Finite Group Databasebeta

← Group #10690982

Character table — Group #10690982

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93
size111122222222222222224444444444444444444444444444444444488888888888888888888888888242424242424242448484848
order12223444444446661212121222244446666888812121212121212121212121224242424242424244468888881212121212242424242424242424242424444488884488
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111111111-1-1111-1-1-1-1-1-1111111111111-1-1-1-111111111-1-1111-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111
χ611111111111111111111-1-1111-1-1-1-1-1-1111111111111-1-1-1-111111111-1-1111-1-1-1-11-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1
χ711111111111111111111-1-1111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111111-1-1-1-1-1-1-1-1111111111111-1-1-1-111-1-1
χ811111111111111111111-1-1111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-111
χ911111-1-1-1-111-1-1111-1-1-1-111-111-1-11111ii−i−i1111-1-1-1-1-1-1-1-1iiii−i−i−i−i1-1-1i−iii−i−i111-1-1ii−i−iiiii−i−i−i−iii−i−iii−i−i1-11-1
χ1011111-1-1-1-111-1-1111-1-1-1-111-111-1-11111ii−i−i1111-1-1-1-1-1-1-1-1iiii−i−i−i−i1-1-1i−iii−i−i111-1-1ii−i−iiiii−i−i−i−i−i−iii−i−iii-11-11
χ1111111-1-1-1-111-1-1111-1-1-1-111-111-1-11111−i−iii1111-1-1-1-1-1-1-1-1−i−i−i−iiiii1-1-1−ii−i−iii111-1-1−i−iii−i−i−i−iiiiiii−i−iii−i−i-11-11
χ1211111-1-1-1-111-1-1111-1-1-1-111-111-1-11111−i−iii1111-1-1-1-1-1-1-1-1−i−i−i−iiiii1-1-1−ii−i−iii111-1-1−i−iii−i−i−i−iiiii−i−iii−i−iii1-11-1
χ1311111-1-1-1-111-1-1111-1-1-1-1-1-1-11111-1-1-1-1ii−i−i1111-1-1-1-11111iiii−i−i−i−i-11-1i−i−i−iii1-1-111ii−i−i−i−i−i−iiiiiii−i−i−i−iii-111-1
χ1411111-1-1-1-111-1-1111-1-1-1-1-1-1-11111-1-1-1-1ii−i−i1111-1-1-1-11111iiii−i−i−i−i-11-1i−i−i−iii1-1-111ii−i−i−i−i−i−iiiii−i−iiiii−i−i1-1-11
χ1511111-1-1-1-111-1-1111-1-1-1-1-1-1-11111-1-1-1-1−i−iii1111-1-1-1-11111−i−i−i−iiiii-11-1−iiii−i−i1-1-111−i−iiiiiii−i−i−i−iii−i−i−i−iii1-1-11
χ1611111-1-1-1-111-1-1111-1-1-1-1-1-1-11111-1-1-1-1−i−iii1111-1-1-1-11111−i−i−i−iiiii-11-1−iiii−i−i1-1-111−i−iiiiiii−i−i−i−i−i−iiiii−i−i-111-1
χ1722222222222-2-2222222222-2-2-2222222000022-2-222-2-2222200000000-2-2-2000000-2-2-2-2-2000000000000000000000000
χ1822222222222-2-22222222-2-2-2-2-2-2-2-2-2-2-2000022-2-222-2-2-2-2-2-20000000022-2000000-22222000000000000000000000000
χ192222222-2-2-2-222222-2-2-2-200-2-220000000000-2-2-2-2222200000000000000-2002i−2i2i−2i2000000002i2i−2i−2i2i2i−2i−2i000000000000
χ202222222-2-2-2-222222-2-2-2-200-2-220000000000-2-2-2-2222200000000000000-200−2i2i−2i2i200000000−2i−2i2i2i−2i−2i2i2i000000000000
χ212222222-2-2-2-2-2-2222-2-2-2-20022-20000002i2i−2i−2i-2-22222-2-200002i2i2i2i−2i−2i−2i−2i002−2i2i0000-20000−2i−2i2i2i00000000000000000000
χ222222222-2-2-2-2-2-2222-2-2-2-20022-2000000−2i−2i2i2i-2-22222-2-20000−2i−2i−2i−2i2i2i2i2i0022i−2i0000-200002i2i−2i−2i00000000000000000000
