424242424242424242424
order1222444422222234444446666666121212121212121266668888888812121212242424242424242424242424242424242244444466661212121212121212121212124444888888888888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ61111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1
χ71111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-11111-1-1-1-1
χ81111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ91111-1-1-1-111-1-1-1-11111-1-1111-1-1-1-111111-1-1-1-111-1-1iiii−i−i−i−i11-1-1iiiiiiii−i−i−i−i−i−i−i−i1-11-1ii−i−i11-1-1iiii−i−i−i−i11-1-111-1-1ii−i−iii−i−i11-1-1
χ101111-1-1-1-111-1-1-1-11111-1-1111-1-1-1-111111-1-1-1-111-1-1iiii−i−i−i−i11-1-1iiiiiiii−i−i−i−i−i−i−i−i1-11-1ii−i−i11-1-1iiii−i−i−i−i11-1-1-1-111−i−iii−i−iii-1-111
χ111111-1-1-1-111-1-1-1-11111-1-1111-1-1-1-111111-1-1-1-111-1-1iiii−i−i−i−i11-1-1iiiiiiii−i−i−i−i−i−i−i−i-11-11−i−iii-1-111−i−i−i−iiiii-1-11111-1-1ii−i−i−i−iii-1-111
χ121111-1-1-1-111-1-1-1-11111-1-1111-1-1-1-111111-1-1-1-111-1-1iiii−i−i−i−i11-1-1iiiiiiii−i−i−i−i−i−i−i−i-11-11−i−iii-1-111−i−i−i−iiiii-1-111-1-111−i−iiiii−i−i11-1-1
χ131111-1-1-1-111-1-1-1-11111-1-1111-1-1-1-111111-1-1-1-111-1-1−i−i−i−iiiii11-1-1−i−i−i−i−i−i−i−iiiiiiiii1-11-1−i−iii11-1-1−i−i−i−iiiii11-1-111-1-1−i−iii−i−iii11-1-1
χ141111-1-1-1-111-1-1-1-11111-1-1111-1-1-1-111111-1-1-1-111-1-1−i−i−i−iiiii11-1-1−i−i−i−i−i−i−i−iiiiiiiii1-11-1−i−iii11-1-1−i−i−i−iiiii11-1-1-1-111ii−i−iii−i−i-1-111
χ151111-1-1-1-111-1-1-1-11111-1-1111-1-1-1-111111-1-1-1-111-1-1−i−i−i−iiiii11-1-1−i−i−i−i−i−i−i−iiiiiiiii-11-11ii−i−i-1-111iiii−i−i−i−i-1-11111-1-1−i−iiiii−i−i-1-111
χ161111-1-1-1-111-1-1-1-11111-1-1111-1-1-1-111111-1-1-1-111-1-1−i−i−i−iiiii11-1-1−i−i−i−i−i−i−i−iiiiiiiii-11-11ii−i−i-1-111iiii−i−i−i−i-1-111-1-111ii−i−i−i−iii11-1-1
χ1722222222222222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ1822222222222222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-211111111111111110000000000000000
χ1922222222222222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-111111111111111112222-2-2-2-2-1-1-1-111111111-1-1-1-10000000000000000
χ2022222222222222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-11111111111111111-2-2-2-222221111-1-1-1-1-1-1-1-111110000000000000000
χ212222222222-2-2-2-22-2-2-222-222-2-2-2-22-2-2-2-2222222-2-200000000-2-222000000000000000000000000000000000000000000002-22-200000000
χ222222222222-2-2-2-22-2-2-222-222-2-2-2-22-2-2-2-2222222-2-200000000-2-22200000000000000000000000000000000000000000000-22-2200000000
χ2322222222-2-222-2-222-2-2-2-2222-2-2-2-22-2-2-2-22222-2-2220000000022-2-200000000000000002-2-22000022-2-200000000-2-2220000000000000000
χ2422222222-2-222-2-222-2-2-2-2222-2-2-2-22-2-2-2-22222-2-2220000000022-2-20000000000000000-222-20000-2-2220000000022-2-20000000000000000
χ2522222222-2-222-2-2-12-2-2-2-22-1-11111-11111-1-1-1-111-1-100000000-1-1113333−3−3−3−33333−3−3−3−32-2-220000-1-11133−3−333−3−311-1-10000000000000000
χ2622222222-2-222-2-2-12-2-2-2-22-1-11111-11111-1-1-1-111-1-100000000-1-1113333−3−3−3−33333−3−3−3−3-222-2000011-1-1−3−333−3−333-1-1110000000000000000
