Finite Group Databasebeta

← Group #10702171

Character table — Group #10702171

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size1111111122222222222222222222222222224444444444444444444444444444444488888888888888888888888824242424242424242424242424242424
order1222222222223444444446666666666666664444444412121212121212121212121212121212121212121212121244444444121212121212121212121212121212124444444488888888
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
χ5111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ6111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ7111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111
χ8111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ911-1-111-1-11-1-1111111-1-1-1-1111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1ii−i−iii−i−iii−i−iii−i−i
χ1011-1-111-1-11-1-1111111-1-1-1-1111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-1−i−iii−i−iii−i−iii−i−iii
χ1111-1-111-1-11-1-1111111-1-1-1-1111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111ii−i−i−i−iiiii−i−i−i−iii
χ1211-1-111-1-11-1-1111111-1-1-1-1111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111−i−iiiii−i−i−i−iiiii−i−i
χ1311-1-111-1-11-1-1111111-1-1-1-1111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111ii−i−iii−i−i−i−iii−i−iii
χ1411-1-111-1-11-1-1111111-1-1-1-1111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111−i−iii−i−iiiii−i−iii−i−i
χ1511-1-111-1-11-1-1111111-1-1-1-1111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1ii−i−i−i−iii−i−iiiii−i−i
χ1611-1-111-1-11-1-1111111-1-1-1-1111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1−i−iiiii−i−iii−i−i−i−iii
χ172222222222222-2-2-2-2-2-2-2-2222222222222222000000000000000000000000-2-2-2-2-2-2-2-22-22-2000022-2-222-2-2000000000000000000000000
χ182222222222222-2-2-2-2-2-2-2-2222222222222222000000000000000000000000-2-2-2-2-2-2-2-2-22-220000-2-222-2-222000000000000000000000000
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
χ21222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111111111111111-1-1-1-1-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-1111111110000000000000000
χ22222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111111111111111-1-1-1-1-1-1-1-1-2-2-2-2222211111111-1-1-1-1-1-1-1-10000000000000000
χ23222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3111111112-22-20000-1-111-1-111−i3−i3i3i3−i3−i3i3i30000000000000000
χ24222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i311111111-22-22000011-1-111-1-1i3i3−i3−i3i3i3−i3−i30000000000000000
χ25222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3111111112-22-20000-1-111-1-111i3i3−i3−i3i3i3−i3−i30000000000000000
χ26222222222222-1-2-2-2-2-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i311111111-22-22000011-1-111-1-1−i3−i3i3i3−i3−i3i3i30000000000000000
χ2722222222-2-2-2-2222-2-22-22-22-2-22222-2-2-2-2-2-22200000000000000000000000022-2-222-2-200000000000000000000000000002-22-200000000
χ2822222222-2-2-2-2222-2-22-22-22-2-22222-2-2-2-2-2-22200000000000000000000000022-2-222-2-20000000000000000000000000000-22-2200000000
χ2922222222-2-2-2-22-2-222-22-222-2-22222-2-2-2-2-2-222000000000000000000000000-2-222-2-2220000000000000000000000002-22-2000000000000
χ3022222222-2-2-2-22-2-222-22-222-2-22222-2-2-2-2-2-222000000000000000000000000-2-222-2-222000000000000000000000000-22-22000000000000
