Finite Group Databasebeta

← Group #10702898

Character table — Group #10702898

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size1111111122222222222222222222222222224444444444444444444444444444444488888888888888888888888824242424242424242424242424242424
order1222222222222222222236666666666666664444444466666666121212121212121212121212121212122244444466661212121212121212121212124444444444444444
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
χ91111-1-1-1-111111-1-1-1-11-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11-11-111-1-111-1-111-1-11111-1-1-1-1ii−i−iii−i−iii−i−iii−i−i
χ101111-1-1-1-111111-1-1-1-11-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11-11-111-1-111-1-111-1-11111-1-1-1-1−i−iii−i−iii−i−iii−i−iii
χ111111-1-1-1-111111-1-1-1-11-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-11-11-1-111-1-111-1-111-1-1-1-11111ii−i−i−i−iiiii−i−i−i−iii
χ121111-1-1-1-111111-1-1-1-11-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-11-11-1-111-1-111-1-111-1-1-1-11111−i−iiiii−i−i−i−iiiii−i−i
χ131111-1-1-1-111111-1-1-1-11-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111-11-1-1-11111-1-111-1-1-1-1-1-11111ii−i−iii−i−i−i−iii−i−iii
χ141111-1-1-1-111111-1-1-1-11-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111-11-1-1-11111-1-111-1-1-1-1-1-11111−i−iii−i−iiiii−i−iii−i−i
χ151111-1-1-1-111111-1-1-1-11-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-11-1111-1-1-1-111-1-1111111-1-1-1-1ii−i−i−i−iii−i−iiiii−i−i
χ161111-1-1-1-111111-1-1-1-11-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-11-1111-1-1-1-111-1-1111111-1-1-1-1−i−iiiii−i−iii−i−i−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
χ212222222222-2-2-22-2-2-2-22-222-2-22222-2-2-2-22-2-220000000022-2-222-2-2000000000000000000000000000000000000000000002-22-200000000
χ222222222222-2-2-22-2-2-2-22-222-2-22222-2-2-2-22-2-220000000022-2-222-2-200000000000000000000000000000000000000000000-22-2200000000
χ2322222222-2-222-2-22-2-2-2-2222-2-22222-2-2-2-22-2-2200000000-2-222-2-22200000000000000000000000000000000000000002-22-2000000000000
χ2422222222-2-222-2-22-2-2-2-2222-2-22222-2-2-2-22-2-2200000000-2-222-2-2220000000000000000000000000000000000000000-22-22000000000000
χ2522222222-2-2-2-22-2-2222-2-2222222222222222200000000-2-2-2-2-2-2-2-2000000000000000022-2-200002222-2-2-2-2000000000000000000000000
χ2622222222-2-2-2-22-2-2222-2-2222222222222222200000000-2-2-2-2-2-2-2-20000000000000000-2-2220000-2-2-2-22222000000000000000000000000
χ2722222222-2-2-2-22-2-2222-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000011111111−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i322-2-20000-1-1-1-11111−i3−i3i3i3−i3−i3i3i30000000000000000
χ2822222222-2-2-2-22-2-2222-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000011111111−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3i3i3i3i3-2-22200001111-1-1-1-1i3i3−i3−i3i3i3−i3−i30000000000000000
χ2922222222-2-2-2-22-2-2222-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000011111111i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i322-2-20000-1-1-1-11111i3i3−i3−i3i3i3−i3−i30000000000000000
χ3022222222-2-2-2-22-2-2222-2-2-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000000011111111i3i3i3i3−i3−i3−i3−i3i3i3i3i3−i3−i3−i3−i3-2-22200001111-1-1-1-1−i3−i3i3i3−i3−i3i3i30000000000000000
χ312222-2-2-2-222222-2-2-2-22-2-2-1-1-1-111111111-1-1-1-12222-2-2-2-2-1-1-1-11111-1-1-1-1-1-1-1-1111111112-22-222-2-2-1-111-1-111-1-1-1-111110000000000000000