χ2722222222-2-222-2-2-12-2-2-2-22-1-11111-11111-1-1-1-111-1-100000000-1-111−3−3−3−33333−3−3−3−333332-2-220000-1-111−3−333−3−33311-1-10000000000000000
χ2822222222-2-222-2-2-12-2-2-2-22-1-11111-11111-1-1-1-111-1-100000000-1-111−3−3−3−33333−3−3−3−33333-222-2000011-1-133−3−333−3−3-1-1110000000000000000
χ2922222222-2-2-2-2222-222-2-2-2222222222222222-2-2-2-200000000-2-2-2-20000000000000000000000000000000000000000000000002-22-20000
χ3022222222-2-2-2-2222-222-2-2-2222222222222222-2-2-2-200000000-2-2-2-2000000000000000000000000000000000000000000000000-22-220000
χ312222-2-2-2-22222222-2-2-2-2-2-22222222-2-2-2-2-2-2-2-2222200000000-2-2-2-2000000000000000000000000000000000000000000002i−2i−2i2i00000000
χ322222-2-2-2-22222222-2-2-2-2-2-22222222-2-2-2-2-2-2-2-2222200000000-2-2-2-200000000000000000000000000000000000000000000−2i2i2i−2i00000000
χ332222-2-2-2-222-2-2-2-2-1222-2-22-1-11111-1-1-1-1-11111-1-1112i2i2i2i−2i−2i−2i−2i-1-111−i−i−i−i−i−i−i−iiiiiiiii2-22-22i2i−2i−2i-1-111−i−i−i−iiiii-1-1110000000000000000
χ342222-2-2-2-222-2-2-2-2-1222-2-22-1-11111-1-1-1-1-11111-1-1112i2i2i2i−2i−2i−2i−2i-1-111−i−i−i−i−i−i−i−iiiiiiiii-22-22−2i−2i2i2i11-1-1iiii−i−i−i−i11-1-10000000000000000
χ352222-2-2-2-222-2-2-2-2-1222-2-22-1-11111-1-1-1-1-11111-1-111−2i−2i−2i−2i2i2i2i2i-1-111iiiiiiii−i−i−i−i−i−i−i−i2-22-2−2i−2i2i2i-1-111iiii−i−i−i−i-1-1110000000000000000
χ362222-2-2-2-222-2-2-2-2-1222-2-22-1-11111-1-1-1-1-11111-1-111−2i−2i−2i−2i2i2i2i2i-1-111iiiiiiii−i−i−i−i−i−i−i−i-22-222i2i−2i−2i11-1-1−i−i−i−iiiii11-1-10000000000000000
χ372222-2-2-2-2-2-222-2-22-22222-222-2-2-2-222222-2-2-2-2-2-22200000000-2-2220000000000000000000000000000000000000000000000002i−2i−2i2i0000
χ382222-2-2-2-2-2-222-2-22-22222-222-2-2-2-222222-2-2-2-2-2-22200000000-2-222000000000000000000000000000000000000000000000000−2i2i2i−2i0000
χ392222-2-2-2-2-2-2-2-22222-2-22222222222-2-2-2-2-2-2-2-2-2-2-2-2000000002222000000000000000022-2-20000222200000000-2-2-2-20000000000000000
χ402222-2-2-2-2-2-2-2-22222-2-22222222222-2-2-2-2-2-2-2-2-2-2-2-20000000022220000000000000000-2-2220000-2-2-2-20000000022220000000000000000
χ412222-2-2-2-2-2-2-2-222-12-2-2222-1-1-1-1-1-1-111111111111100000000-1-1-1-1−i3−i3−i3−i3i3i3i3i3i3i3i3i3−i3−i3−i3−i322-2-20000-1-1-1-1−i3−i3i3i3i3i3−i3−i311110000000000000000
χ422222-2-2-2-2-2-2-2-222-12-2-2222-1-1-1-1-1-1-111111111111100000000-1-1-1-1−i3−i3−i3−i3i3i3i3i3i3i3i3i3−i3−i3−i3−i3-2-22200001111i3i3−i3−i3−i3−i3i3i3-1-1-1-10000000000000000
χ432222-2-2-2-2-2-2-2-222-12-2-2222-1-1-1-1-1-1-111111111111100000000-1-1-1-1i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i322-2-20000-1-1-1-1i3i3−i3−i3−i3−i3i3i311110000000000000000
χ442222-2-2-2-2-2-2-2-222-12-2-2222-1-1-1-1-1-1-111111111111100000000-1-1-1-1i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i3-2-22200001111−i3−i3i3i3i3i3−i3−i3-1-1-1-10000000000000000
χ4522-2-222-2-22-22-22-2222-2-22-2-2-222-2-2222-2-222-2-22-22-2000000002-2-2200000000000000000000000000000000000000000000000000002i−2i2i−2i
χ4622-2-222-2-22-22-22-2222-2-22-2-2-222-2-2222-2-222-2-22-22-2000000002-2-220000000000000000000000000000000000000000000000000000−2i2i−2i2i
χ4722-2-222-2-22-2-22-222-2-22-222-2-2-2-2222-2-22222-2-22-2-2200000000-22-22000000000000000000002-22-200002-22-22-22-200000000000000000000
