Finite Group Databasebeta

← Group #10702224

Character table — Group #10702224

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size1111111122222222222222222222222222224444444444444444444444444444444488888888888888888888888824242424242424242424242424242424
order12222222222234444444466666661212121212121212444444446666121212121212121212121212121212121212121244448888121212121212121224242424242424242222444444448888
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111
χ5111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ6111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ7111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111111111-1-1-1-111-1-1-1-1
χ8111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-11111
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χ101-1-1111-1-111-1-11111-1-1-1-11-1-1-1-11111111-1-1-1-1iiii−i−i−i−i11-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-1ii−i−i1111-1-1-1-1iiii−i−i−i−i-1-111−ii−i−iii−ii-1-111
χ111-1-1111-1-111-1-11111-1-1-1-11-1-1-1-11111111-1-1-1-1iiii−i−i−i−i11-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-111−i−iii-1-1-1-11111−i−i−i−iiiii11-1-1−iiii−i−i−ii-1-111
χ121-1-1111-1-111-1-11111-1-1-1-11-1-1-1-11111111-1-1-1-1iiii−i−i−i−i11-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-111−i−iii-1-1-1-11111−i−i−i−iiiii-1-111i−i−i−iiii−i11-1-1
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χ151-1-1111-1-111-1-11111-1-1-1-11-1-1-1-11111111-1-1-1-1−i−i−i−iiiii11-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-111ii−i−i-1-1-1-11111iiii−i−i−i−i11-1-1i−i−i−iiii−i-1-111
χ161-1-1111-1-111-1-11111-1-1-1-11-1-1-1-11111111-1-1-1-1−i−i−i−iiiii11-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-111ii−i−i-1-1-1-11111iiii−i−i−i−i-1-111−iiii−i−i−ii11-1-1
χ172222222222222-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-2000000002222-2-2-2-200000000000000000000000000000000000000000000002-22-2000000
χ182222222222222-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2-2000000002222-2-2-2-20000000000000000000000000000000000000000000000-22-22000000
χ19222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ20222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-211111111111111110000000000000000
χ21222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111111111112222-2-2-2-2-1-1-1-1-1-1-1-1111111110000000000000000
χ22222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111-2-2-2-2222211111111-1-1-1-1-1-1-1-10000000000000000
χ2322222222-2-2-2-2222-22-2-22-222222222222222200000000-2-2-2-2-2-2-2-200000000000000000000000000000000000000000000220000-2-20000
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χ2722222222-2-2-2-2-1-2-22-222-22-1-1-1-1-1-1-111111111000000001111-1-1-1-13333−3−3−3−33333−3−3−3−32-22-20000-1-111-1-11133−3−333−3−30000000000000000
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χ2922222222-2-2-2-2-1-2-22-222-22-1-1-1-1-1-1-111111111000000001111-1-1-1-1−3−3−3−33333−3−3−3−333332-22-20000-1-111-1-111−3−333−3−3330000000000000000
χ3022222222-2-2-2-2-1-2-22-222-22-1-1-1-1-1-1-111111111000000001111-1-1-1-1−3−3−3−33333−3−3−3−33333-22-22000011-1-111-1-133−3−333−3−30000000000000000
χ312222-2-2-2-22-22-222-2222-2-2-222-2-22-2-222-2-222-2-2000000002-22-22-22-200000000000000000000000000000000000000002-22-2000000000000
χ322222-2-2-2-22-22-222-2222-2-2-222-2-22-2-222-2-222-2-2000000002-22-22-22-20000000000000000000000000000000000000000-22-22000000000000
χ332222-2-2-2-22-22-22-22-2-2-222222-2-22-2-2-2-222-2-2222i2i−2i−2i2i2i−2i−2i2-22-2-22-222i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i0000000000000000000000000000000000000000
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χ352222-2-2-2-22-22-2-1-22-2-2-2222-1-111-11111-1-111-1-12i2i−2i−2i2i2i−2i−2i-11-111-11-1−i−iii−i−iii−i−iii−i−iii000000003−33−33−33−3−i3i3−i3i3−i3i3−i3i30000000000000000
