Finite Group Databasebeta

← Group #10703026

Character table — Group #10703026

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
χ91111-1-1-1-111-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1iiii−i−i−i−i-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i11-1-1ii−i−i1111-1-1-1-1iiii−i−i−i−i1-11-1ii−i−iii−i−i11-1-1
χ101111-1-1-1-111-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1iiii−i−i−i−i-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i11-1-1ii−i−i1111-1-1-1-1iiii−i−i−i−i-11-11−i−iii−i−iii-1-111
χ111111-1-1-1-111-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1iiii−i−i−i−i-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i-1-111−i−iii-1-1-1-11111−i−i−i−iiiii1-11-1ii−i−i−i−iii-1-111
χ121111-1-1-1-111-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1iiii−i−i−i−i-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i-1-111−i−iii-1-1-1-11111−i−i−i−iiiii-11-11−i−iiiii−i−i11-1-1
χ131111-1-1-1-111-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii11-1-1−i−iii1111-1-1-1-1−i−i−i−iiiii1-11-1−i−iii−i−iii11-1-1
χ141111-1-1-1-111-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii11-1-1−i−iii1111-1-1-1-1−i−i−i−iiiii-11-11ii−i−iii−i−i-1-111
χ151111-1-1-1-111-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii-1-111ii−i−i-1-1-1-11111iiii−i−i−i−i1-11-1−i−iiiii−i−i-1-111
χ161111-1-1-1-111-1-1-1-11111-1-111111111-1-1-1-1-1-1-1-1−i−i−i−iiiii-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii-1-111ii−i−i-1-1-1-11111iiii−i−i−i−i-11-11ii−i−i−i−iii11-1-1
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
χ212222222222-2-2-2-22-2-2-222-222222222222222200000000-2-2-2-2-2-2-2-2000000000000000000000000000000000000000000002i−2i2i−2i00000000
χ222222222222-2-2-2-22-2-2-222-222222222222222200000000-2-2-2-2-2-2-2-200000000000000000000000000000000000000000000−2i2i−2i2i00000000
χ2322222222-2-22-22-222-2-2-2-22-2-2-2-222222-2-2-2-2220000000022-2-222-2-200000000000000000000000000000000000000002-2-22000000000000
χ2422222222-2-22-22-222-2-2-2-22-2-2-2-222222-2-2-2-2220000000022-2-222-2-20000000000000000000000000000000000000000-222-2000000000000
χ2522222222-2-2-22-222-222-2-2-2-2-2-2-222222-2-2-2-22222-2-222-2-2-2-222-2-2222222-2-2-2-22222-2-2-2-20000000000000000000000000000000000000000
χ2622222222-2-2-22-222-222-2-2-2-2-2-2-222222-2-2-2-222-2-222-2-222-2-222-2-222-2-2-2-22222-2-2-2-222220000000000000000000000000000000000000000
χ2722222222-2-2-22-22-1-222-2-2-21111-1-1-1-1-11111-1-122-2-222-2-211-1-111-1-1-1-1-1-11111-1-1-1-1111100000000−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i30000000000000000
χ2822222222-2-2-22-22-1-222-2-2-21111-1-1-1-1-11111-1-122-2-222-2-211-1-111-1-1-1-1-1-11111-1-1-1-1111100000000i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i30000000000000000
χ2922222222-2-2-22-22-1-222-2-2-21111-1-1-1-1-11111-1-1-2-222-2-22211-1-111-1-11111-1-1-1-11111-1-1-1-100000000−i3−i3i3i3−i3−i3i3i3i3i3−i3−i3i3i3−i3−i30000000000000000
χ3022222222-2-2-22-22-1-222-2-2-21111-1-1-1-1-11111-1-1-2-222-2-22211-1-111-1-11111-1-1-1-11111-1-1-1-100000000i3i3−i3−i3i3i3−i3−i3−i3−i3i3i3−i3−i3i3i30000000000000000
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
χ332222-2-2-2-222-2-2-2-2-1222-2-22-1-1-1-1-1-1-1111111112i2i2i2i−2i−2i−2i−2i1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii22-2-22i2i−2i−2i-1-1-1-11111−i−i−i−iiiii0000000000000000