χ3122-2-222-2-22-2-222-2-2-2-22222222-2-2-2-2-2-2-2-22222000000000000000000000000-2-2-2-222222-2-22000022-2-2-2-222000000000000000000000000
χ3222-2-222-2-22-2-222-2-2-2-22222222-2-2-2-2-2-2-2-22222000000000000000000000000-2-2-2-22222-222-20000-2-22222-2-2000000000000000000000000
χ3322-2-222-2-22-2-22-12222-2-2-2-2-1-1-111111111-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-111111111-1-1-1-1111122-2-222-2-2-1-1-1-11111-1-1-1-111110000000000000000
χ3422-2-222-2-22-2-22-12222-2-2-2-2-1-1-111111111-1-1-1-12222-2-2-2-2-1-1-1-1-1-1-1-111111111-1-1-1-11111-2-222-2-2221111-1-1-1-11111-1-1-1-10000000000000000
χ3522-2-222-2-22-2-22-12222-2-2-2-2-1-1-111111111-1-1-1-1-2-2-2-2222211111111-1-1-1-1-1-1-1-1-1-1-1-1111122-2-2-2-222-1-1-1-111111111-1-1-1-10000000000000000
χ3622-2-222-2-22-2-22-12222-2-2-2-2-1-1-111111111-1-1-1-1-2-2-2-2222211111111-1-1-1-1-1-1-1-1-1-1-1-11111-2-22222-2-21111-1-1-1-1-1-1-1-111110000000000000000
χ3722-2-222-2-22-2-22-1-2-2-2-22222-1-1-111111111-1-1-1-100000000−i3−i3−i3−i3i3i3i3i3i3i3i3i3−i3−i3−i3−i31111-1-1-1-12-2-220000-1-11111-1-1−i3−i3i3i3i3i3−i3−i30000000000000000
χ3822-2-222-2-22-2-22-1-2-2-2-22222-1-1-111111111-1-1-1-100000000−i3−i3−i3−i3i3i3i3i3i3i3i3i3−i3−i3−i3−i31111-1-1-1-1-222-2000011-1-1-1-111i3i3−i3−i3−i3−i3i3i30000000000000000
χ3922-2-222-2-22-2-22-1-2-2-2-22222-1-1-111111111-1-1-1-100000000i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i31111-1-1-1-12-2-220000-1-11111-1-1i3i3−i3−i3−i3−i3i3i30000000000000000
χ4022-2-222-2-22-2-22-1-2-2-2-22222-1-1-111111111-1-1-1-100000000i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i31111-1-1-1-1-222-2000011-1-1-1-111−i3−i3i3i3i3i3−i3−i30000000000000000
χ4122-2-222-2-2-222-2222-2-2-22-222-2-2-2-2-2-22222-2-22200000000000000000000000022-2-2-2-22200000000000000000000000000002i−2i−2i2i00000000
χ4222-2-222-2-2-222-2222-2-2-22-222-2-2-2-2-2-22222-2-22200000000000000000000000022-2-2-2-2220000000000000000000000000000−2i2i2i−2i00000000
χ4322-2-222-2-2-222-22-2-2222-22-22-2-2-2-2-2-22222-2-222000000000000000000000000-2-22222-2-20000000000000000000000002i−2i−2i2i000000000000
χ4422-2-222-2-2-222-22-2-2222-22-22-2-2-2-2-2-22222-2-222000000000000000000000000-2-22222-2-2000000000000000000000000−2i2i2i−2i000000000000
χ452-222-22-2-222-2-222-22-222-2-2-22222-2-222-2-2-2-2-220000000000000000000000002-22-22-22-200002-22-2000000002-22-22-22-20000000000000000
χ462-222-22-2-222-2-222-22-222-2-2-22222-2-222-2-2-2-2-220000000000000000000000002-22-22-22-20000-22-2200000000-22-22-22-220000000000000000
χ472-222-22-2-222-2-22-22-22-2-222-22222-2-222-2-2-2-2-222i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i-22-22-22-220000000000000000000000000000000000000000
χ482-222-22-2-222-2-22-22-22-2-222-22222-2-222-2-2-2-2-22−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i−2i−2i2i2i-22-22-22-220000000000000000000000000000000000000000
χ492-222-22-2-222-2-2-12-22-222-2-21-1-1-1-111-1-111111-10000000033−3−3−3−33333−3−3−3−333-11-11-11-1100002-22-23−33−33−33−3-11-11-11-110000000000000000
χ502-222-22-2-222-2-2-12-22-222-2-21-1-1-1-111-1-111111-10000000033−3−3−3−33333−3−3−3−333-11-11-11-110000-22-22−33−33−33−331-11-11-11-10000000000000000
χ512-222-22-2-222-2-2-12-22-222-2-21-1-1-1-111-1-111111-100000000−3−33333−3−3−3−33333−3−3-11-11-11-1100002-22-2−33−33−33−33-11-11-11-110000000000000000