χ322222-2-2-2-222222-2-2-2-22-2-2-1-1-1-111111111-1-1-1-12222-2-2-2-2-1-1-1-11111-1-1-1-1-1-1-1-111111111-22-22-2-22211-1-111-1-11111-1-1-1-10000000000000000
χ332222-2-2-2-222222-2-2-2-22-2-2-1-1-1-111111111-1-1-1-1-2-2-2-22222-1-1-1-1111111111111-1-1-1-1-1-1-1-12-22-2-2-222-1-111-1-1111111-1-1-1-10000000000000000
χ342222-2-2-2-222222-2-2-2-22-2-2-1-1-1-111111111-1-1-1-1-2-2-2-22222-1-1-1-1111111111111-1-1-1-1-1-1-1-1-22-2222-2-211-1-111-1-1-1-1-1-111110000000000000000
χ352222-2-2-2-222-2-2-2-2222-2-2222-2-2-2-2-2-222222-2-220000000022-2-2-2-222000000000000000000000000000000000000000000002i−2i−2i2i00000000
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χ382222-2-2-2-2-2-222-22-222-22-222-2-2-2-2-2-222222-2-2200000000-2-22222-2-20000000000000000000000000000000000000000−2i2i2i−2i000000000000
χ392222-2-2-2-2-2-2-2-2222-2-22222222-2-2-2-2-2-2-2-2222200000000-2-2-2-2222200000000000000002-2-22000022-2-2-2-222000000000000000000000000
χ402222-2-2-2-2-2-2-2-2222-2-22222222-2-2-2-2-2-2-2-2222200000000-2-2-2-222220000000000000000-222-20000-2-22222-2-2000000000000000000000000
χ412222-2-2-2-2-2-2-2-2222-2-2222-1-1-1-111111111-1-1-1-1000000001111-1-1-1-1−i3−i3−i3−i3i3i3i3i3i3i3i3i3−i3−i3−i3−i32-2-220000-1-11111-1-1−i3−i3i3i3i3i3−i3−i30000000000000000
χ422222-2-2-2-2-2-2-2-2222-2-2222-1-1-1-111111111-1-1-1-1000000001111-1-1-1-1−i3−i3−i3−i3i3i3i3i3i3i3i3i3−i3−i3−i3−i3-222-2000011-1-1-1-111i3i3−i3−i3−i3−i3i3i30000000000000000
χ432222-2-2-2-2-2-2-2-2222-2-2222-1-1-1-111111111-1-1-1-1000000001111-1-1-1-1i3i3i3i3−i3−i3−i3−i3−i3−i3−i3−i3i3i3i3i32-2-220000-1-11111-1-1i3i3−i3−i3−i3−i3i3i30000000000000000
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χ452-22-222-2-22-22-222-22-2-2-222-22222-2-222-2-22-2-2-2000000002-22-22-22-2000000000000000000002i−2i2i−2i000000002i−2i2i−2i2i−2i2i−2i0000000000000000
χ462-22-222-2-22-22-222-22-2-2-222-22222-2-222-2-22-2-2-2000000002-22-22-22-200000000000000000000−2i2i−2i2i00000000−2i2i−2i2i−2i2i−2i2i0000000000000000
χ472-22-222-2-22-22-222-22-2-2-22-11-1-1-1-111-1-111-111100000000-11-11-11-1133−3−333−3−333−3−333−3−300002i−2i2i−2i−i3i3−i3i3−i3i3−i3i3−ii−ii−ii−ii0000000000000000
χ482-22-222-2-22-22-222-22-2-2-22-11-1-1-1-111-1-111-111100000000-11-11-11-1133−3−333−3−333−3−333−3−30000−2i2i−2i2ii3−i3i3−i3i3−i3i3−i3i−ii−ii−ii−i0000000000000000
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χ522-22-222-2-22-2-22-222-222-2-22-2-2-222-2-2-2-222222-2000000002-2-222-2-22000000000000000000000000000000000000000000000000−2i2i−2i2i0000
χ532-22-222-2-2-222-2-2-2-2-222222-2-2-222-2-2-2-222222-200000000-222-2-222-200000000000000000000000000000000000000000000000000002-22-2
χ542-22-222-2-2-222-2-2-2-2-222222-2-2-222-2-2-2-222222-200000000-222-2-222-20000000000000000000000000000000000000000000000000000-22-22
χ552-22-222-2-2-22-222-222-2-22-22-22222-2-222-2-22-2-2-22i2i−2i−2i2i2i−2i−2i-22-22-22-222i2i−2i−2i−2i−2i2i2i2i2i−2i−2i−2i−2i2i2i0000000000000000000000000000000000000000
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χ572-22-222-2-2-22-222-222-2-22-2-11-1-1-1-111-1-111-11112i2i−2i−2i2i2i−2i−2i1-11-11-11-1−i−iiiii−i−i−i−iiiii−i−i00000000−i3i3−i3i3i3−i3i3−i33−3−333−3−330000000000000000
χ582-22-222-2-2-22-222-222-2-22-2-11-1-1-1-111-1-111-11112i2i−2i−2i2i2i−2i−2i1-11-11-11-1−i−iiiii−i−i−i−iiiii−i−i00000000i3−i3i3−i3−i3i3−i3i3−333−3−333−30000000000000000
χ592-22-222-2-2-22-222-222-2-22-2-11-1-1-1-111-1-111-1111−2i−2i2i2i−2i−2i2i2i1-11-11-11-1ii−i−i−i−iiiii−i−i−i−iii00000000−i3i3−i3i3i3−i3i3−i3−333−3−333−30000000000000000