χ362222-2-2-2-22-22-2-1-22-2-2-2222-1-111-11111-1-111-1-12i2i−2i−2i2i2i−2i−2i-11-111-11-1−i−iii−i−iii−i−iii−i−iii00000000−33−33−33−33i3−i3i3−i3i3−i3i3−i30000000000000000
χ372222-2-2-2-22-22-2-1-22-2-2-2222-1-111-11111-1-111-1-1−2i−2i2i2i−2i−2i2i2i-11-111-11-1ii−i−iii−i−iii−i−iii−i−i000000003−33−33−33−3i3−i3i3−i3i3−i3i3−i30000000000000000
χ382222-2-2-2-22-22-2-1-22-2-2-2222-1-111-11111-1-111-1-1−2i−2i2i2i−2i−2i2i2i-11-111-11-1ii−i−iii−i−iii−i−iii−i−i00000000−33−33−33−33−i3i3−i3i3−i3i3−i3i30000000000000000
χ392222-2-2-2-2-22-2222-2-22-22-2222-2-22-2-222-2-222-2-200000000-22-22-22-22000000000000000000002i−2i2i−2i000000002i−2i−2i2i2i−2i−2i2i0000000000000000
χ402222-2-2-2-2-22-2222-2-22-22-2222-2-22-2-222-2-222-2-200000000-22-22-22-2200000000000000000000−2i2i−2i2i00000000−2i2i2i−2i−2i2i2i−2i0000000000000000
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χ422222-2-2-2-2-22-222-222-22-22-222-2-22-2-2-2-222-2-22200000000-22-222-22-20000000000000000000000000000000000000000000000000000−2i2i−2i2i
χ432222-2-2-2-2-22-22-12-2-22-22-22-1-111-111-1-111-1-111000000001-11-11-11-1−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i300002i−2i2i−2i−333−3−333−3−iii−i−iii−i0000000000000000
χ442222-2-2-2-2-22-22-12-2-22-22-22-1-111-111-1-111-1-111000000001-11-11-11-1−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i30000−2i2i−2i2i3−3−333−3−33i−i−iii−i−ii0000000000000000
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χ462222-2-2-2-2-22-22-12-2-22-22-22-1-111-111-1-111-1-111000000001-11-11-11-1i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i30000−2i2i−2i2i−333−3−333−3i−i−iii−i−ii0000000000000000
χ472-2-2222-2-222-2-22-2-2-22222-2-2-2-2-2222-2-2-2-222220000000022-2-2-2-22200000000000000000000000000000000000000000000002i−2i−2i2i000000
χ482-2-2222-2-222-2-22-2-2-22222-2-2-2-2-2222-2-2-2-222220000000022-2-2-2-2220000000000000000000000000000000000000000000000−2i2i2i−2i000000
χ492-2-2222-2-222-2-2-1222-2-2-2-221111-1-1-1-1-1-1-111112i2i2i2i−2i−2i−2i−2i-1-111-1-111−i−i−i−i−i−i−i−iiiiiiiii22-2-22i2i−2i−2i-1-1-1-11111−i−i−i−iiiii0000000000000000
χ502-2-2222-2-222-2-2-1222-2-2-2-221111-1-1-1-1-1-1-111112i2i2i2i−2i−2i−2i−2i-1-111-1-111−i−i−i−i−i−i−i−iiiiiiiii-2-222−2i−2i2i2i1111-1-1-1-1iiii−i−i−i−i0000000000000000
χ512-2-2222-2-222-2-2-1222-2-2-2-221111-1-1-1-1-1-1-11111−2i−2i−2i−2i2i2i2i2i-1-111-1-111iiiiiiii−i−i−i−i−i−i−i−i22-2-2−2i−2i2i2i-1-1-1-11111iiii−i−i−i−i0000000000000000
χ522-2-2222-2-222-2-2-1222-2-2-2-221111-1-1-1-1-1-1-11111−2i−2i−2i−2i2i2i2i2i-1-111-1-111iiiiiiii−i−i−i−i−i−i−i−i-2-2222i2i−2i−2i1111-1-1-1-1−i−i−i−iiiii0000000000000000
χ532-2-2222-2-2-2-222222-2-222-2-2-2-2-2-22222222-2-2-2-200000000-2-222-2-222000000000000000000000000000000000000000000002i−2i0000−2i2i0000
χ542-2-2222-2-2-2-222222-2-222-2-2-2-2-2-22222222-2-2-2-200000000-2-222-2-22200000000000000000000000000000000000000000000−2i2i00002i−2i0000
χ552-2-2222-2-2-2-2222-2-222-2-222-2-2-2-2222-2-2-2-2222200000000-2-22222-2-200000000000000002-2-22000022-2-2-2-222000000000000000000000000
χ562-2-2222-2-2-2-2222-2-222-2-222-2-2-2-2222-2-2-2-2222200000000-2-22222-2-20000000000000000-222-20000-2-22222-2-2000000000000000000000000
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χ632-2-22-2-2222-2-222-22-222-2-22-2-2222-2-2-2-22222-2-222-2-2-2-2222-2-22-222-222-2-222-2-2-2-222-2-2220000000000000000000000000000000000000000
χ642-2-22-2-2222-2-222-22-222-2-22-2-2222-2-2-2-22222-2-2-2-22222-2-22-2-22-222-2-2-222-2-22222-2-222-2-20000000000000000000000000000000000000000
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χ672-2-22-2-2222-2-22-1-22-222-2-2211-1-1-11111-1-1-1-111-2-22222-2-2-111-11-1-1111-1-111-1-1-1-111-1-111000000003−33−3−33−333−33−3−33−330000000000000000
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χ732-2-22-2-222-222-2-12-2-2-22-22211-1-1-111-1-11111-1-1000000001-1-111-1-1133−3−3−3−333−3−33333−3−300002-2-223−3−33−333−3-111-11-1-110000000000000000
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.