Finite Group Databasebeta

← Group #10702897

Character table — Group #10702897

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size1111111122222222222222222222222222224444444444444444444444444444444488888888888888888888888824242424242424242424242424242424
order12222222222222222222366666666666666644444444666666661212121212121212121212121212121244444444121212121212121212121212121212122244444444444444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ5111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ6111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ7111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ8111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ911-1-111-1-111111-1-1-1-1-11-11111111-1-1-1-1-1-1-1-111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i1-11-1ii−i−i11-1-1ii−i−i
χ1011-1-111-1-111111-1-1-1-1-11-11111111-1-1-1-1-1-1-1-111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1ii−i−iii−i−iiiii−i−i−i−iiiii−i−i−i−i-11-11−i−iii-1-111−i−iii
χ1111-1-111-1-111111-1-1-1-1-11-11111111-1-1-1-1-1-1-1-111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii1-11-1−i−iii11-1-1−i−iii
χ1211-1-111-1-111111-1-1-1-1-11-11111111-1-1-1-1-1-1-1-111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1−i−iii−i−iii−i−i−i−iiiii−i−i−i−iiiii-11-11ii−i−i-1-111ii−i−i
χ1311-1-111-1-111111-1-1-1-1-11-11111111-1-1-1-1-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii1-11-1ii−i−i-1-111−i−iii
χ1411-1-111-1-111111-1-1-1-1-11-11111111-1-1-1-1-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111ii−i−i−i−iiiiiii−i−i−i−i−i−i−i−iiiii-11-11−i−iii11-1-1ii−i−i
χ1511-1-111-1-111111-1-1-1-1-11-11111111-1-1-1-1-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i1-11-1−i−iii-1-111ii−i−i
χ1611-1-111-1-111111-1-1-1-1-11-11111111-1-1-1-1-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111−i−iiiii−i−i−i−i−i−iiiiiiiii−i−i−i−i-11-11ii−i−i11-1-1−i−iii
χ1722222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ1822222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-211111111111111110000000000000000
χ1922222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-111111111111111112222-2-2-2-2-1-1-1-1-1-1-1-1111111110000000000000000
χ2022222222222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-11111111111111111-2-2-2-2222211111111-1-1-1-1-1-1-1-10000000000000000
χ212222222222-2-2-22-2-2-22-2-2222222222222222200000000-2-2-2-2-2-2-2-200000000000000002-22-2000022-2-222-2-2000000000000000000000000
χ222222222222-2-2-22-2-2-22-2-2222222222222222200000000-2-2-2-2-2-2-2-20000000000000000-22-220000-2-222-2-222000000000000000000000000
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χ242222222222-2-2-22-2-2-22-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000011111111−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3-22-22000011-1-111-1-1i3i3−i3−i3i3i3−i3−i30000000000000000
χ252222222222-2-2-22-2-2-22-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000011111111i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i32-22-20000-1-111-1-111i3i3−i3−i3i3i3−i3−i30000000000000000
χ262222222222-2-2-22-2-2-22-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000011111111i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3-22-22000011-1-111-1-1−i3−i3i3i3−i3−i3i3i30000000000000000
χ2722222222-2-222-2-22-2-2-2-22222-2-2-2-222-2-222-2-220000000022-2-222-2-2000000000000000000000000000000000000000000002-22-200000000
χ2822222222-2-222-2-22-2-2-2-22222-2-2-2-222-2-222-2-220000000022-2-222-2-200000000000000000000000000000000000000000000-22-2200000000
χ2922222222-2-2-2-22-2-222-22-2222-2-2-2-222-2-222-2-2200000000-2-222-2-222000000000000000000000000000000000000000022-2-2000000000000
χ3022222222-2-2-2-22-2-222-22-2222-2-2-2-222-2-222-2-2200000000-2-222-2-2220000000000000000000000000000000000000000-2-222000000000000
χ3122-2-222-2-222222-2-2-2-2-22-2-1-1-1-1-1-1-111111111-12222-2-2-2-2-1-1-1-11111-1-1-1-1-1-1-1-1111111112i2i−2i−2i2i2i−2i−2i−i−i−i−iiiii−i−i−i−iiiii0000000000000000
χ3222-2-222-2-222222-2-2-2-2-22-2-1-1-1-1-1-1-111111111-12222-2-2-2-2-1-1-1-11111-1-1-1-1-1-1-1-111111111−2i−2i2i2i−2i−2i2i2iiiii−i−i−i−iiiii−i−i−i−i0000000000000000
χ3322-2-222-2-222222-2-2-2-2-22-2-1-1-1-1-1-1-111111111-1-2-2-2-22222-1-1-1-1111111111111-1-1-1-1-1-1-1-12i2i−2i−2i−2i−2i2i2i−i−i−i−iiiiiiiii−i−i−i−i0000000000000000
