Finite Group Databasebeta

← Group #10822559

Character table — Group #10822559

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size1111111122222222222222222222222222224444444444444444444444444444444488888888888888888888888824242424242424242424242424242424
order12224444222222344444466666661212121212121212444444446666121212121212121212121212121212121212121244448888121212121212121224242424242424242244444444448888
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
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
χ7111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-11111-1-1-1-1
χ8111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111
χ91111-1-1-1-11-1-1-1-11111-1-111-1-1-1-111111-1-1-1-1111111-1-1-1-11-1-1111-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-111-1-111-1-111-1-111-1-1
χ101111-1-1-1-11-1-1-1-11111-1-111-1-1-1-111111-1-1-1-1111111-1-1-1-11-1-1111-1-111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-111-1-111-1-111-1-111
χ111111-1-1-1-11-1-1-1-11111-1-111-1-1-1-111111-1-1-1-1111111-1-1-1-11-1-1111-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-111-1-111
χ121111-1-1-1-11-1-1-1-11111-1-111-1-1-1-111111-1-1-1-1111111-1-1-1-11-1-1111-1-111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111-1-111-1-11111-1-111-1-1
χ131111-1-1-1-11-1-1-1-11111-1-111-1-1-1-111111-1-1-1-111-1-1-1-111111-1-1111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-11111-1-1
χ141111-1-1-1-11-1-1-1-11111-1-111-1-1-1-111111-1-1-1-111-1-1-1-111111-1-1111-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-11111-1-111-1-1-1-111
χ151111-1-1-1-11-1-1-1-11111-1-111-1-1-1-111111-1-1-1-111-1-1-1-111111-1-1111-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-111111111-1-1-1-111-1-1-1-11111-1-1-1-111
χ161111-1-1-1-11-1-1-1-11111-1-111-1-1-1-111111-1-1-1-111-1-1-1-111111-1-1111-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-1-1-11111-1-1
χ1722222222222222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ1822222222222222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-211111111111111110000000000000000
χ1922222222222222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111111111112222-2-2-2-2-1-1-1-1-1-1-1-1111111110000000000000000
χ2022222222222222-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111-2-2-2-2222211111111-1-1-1-1-1-1-1-10000000000000000
χ21222222222-2-2-2-222-2-222-2-2-2-2-2-2222-2-22222-2-2000000002-2-22-2-222000000000000000000000000000000000000000000002-22-200000000
χ22222222222-2-2-2-222-2-222-2-2-2-2-2-2222-2-22222-2-2000000002-2-22-2-22200000000000000000000000000000000000000000000-22-2200000000
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χ2422222222-222-2-2-222-2-2-22-222222222222222200000000-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000000000-22-220000
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χ2622222222-2-2-222-22-22-2-2-22-2-2-2-2222-2-22222-2-200000000-222-222-2-20000000000000000-22-220000-2-222-2-222000000000000000000000000