χ522-222-22-2-222-2-2-12-22-222-2-21-1-1-1-111-1-111111-100000000−3−33333−3−3−3−33333−3−3-11-11-11-110000-22-223−33−33−33−31-11-11-11-10000000000000000
χ532-222-22-2-222-2-2-1-22-22-2-2221-1-1-1-111-1-111111-12i2i−2i−2i2i2i−2i−2i−i−iii−i−iii−i−iii−i−iii1-11-11-11-1000000003−3−333−3−33−i3i3i3−i3−i3i3i3−i30000000000000000
χ542-222-22-2-222-2-2-1-22-22-2-2221-1-1-1-111-1-111111-12i2i−2i−2i2i2i−2i−2i−i−iii−i−iii−i−iii−i−iii1-11-11-11-100000000−333−3−333−3i3−i3−i3i3i3−i3−i3i30000000000000000
χ552-222-22-2-222-2-2-1-22-22-2-2221-1-1-1-111-1-111111-1−2i−2i2i2i−2i−2i2i2iii−i−iii−i−iii−i−iii−i−i1-11-11-11-1000000003−3−333−3−33i3−i3−i3i3i3−i3−i3i30000000000000000
χ562-222-22-2-222-2-2-1-22-22-2-2221-1-1-1-111-1-111111-1−2i−2i2i2i−2i−2i2i2iii−i−iii−i−iii−i−iii−i−i1-11-11-11-100000000−333−3−333−3−i3i3i3−i3−i3i3i3−i30000000000000000
χ572-222-22-2-2-2-22222-2-222-2-22-2-2-222-2-2-2-22222-220000000000000000000000002-2-222-2-22000000000000000000000000000000002i−2i2i−2i0000
χ582-222-22-2-2-2-22222-2-222-2-22-2-2-222-2-2-2-22222-220000000000000000000000002-2-222-2-2200000000000000000000000000000000−2i2i−2i2i0000
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χ602-222-22-2-2-2-2222-222-2-222-2-2-2-222-2-2-2-22222-22000000000000000000000000-222-2-222-2000000000000000000000000000000000000−2i2i−2i2i
χ612-2-2-2-22222-22-222-22-2-2-222-222-2-222-2-222-2-2-220000000000000000000000002-22-2-22-2200002-2-22000000002-22-2-22-220000000000000000
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χ632-2-2-2-22222-22-22-22-2222-2-2-222-2-222-2-222-2-2-222i2i−2i−2i−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i−2i−2i2i2i−2i−2i2i2i-22-222-22-20000000000000000000000000000000000000000
χ642-2-2-2-22222-22-22-22-2222-2-2-222-2-222-2-222-2-2-22−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i−2i−2i2i2i2i2i−2i−2i2i2i−2i−2i-22-222-22-20000000000000000000000000000000000000000
χ652-2-2-2-22222-22-2-12-22-2-2-2221-1-111-1-111-1-1111-10000000033−3−3−3−333−3−33333−3−3-11-111-11-100002-2-223−33−3−33−33-11-111-11-10000000000000000
χ662-2-2-2-22222-22-2-12-22-2-2-2221-1-111-1-111-1-1111-10000000033−3−3−3−333−3−33333−3−3-11-111-11-10000-222-2−33−333−33−31-11-1-11-110000000000000000
χ672-2-2-2-22222-22-2-12-22-2-2-2221-1-111-1-111-1-1111-100000000−3−33333−3−333−3−3−3−333-11-111-11-100002-2-22−33−333−33−3-11-111-11-10000000000000000
χ682-2-2-2-22222-22-2-12-22-2-2-2221-1-111-1-111-1-1111-100000000−3−33333−3−333−3−3−3−333-11-111-11-10000-222-23−33−3−33−331-11-1-11-110000000000000000
χ692-2-2-2-22222-22-2-1-22-2222-2-21-1-111-1-111-1-1111-12i2i−2i−2i−2i−2i2i2i−i−iii−i−iiiii−i−iii−i−i1-11-1-11-11000000003−3−33−333−3−i3i3i3−i3i3−i3−i3i30000000000000000
χ702-2-2-2-22222-22-2-1-22-2222-2-21-1-111-1-111-1-1111-12i2i−2i−2i−2i−2i2i2i−i−iii−i−iiiii−i−iii−i−i1-11-1-11-1100000000−333−33−3−33i3−i3−i3i3−i3i3i3−i30000000000000000
χ712-2-2-2-22222-22-2-1-22-2222-2-21-1-111-1-111-1-1111-1−2i−2i2i2i2i2i−2i−2iii−i−iii−i−i−i−iii−i−iii1-11-1-11-11000000003−3−33−333−3i3−i3−i3i3−i3i3i3−i30000000000000000
χ722-2-2-2-22222-22-2-1-22-2222-2-21-1-111-1-111-1-1111-1−2i−2i2i2i2i2i−2i−2iii−i−iii−i−i−i−iii−i−iii1-11-1-11-1100000000−333−33−3−33−i3i3i3−i3i3−i3−i3i30000000000000000
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χ762-2-2-2-2222-22-222-222-22-2-22-2-2-2-2-22222-2-222-22000000000000000000000000-222-22-2-22000000000000000000000000000000000000-222-2
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.