χ342222-2-2-2-222-2-2-2-2-1222-2-22-1-1-1-1-1-1-1111111112i2i2i2i−2i−2i−2i−2i1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-2-222−2i−2i2i2i1111-1-1-1-1iiii−i−i−i−i0000000000000000
χ352222-2-2-2-222-2-2-2-2-1222-2-22-1-1-1-1-1-1-111111111−2i−2i−2i−2i2i2i2i2i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i22-2-2−2i−2i2i2i-1-1-1-11111iiii−i−i−i−i0000000000000000
χ362222-2-2-2-222-2-2-2-2-1222-2-22-1-1-1-1-1-1-111111111−2i−2i−2i−2i2i2i2i2i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-2-2222i2i−2i−2i1111-1-1-1-1−i−i−i−iiiii0000000000000000
χ372222-2-2-2-2-2-22-22-22-22222-2-2-2-2-2222-2-22222-2-22i2i−2i−2i−2i−2i2i2i22-2-2-2-2222i2i2i2i−2i−2i−2i−2i−2i−2i−2i−2i2i2i2i2i0000000000000000000000000000000000000000
χ382222-2-2-2-2-2-22-22-22-22222-2-2-2-2-2222-2-22222-2-2−2i−2i2i2i2i2i−2i−2i22-2-2-2-222−2i−2i−2i−2i2i2i2i2i2i2i2i2i−2i−2i−2i−2i0000000000000000000000000000000000000000
χ392222-2-2-2-2-2-22-22-2-1-22222-21111-1-1-111-1-1-1-1112i2i−2i−2i−2i−2i2i2i-1-11111-1-1−i−i−i−iiiiiiiii−i−i−i−i00000000−i3−i3i3i3i3i3−i3−i333−3−3−3−3330000000000000000
χ402222-2-2-2-2-2-22-22-2-1-22222-21111-1-1-111-1-1-1-1112i2i−2i−2i−2i−2i2i2i-1-11111-1-1−i−i−i−iiiiiiiii−i−i−i−i00000000i3i3−i3−i3−i3−i3i3i3−3−33333−3−30000000000000000
χ412222-2-2-2-2-2-22-22-2-1-22222-21111-1-1-111-1-1-1-111−2i−2i2i2i2i2i−2i−2i-1-11111-1-1iiii−i−i−i−i−i−i−i−iiiii00000000−i3−i3i3i3i3i3−i3−i3−3−33333−3−30000000000000000
χ422222-2-2-2-2-2-22-22-2-1-22222-21111-1-1-111-1-1-1-111−2i−2i2i2i2i2i−2i−2i-1-11111-1-1iiii−i−i−i−i−i−i−i−iiiii00000000i3i3−i3−i3−i3−i3i3i333−3−3−3−3330000000000000000
χ432222-2-2-2-2-2-2-22-2222-2-2222-2-2-2-2222-2-22222-2-200000000-2-22222-2-2000000000000000000000000000000000000000022-2-2000000000000
χ442222-2-2-2-2-2-2-22-2222-2-2222-2-2-2-2222-2-22222-2-200000000-2-22222-2-20000000000000000000000000000000000000000-2-222000000000000
χ452-2-2222-2-22-222-2-22-22-22-2222-2-22-2-22222-2-2-2-2000000002-2-222-22-2000000000000000000002i−2i2i−2i000000002i−2i2i−2i2i−2i2i−2i0000000000000000
χ462-2-2222-2-22-222-2-22-22-22-2222-2-22-2-22222-2-2-2-2000000002-2-222-22-200000000000000000000−2i2i−2i2i00000000−2i2i−2i2i−2i2i−2i2i0000000000000000
χ472-2-2222-2-22-222-2-2-1-22-22-22-1-111-111-1-1-1-1111100000000-111-1-11-11−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i300002i−2i2i−2i3−33−33−33−3−ii−ii−ii−ii0000000000000000
χ482-2-2222-2-22-222-2-2-1-22-22-22-1-111-111-1-1-1-1111100000000-111-1-11-11−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i30000−2i2i−2i2i−33−33−33−33i−ii−ii−ii−i0000000000000000
χ492-2-2222-2-22-222-2-2-1-22-22-22-1-111-111-1-1-1-1111100000000-111-1-11-11i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i300002i−2i2i−2i−33−33−33−33−ii−ii−ii−ii0000000000000000
χ502-2-2222-2-22-222-2-2-1-22-22-22-1-111-111-1-1-1-1111100000000-111-1-11-11i3i3−i3−i3i3i3−i3−i3i3i3−i3−i3i3i3−i3−i30000−2i2i−2i2i3−33−33−33−3i−ii−ii−ii−i0000000000000000
χ512-2-2222-2-22-2-2-22222-222-2-222-2-22-2-22222-2-2-2-200000000-222-2-22-2200000000000000000000000000000000000000000000000000002i−2i2i−2i
χ522-2-2222-2-22-2-2-22222-222-2-222-2-22-2-22222-2-2-2-200000000-222-2-22-220000000000000000000000000000000000000000000000000000−2i2i−2i2i
χ532-2-2222-2-2-222-2-222-2-22-222-2-2222-2-222-2-222-2-2000000002-22-22-2-220000000000000000000000000000000000000000000000002i−2i2i−2i0000
χ542-2-2222-2-2-222-2-222-2-22-222-2-2222-2-222-2-222-2-2000000002-22-22-2-22000000000000000000000000000000000000000000000000−2i2i−2i2i0000