χ602-22-222-2-2-22-222-222-2-22-2-11-1-1-1-111-1-111-1111−2i−2i2i2i−2i−2i2i2i1-11-11-11-1ii−i−i−i−iiiii−i−i−i−iii00000000i3−i3i3−i3−i3i3−i3i33−3−333−3−330000000000000000
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χ632-22-2-2-2222-22-22-22-22-22-2-11-1-111-1-111-1-1-111100000000-11-111-11-133−3−333−3−3−3−333−3−33300002i−2i−2i2i−i3i3i3−i3−i3i3i3−i3−ii−iii−ii−i0000000000000000
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χ8844-4-4-44-440000000000004400-44-440000-400-4−2i2i−2i2i2i−2i2i−2i00000000−2i2i−2i2i−2i2i−2i2i2i−2i2i−2i2i−2i2i−2i0000000000000000000000000000000000000000
χ8944-4-4-44-44000000000000-2-2−2i32i32-22-22i3−2i32i3−2i32−2i32i322i−2i2i−2i−2i2i−2i2i000000002ζ7−2ζ72ζ7−2ζ72ζ11−2ζ112ζ11−2ζ11−2ζ72ζ7−2ζ72ζ7−2ζ112ζ11−2ζ112ζ110000000000000000000000000000000000000000
χ9044-4-4-44-44000000000000-2-2−2i32i32-22-22i3−2i32i3−2i32−2i32i32−2i2i−2i2i2i−2i2i−2i00000000−2ζ72ζ7−2ζ72ζ7−2ζ112ζ11−2ζ112ζ112ζ7−2ζ72ζ7−2ζ72ζ11−2ζ112ζ11−2ζ110000000000000000000000000000000000000000
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χ9244-4-4-44-44000000000000-2-22i3−2i32-22-2−2i32i3−2i32i322i3−2i32−2i2i−2i2i2i−2i2i−2i00000000−2ζ112ζ11−2ζ112ζ11−2ζ72ζ7−2ζ72ζ72ζ11−2ζ112ζ11−2ζ112ζ7−2ζ72ζ7−2ζ70000000000000000000000000000000000000000
χ934-44-444-4-44-4-44-444-444-4-4-2222-2-22222-2-2-2-2-2200000000-222-2-222-200000000000000000000000000000000000000000000000000000000
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χ974-4-444-4-440000000000004-4004-4-440000-40042-2-222-2-22000000002-2-22-222-22-2-22-222-20000000000000000000000000000000000000000
χ984-4-444-4-440000000000004-4004-4-440000-4004-222-2-222-200000000-222-22-2-22-222-22-2-220000000000000000000000000000000000000000
χ994-4-444-4-44000000000000-22−2i32i3-222-2−2i32i32i3−2i322i3−2i3-22-2-222-2-2200000000−1+i31−i31−i3−1+i31+i3−1−i3−1−i31+i3−1+i31−i31−i3−1+i31+i3−1−i3−1−i31+i30000000000000000000000000000000000000000
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χ1014-4-444-4-44000000000000-222i3−2i3-222-22i3−2i3−2i32i32−2i32i3-22-2-222-2-2200000000−1−i31+i31+i3−1−i31−i3−1+i3−1+i31−i3−1−i31+i31+i3−1−i31−i3−1+i3−1+i31−i30000000000000000000000000000000000000000
χ1024-4-444-4-44000000000000-222i3−2i3-222-22i3−2i3−2i32i32−2i32i3-2-222-2-222-2000000001+i3−1−i3−1−i31+i3−1+i31−i31−i3−1+i31+i3−1−i3−1−i31+i3−1+i31−i31−i3−1+i30000000000000000000000000000000000000000
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χ1044-4-44-444-40000000000004-400-444-40000-4004-222-22-2-2200000000-222-22-2-222-2-22-222-20000000000000000000000000000000000000000
χ1054-4-44-444-4000000000000-22−2i32i32-2-222i3−2i3−2i32i322i3−2i3-22-2-22-222-200000000−1+i31−i31−i3−1+i31+i3−1−i3−1−i31+i31−i3−1+i3−1+i31−i3−1−i31+i31+i3−1−i30000000000000000000000000000000000000000
χ1064-4-44-444-4000000000000-22−2i32i32-2-222i3−2i3−2i32i322i3−2i3-2-222-22-2-22000000001−i3−1+i3−1+i31−i3−1−i31+i31+i3−1−i3−1+i31−i31−i3−1+i31+i3−1−i3−1−i31+i30000000000000000000000000000000000000000
χ1074-4-44-444-4000000000000-222i3−2i32-2-22−2i32i32i3−2i32−2i32i3-22-2-22-222-200000000−1−i31+i31+i3−1−i31−i3−1+i3−1+i31−i31+i3−1−i3−1−i31+i3−1+i31−i31−i3−1+i30000000000000000000000000000000000000000
χ1084-4-44-444-4000000000000-222i3−2i32-2-22−2i32i32i3−2i32−2i32i3-2-222-22-2-22000000001+i3−1−i3−1−i31+i3−1+i31−i31−i3−1+i3−1−i31+i31+i3−1−i31−i3−1+i3−1+i31−i30000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.