χ2722222222-2-2-222-2-1-22-2-2-221111-1-1-111-1-1-1-111000000001-1-11-1-1113333−3−3−3−33333−3−3−3−32-22-20000-1-111-1-11133−3−333−3−30000000000000000
χ2822222222-2-2-222-2-1-22-2-2-221111-1-1-111-1-1-1-111000000001-1-11-1-1113333−3−3−3−33333−3−3−3−3-22-22000011-1-111-1-1−3−333−3−3330000000000000000
χ2922222222-2-2-222-2-1-22-2-2-221111-1-1-111-1-1-1-111000000001-1-11-1-111−3−3−3−33333−3−3−3−333332-22-20000-1-111-1-111−3−333−3−3330000000000000000
χ3022222222-2-2-222-2-1-22-2-2-221111-1-1-111-1-1-1-111000000001-1-11-1-111−3−3−3−33333−3−3−3−33333-22-22000011-1-111-1-133−3−333−3−30000000000000000
χ312222-2-2-2-22222222-2-2-2-2-2-22222222-2-2-2-2-2-2-2-2000000002222-2-2-2-2000000000000000000000000000000000000000000002-2-2200000000
χ322222-2-2-2-22222222-2-2-2-2-2-22222222-2-2-2-2-2-2-2-2000000002222-2-2-2-200000000000000000000000000000000000000000000-222-200000000
χ332222-2-2-2-22-2-2-2-22-122-2-2221111-1-1-1-1-11111-1-12222-2-2-2-2-111-1-1-111-1-1-1-1-1-1-1-11111111122-2-222-2-2-1-1-1-11111-1-1-1-111110000000000000000
χ342222-2-2-2-22-2-2-2-22-122-2-2221111-1-1-1-1-11111-1-12222-2-2-2-2-111-1-1-111-1-1-1-1-1-1-1-111111111-2-222-2-2221111-1-1-1-11111-1-1-1-10000000000000000
χ352222-2-2-2-22-2-2-2-22-122-2-2221111-1-1-1-1-11111-1-1-2-2-2-22222-111-1-1-11111111111-1-1-1-1-1-1-1-122-2-2-2-222-1-1-1-111111111-1-1-1-10000000000000000
χ362222-2-2-2-22-2-2-2-22-122-2-2221111-1-1-1-1-11111-1-1-2-2-2-22222-111-1-1-11111111111-1-1-1-1-1-1-1-1-2-22222-2-21111-1-1-1-1-1-1-1-111110000000000000000
χ372222-2-2-2-2-222-2-2-22-2222-222222222-2-2-2-2-2-2-2-200000000-2-2-2-2222200000000000000002-2-22000022-2-2-2-222000000000000000000000000
χ382222-2-2-2-2-222-2-2-22-2222-222222222-2-2-2-2-2-2-2-200000000-2-2-2-222220000000000000000-222-20000-2-22222-2-2000000000000000000000000
χ392222-2-2-2-2-222-2-2-2-1-2222-22-1-1-1-1-1-1-111111111000000001111-1-1-1-13333−3−3−3−3−3−3−3−333332-2-220000-1-11111-1-133−3−3−3−3330000000000000000
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χ422222-2-2-2-2-222-2-2-2-1-2222-22-1-1-1-1-1-1-111111111000000001111-1-1-1-1−3−3−3−333333333−3−3−3−3-222-2000011-1-1-1-11133−3−3−3−3330000000000000000
χ432222-2-2-2-2-2-2-222-222-2222-2-2-2-2-222222-2-2-2-22200000000-222-2-2-2220000000000000000000000000000000000000000000000002-2-220000
χ442222-2-2-2-2-2-2-222-222-2222-2-2-2-2-222222-2-2-2-22200000000-222-2-2-222000000000000000000000000000000000000000000000000-222-20000
χ4522-2-222-2-222-22-2-22222-2-2-222-2-22-2-22222-2-2-2-20000000022-2-22-22-200000000000000000000000000000000000000002-22-2000000000000
χ4622-2-222-2-222-22-2-22222-2-2-222-2-22-2-22222-2-2-2-20000000022-2-22-22-20000000000000000000000000000000000000000-22-22000000000000
χ4722-2-222-2-22-22-22-22-2-22-222-2-2222-2-2-2-222-2-2222i2i−2i−2i2i2i−2i−2i2-22-2-222-22i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i0000000000000000000000000000000000000000