χ552-2-2222-2-2-22-222-2222-2-22-2-2-2222-2-222-2-222-2-200000000-22-22-222-200000000000000002i−2i2i−2i00002i−2i−2i2i2i−2i−2i2i000000000000000000000000
χ562-2-2222-2-2-22-222-2222-2-22-2-2-2222-2-222-2-222-2-200000000-22-22-222-20000000000000000−2i2i−2i2i0000−2i2i2i−2i−2i2i2i−2i000000000000000000000000
χ572-2-2222-2-2-22-222-2-122-2-22-211-1-1-111-1-111-1-111000000001-11-11-1-11−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i32i−2i2i−2i0000−iii−i−iii−i3−3−333−3−330000000000000000
χ582-2-2222-2-2-22-222-2-122-2-22-211-1-1-111-1-111-1-111000000001-11-11-1-11−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−2i2i−2i2i0000i−i−iii−i−ii−333−3−333−30000000000000000
χ592-2-2222-2-2-22-222-2-122-2-22-211-1-1-111-1-111-1-111000000001-11-11-1-11i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i32i−2i2i−2i0000−iii−i−iii−i−333−3−333−30000000000000000
χ602-2-2222-2-2-22-222-2-122-2-22-211-1-1-111-1-111-1-111000000001-11-11-1-11i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3−2i2i−2i2i0000i−i−iii−i−ii3−3−333−3−330000000000000000
χ612-2-22-2-2222-222-2-222-22-22-222-2-22-2-2-2-2-2-22222000000002-2-22-22-2200000000000000000000000000000000000000000000000000002i−2i−2i2i
χ622-2-22-2-2222-222-2-222-22-22-222-2-22-2-2-2-2-2-22222000000002-2-22-22-220000000000000000000000000000000000000000000000000000−2i2i2i−2i
χ632-2-22-2-2222-2-2-2222-22-2-22222-2-22-2-2-2-2-2-2222200000000-222-22-22-2000000000000000000002-2-22000000002-22-2-22-220000000000000000
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χ652-2-22-2-2222-2-2-222-1-22-2-222-1-111-1111111-1-1-1-1000000001-1-11-11-1133−3−333−3−3−3−333−3−33300002-2-22−33−333−33−3-11-111-11-10000000000000000
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χ672-2-22-2-2222-2-2-222-1-22-2-222-1-111-1111111-1-1-1-1000000001-1-11-11-11−3−333−3−33333−3−333−3−300002-2-223−33−3−33−33-11-111-11-10000000000000000
χ682-2-22-2-2222-2-2-222-1-22-2-222-1-111-1111111-1-1-1-1000000001-1-11-11-11−3−333−3−33333−3−333−3−30000-222-2−33−333−33−31-11-1-11-110000000000000000
χ692-2-22-2-222-222-2-22222-22-2-2-2-2222-2-2-2-222-2-222000000002-22-2-222-200000000000000002i−2i−2i2i00002i−2i−2i2i−2i2i2i−2i000000000000000000000000
χ702-2-22-2-222-222-2-22222-22-2-2-2-2222-2-2-2-222-2-222000000002-22-2-222-20000000000000000−2i2i2i−2i0000−2i2i2i−2i2i−2i−2i2i000000000000000000000000
χ712-2-22-2-222-222-2-22-122-22-2-211-1-1-11111-1-111-1-100000000-11-111-1-1133−3−3−3−333−3−33333−3−32i−2i−2i2i0000−iii−ii−i−iii3−i3−i3i3−i3i3i3−i30000000000000000
χ722-2-22-2-222-222-2-22-122-22-2-211-1-1-11111-1-111-1-100000000-11-111-1-1133−3−3−3−333−3−33333−3−3−2i2i2i−2i0000i−i−ii−iii−i−i3i3i3−i3i3−i3−i3i30000000000000000
χ732-2-22-2-222-222-2-22-122-22-2-211-1-1-11111-1-111-1-100000000-11-111-1-11−3−33333−3−333−3−3−3−3332i−2i−2i2i0000−iii−ii−i−ii−i3i3i3−i3i3−i3−i3i30000000000000000
χ742-2-22-2-222-222-2-22-122-22-2-211-1-1-11111-1-111-1-100000000-11-111-1-11−3−33333−3−333−3−3−3−333−2i2i2i−2i0000i−i−ii−iii−ii3−i3−i3i3−i3i3i3−i30000000000000000
χ752-2-22-2-222-22-222-22-2-222-22-2-2222-2-2-2-222-2-22200000000-22-222-2-220000000000000000000000000000000000000000000000002-2-220000
χ762-2-22-2-222-22-222-22-2-222-22-2-2222-2-2-2-222-2-22200000000-22-222-2-22000000000000000000000000000000000000000000000000-222-20000
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.