χ3422-2-222-2-222222-2-2-2-2-22-2-1-1-1-1-1-1-111111111-1-2-2-2-22222-1-1-1-1111111111111-1-1-1-1-1-1-1-1−2i−2i2i2i2i2i−2i−2iiiii−i−i−i−i−i−i−i−iiiii0000000000000000
χ3522-2-222-2-222-2-2-2-2222-2-222222222-2-2-2-2-2-2-2-2200000000-2-2-2-2222200000000000000002i−2i−2i2i00002i2i−2i−2i−2i−2i2i2i000000000000000000000000
χ3622-2-222-2-222-2-2-2-2222-2-222222222-2-2-2-2-2-2-2-2200000000-2-2-2-222220000000000000000−2i2i2i−2i0000−2i−2i2i2i2i2i−2i−2i000000000000000000000000
χ3722-2-222-2-222-2-2-2-2222-2-22-1-1-1-1-1-1-111111111-1000000001111-1-1-1-1−i3−i3−i3−i3i3i3i3i3i3i3i3i3−i3−i3−i3−i32i−2i−2i2i0000−i−iiiii−i−i33−3−3−3−3330000000000000000
χ3822-2-222-2-222-2-2-2-2222-2-22-1-1-1-1-1-1-111111111-1000000001111-1-1-1-1−i3−i3−i3−i3i3i3i3i3i3i3i3i3−i3−i3−i3−i3−2i2i2i−2i0000ii−i−i−i−iii−3−33333−3−30000000000000000
χ3922-2-222-2-222-2-2-2-2222-2-22-1-1-1-1-1-1-111111111-1000000001111-1-1-1-1i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i32i−2i−2i2i0000−i−iiiii−i−i−3−33333−3−30000000000000000
χ4022-2-222-2-222-2-2-2-2222-2-22-1-1-1-1-1-1-111111111-1000000001111-1-1-1-1i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i3−2i2i2i−2i0000ii−i−i−i−iii33−3−3−3−3330000000000000000
χ4122-2-222-2-2-2-222-22-2222-2-2222-2-2-2-2-2-222-2-22220000000022-2-2-2-222000000000000000000000000000000000000000000002i−2i−2i2i00000000
χ4222-2-222-2-2-2-222-22-2222-2-2222-2-2-2-2-2-222-2-22220000000022-2-2-2-22200000000000000000000000000000000000000000000−2i2i2i−2i00000000
χ4322-2-222-2-2-2-2-2-2222-2-2222222-2-2-2-2-2-222-2-222200000000-2-22222-2-200000000000000000000000000000000000000002-2-22000000000000
χ4422-2-222-2-2-2-2-2-2222-2-2222222-2-2-2-2-2-222-2-222200000000-2-22222-2-20000000000000000000000000000000000000000-222-2000000000000
χ452-222-22-2-22-22-222-22-2-2-2222-222-2-2-2-22222-2-2-22i2i−2i−2i2i2i−2i−2i2-22-22-22-22i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i0000000000000000000000000000000000000000
χ462-222-22-2-22-22-222-22-2-2-2222-222-2-2-2-22222-2-2-2−2i−2i2i2i−2i−2i2i2i2-22-22-22-2−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000000000000000
χ472-222-22-2-22-22-222-22-2-2-22-1-11-1-11111-1-1-1-11112i2i−2i−2i2i2i−2i−2i-11-11-11-11−i−iii−i−iii−i−iii−i−iii00000000−i3i3−i3i3−i3i3−i3i33−33−33−33−30000000000000000
χ482-222-22-2-22-22-222-22-2-2-22-1-11-1-11111-1-1-1-11112i2i−2i−2i2i2i−2i−2i-11-11-11-11−i−iii−i−iii−i−iii−i−iii00000000i3−i3i3−i3i3−i3i3−i3−33−33−33−330000000000000000
χ492-222-22-2-22-22-222-22-2-2-22-1-11-1-11111-1-1-1-1111−2i−2i2i2i−2i−2i2i2i-11-11-11-11ii−i−iii−i−iii−i−iii−i−i00000000−i3i3−i3i3−i3i3−i3i3−33−33−33−330000000000000000
χ502-222-22-2-22-22-222-22-2-2-22-1-11-1-11111-1-1-1-1111−2i−2i2i2i−2i−2i2i2i-11-11-11-11ii−i−iii−i−iii−i−iii−i−i00000000i3−i3i3−i3i3−i3i3−i33−33−33−33−30000000000000000
χ512-222-22-2-22-2-22-222-22-22-222-222-2-2-2-22222-2-2-200000000-22-22-22-22000000000000000000002i−2i2i−2i000000002i−2i−2i2i2i−2i−2i2i0000000000000000
χ522-222-22-2-22-2-22-222-22-22-222-222-2-2-2-22222-2-2-200000000-22-22-22-2200000000000000000000−2i2i−2i2i00000000−2i2i2i−2i−2i2i2i−2i0000000000000000
χ532-222-22-2-22-2-22-222-22-22-2-1-11-1-11111-1-1-1-1111000000001-11-11-11-133−3−3−3−33333−3−3−3−33300002i−2i2i−2i−i3i3i3−i3−i3i3i3−i3−iii−i−iii−i0000000000000000
χ542-222-22-2-22-2-22-222-22-22-2-1-11-1-11111-1-1-1-1111000000001-11-11-11-133−3−3−3−33333−3−3−3−3330000−2i2i−2i2ii3−i3−i3i3i3−i3−i3i3i−i−iii−i−ii0000000000000000
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χ572-222-22-2-2-222-2-2-2-2-2222222-2-2-222-2-2-2-22222-2000000002-2-222-2-2200000000000000000000000000000000000000000000000000002-22-2
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χ622-2-2-2-22222-22-22-22-222-2-222-222-2-222-2-2-2-222-2−2i−2i2i2i2i2i−2i−2i2-22-2-22-22−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i0000000000000000000000000000000000000000
χ632-2-2-2-22222-22-22-22-222-2-2-1-11-1-111-1-11111-1-112i2i−2i−2i−2i−2i2i2i-11-111-11-1−i−iii−i−iiiii−i−iii−i−i000000003−33−3−33−33i3−i3i3−i3−i3i3−i3i30000000000000000
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χ702-2-2-2-22222-2-22-2-2-22-2222-1-11-1-111-1-11111-1-11000000001-11-1-11-1133−3−3−3−333−3−33333−3−30000-222-23−3−33−333−31-1-11-111-10000000000000000
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.