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χ4922-2-222-2-22-22-22-2-1-2-22-22211-1-1-11111-1-111-1-12i2i−2i−2i2i2i−2i−2i-11-111-1-11−i−iii−i−iii−i−iii−i−iii000000003−33−33−33−3−i3i3−i3i3−i3i3−i3i30000000000000000
χ5022-2-222-2-22-22-22-2-1-2-22-22211-1-1-11111-1-111-1-12i2i−2i−2i2i2i−2i−2i-11-111-1-11−i−iii−i−iii−i−iii−i−iii00000000−33−33−33−33i3−i3i3−i3i3−i3i3−i30000000000000000
χ5122-2-222-2-22-22-22-2-1-2-22-22211-1-1-11111-1-111-1-1−2i−2i2i2i−2i−2i2i2i-11-111-1-11ii−i−iii−i−iii−i−iii−i−i000000003−33−33−33−3i3−i3i3−i3i3−i3i3−i30000000000000000
χ5222-2-222-2-22-22-22-2-1-2-22-22211-1-1-11111-1-111-1-1−2i−2i2i2i−2i−2i2i2i-11-111-1-11ii−i−iii−i−iii−i−iii−i−i00000000−33−33−33−33−i3i3−i3i3−i3i3−i3i30000000000000000
χ5322-2-222-2-2-22-2-22222-2-22-2222-2-22-2-22222-2-2-2-200000000-2-222-22-22000000000000000000002i−2i2i−2i000000002i−2i−2i2i2i−2i−2i2i0000000000000000
χ5422-2-222-2-2-22-2-22222-2-22-2222-2-22-2-22222-2-2-2-200000000-2-222-22-2200000000000000000000−2i2i−2i2i00000000−2i2i2i−2i−2i2i2i−2i0000000000000000
χ5522-2-222-2-2-22-2-222-12-2-22-22-1-111-111-1-1-1-111110000000011-1-11-11-1−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i300002i−2i2i−2i−333−3−333−3−iii−i−iii−i0000000000000000
χ5622-2-222-2-2-22-2-222-12-2-22-22-1-111-111-1-1-1-111110000000011-1-11-11-1−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i30000−2i2i−2i2i3−3−333−3−33i−i−iii−i−ii0000000000000000
χ5722-2-222-2-2-22-2-222-12-2-22-22-1-111-111-1-1-1-111110000000011-1-11-11-1i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i300002i−2i2i−2i3−3−333−3−33−iii−i−iii−i0000000000000000
χ5822-2-222-2-2-22-2-222-12-2-22-22-1-111-111-1-1-1-111110000000011-1-11-11-1i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i30000−2i2i−2i2i−333−3−333−3i−i−iii−i−ii0000000000000000
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χ6122-2-2-2-22222-22-2-22-2-2-222222-2-22-2-2-2-2-2-222222i2i−2i−2i−2i−2i2i2i22-2-2-22-222i2i−2i−2i2i2i−2i−2i−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000000000000000
χ6222-2-2-2-22222-22-2-22-2-2-222222-2-22-2-2-2-2-2-22222−2i−2i2i2i2i2i−2i−2i22-2-2-22-22−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i0000000000000000000000000000000000000000
χ6322-2-2-2-22222-22-2-2-1-2-2-2222-1-111-1111111-1-1-1-12i2i−2i−2i−2i−2i2i2i-1-1111-11-1−i−iii−i−iiiii−i−iii−i−i000000003−33−3−33−33−i3i3−i3i3i3−i3i3−i30000000000000000
χ6422-2-2-2-22222-22-2-2-1-2-2-2222-1-111-1111111-1-1-1-12i2i−2i−2i−2i−2i2i2i-1-1111-11-1−i−iii−i−iiiii−i−iii−i−i00000000−33−333−33−3i3−i3i3−i3−i3i3−i3i30000000000000000
χ6522-2-2-2-22222-22-2-2-1-2-2-2222-1-111-1111111-1-1-1-1−2i−2i2i2i2i2i−2i−2i-1-1111-11-1ii−i−iii−i−i−i−iii−i−iii000000003−33−3−33−33i3−i3i3−i3−i3i3−i3i30000000000000000
χ6622-2-2-2-22222-22-2-2-1-2-2-2222-1-111-1111111-1-1-1-1−2i−2i2i2i2i2i−2i−2i-1-1111-11-1ii−i−iii−i−i−i−iii−i−iii00000000−33−333−33−3−i3i3−i3i3i3−i3i3−i30000000000000000
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.