χ4822-2-222-2-22-2-22-222-2-22-222-2-2-2-2222-2-22222-2-22-2-2200000000-22-2200000000000000000000-22-220000-22-22-22-2200000000000000000000
χ4922-2-222-2-22-2-22-22-1-2-22-2221111-1-1-111-1-1-1-111-111-1000000001-11-1−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i300002-22-2−i3i3−i3i3-11-11-11-11−i3i3−i3i30000000000000000
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χ5122-2-222-2-22-2-22-22-1-2-22-2221111-1-1-111-1-1-1-111-111-1000000001-11-1i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i300002-22-2i3−i3i3−i3-11-11-11-11i3−i3i3−i30000000000000000
χ5222-2-222-2-22-2-22-22-1-2-22-2221111-1-1-111-1-1-1-111-111-1000000001-11-1i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i30000-22-22−i3i3−i3i31-11-11-11-1−i3i3−i3i30000000000000000
χ5322-2-222-2-2-222-2-2222-222-2-2-2-2-2-2222-2-22222-2-2-222-2000000002-22-200000000000000000000000000000000000000002i−2i2i−2i000000000000
χ5422-2-222-2-2-222-2-2222-222-2-2-2-2-2-2222-2-22222-2-2-222-2000000002-22-20000000000000000000000000000000000000000−2i2i−2i2i000000000000
χ5522-2-222-2-2-22-222-22-22-22-22-2-222-2-2222-2-222-2-2-22-222i2i−2i−2i2i2i−2i−2i-222-22i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i0000000000000000000000000000000000000000
χ5622-2-222-2-2-22-222-22-22-22-22-2-222-2-2222-2-222-2-2-22-22−2i−2i2i2i−2i−2i2i2i-222-2−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000000000000000
χ5722-2-222-2-2-22-222-2-1-22-22-2211-1-111-1-1-111-1-1111-11-12i2i−2i−2i2i2i−2i−2i1-1-11−i−iiiii−i−i−i−iiiii−i−i00000000−i3i3i3−i33−3−333−3−33i3−i3−i3i30000000000000000
χ5822-2-222-2-2-22-222-2-1-22-22-2211-1-111-1-1-111-1-1111-11-12i2i−2i−2i2i2i−2i−2i1-1-11−i−iiiii−i−i−i−iiiii−i−i00000000i3−i3−i3i3−333−3−333−3−i3i3i3−i30000000000000000
χ5922-2-222-2-2-22-222-2-1-22-22-2211-1-111-1-1-111-1-1111-11-1−2i−2i2i2i−2i−2i2i2i1-1-11ii−i−i−i−iiiii−i−i−i−iii00000000−i3i3i3−i3−333−3−333−3i3−i3−i3i30000000000000000
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χ6222-2-2-2-2222-22-22-22-2-222-22-2-222-2-22-2-222-2-2222-22-200000000-222-200000000000000000000−2i2i2i−2i0000−2i2i−2i2i2i−2i2i−2i00000000000000000000
χ6322-2-2-2-2222-22-22-2-1-2-222-2211-1-111-111-1-111-1-1-11-11000000001-1-1133−3−333−3−3−3−333−3−33300002i−2i−2i2i−i3i3i3−i3−ii−iii−ii−i−i3i3i3−i30000000000000000
χ6422-2-2-2-2222-22-22-2-1-2-222-2211-1-111-111-1-111-1-1-11-11000000001-1-1133−3−333−3−3−3−333−3−3330000−2i2i2i−2ii3−i3−i3i3i−ii−i−ii−iii3−i3−i3i30000000000000000
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χ7022-2-2-2-222-222-2-222-22-2-222-2-2-2-222222-2-2-2-222-222-2-2-22222-2-2-22-22-2-22222-2-222-2-2-2-2220000000000000000000000000000000000000000
χ7122-2-2-2-222-222-2-22-1-22-2-2221111-1-1-1-1-11111-1-11-1-1122-2-2-2-2221-11-1-1-11111-1-111-1-1-1-11100000000−i3i3−i3i3−i3i3i3−i3i3−i3−i3i3i3−i3i3−i30000000000000000
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χ7622-2-2-2-222-22-222-222-22-22-2-2-222-2-22-2-222-2-222-22-22000000002-2-220000000000000000000000000000000000000000−2i2i2i−2i000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.