χ2322222-2-222-2-222222222200-22-20000002222-2-222-2-22200002222222200-2-2-20000-20000-2-2-2-200000000000000000000
χ2422222-2-222-2-222222222200-22-2000000-2-2-2-2-2-222-2-2220000-2-2-2-2-2-2-2-200-2220000-20000222200000000000000000000
χ2522222-2-222-2-2-2-22222222002-220000000000-2-2-2-2-2-2-2-2000000000000002002-2-2220000000022-2-2-2-222000000000000
χ2622222-2-222-2-2-2-22222222002-220000000000-2-2-2-2-2-2-2-200000000000000200-222-2200000000-2-22222-2-2000000000000
χ2722222-2-2-2-22222222-2-2-2-2222-2-2-2-22222000022-2-2-2-222-2-2-2-200000000-222000000-2-2-222000000000000000000000000
χ2822222-2-2-2-22222222-2-2-2-2-2-22-2-222-2-2-2-2000022-2-2-2-2222222000000002-22000000-222-2-2000000000000000000000000
χ292222-122222222-1-1-1-1-1-1-12222222-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ302222-122222222-1-1-1-1-1-1-12222222-1-1-1-1-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-11111111122-1-2-2-2-2-2-2-1-1-1-1-1111111111111000000000000
χ312222-122222222-1-1-1-1-1-1-1-2-2222-2-211112222-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-2-2-122-2-2-2-2-11111-1-1-1-111111111000000000000
χ322222-122222222-1-1-1-1-1-1-1-2-2222-2-21111-2-2-2-2-1-1-1-1-1-1-1-1111111111111-2-2-1-2-22222-111111111-1-1-1-1-1-1-1-1000000000000
χ332222-1222222-2-2-1-1-1-1-1-1-122-2-2-222-1-1-1-10000-1-111-1-111-1-1-1-1−i3−i3i3i3−i3−i3i3i3-2-2100000011111−i3i3−i3i3−i3i3−i3i3−i3i3−i3i3000000000000
χ342222-1222222-2-2-1-1-1-1-1-1-122-2-2-222-1-1-1-10000-1-111-1-111-1-1-1-1i3i3−i3−i3i3i3−i3−i3-2-2100000011111i3−i3i3−i3i3−i3i3−i3i3−i3i3−i3000000000000
χ352222-1222222-2-2-1-1-1-1-1-1-1-2-2-2-2-2-2-211110000-1-111-1-1111111−i3−i3i3i3−i3−i3i3i32210000001-1-1-1-1−i3i3−i3i3i3−i3i3−i3i3−i3i3−i3000000000000
χ362222-1222222-2-2-1-1-1-1-1-1-1-2-2-2-2-2-2-211110000-1-111-1-1111111i3i3−i3−i3i3i3−i3−i32210000001-1-1-1-1i3−i3i3−i3−i3i3−i3i3−i3i3−i3i3000000000000
χ372222-122-2-2-2-222-1-1-1111100-2-2200−i3−i3i3i300001111-1-1-1-1−i3−i3i3i333−3−3−3−333001002i−2i2i−2i-1−i3i3−i3i3−333−3−i−iii−i−iii000000000000
χ382222-122-2-2-2-222-1-1-1111100-2-2200−i3−i3i3i300001111-1-1-1-1−i3−i3i3i3−3−33333−3−300100−2i2i−2i2i-1−i3i3−i3i33−3−33ii−i−iii−i−i000000000000
χ392222-122-2-2-2-222-1-1-1111100-2-2200i3i3−i3−i300001111-1-1-1-1i3i3−i3−i333−3−3−3−33300100−2i2i−2i2i-1i3−i3i3−i3−333−3ii−i−iii−i−i000000000000
χ402222-122-2-2-2-222-1-1-1111100-2-2200i3i3−i3−i300001111-1-1-1-1i3i3−i3−i3−3−33333−3−3001002i−2i2i−2i-1i3−i3i3−i33−3−33−i−iii−i−iii000000000000
χ412222-122-2-2-2-2-2-2-1-1-111110022-200−i3−i3i3i32i2i−2i−2i11-1-1-1-111−i3−i3i3i3−i−i−i−iiiii00-1−2i2i00001i3−i3i3−i3ii−i−i3−3−333−3−33000000000000
χ422222-122-2-2-2-2-2-2-1-1-111110022-200−i3−i3i3i3−2i−2i2i2i11-1-1-1-111−i3−i3i3i3iiii−i−i−i−i00-12i−2i00001i3−i3i3−i3−i−iii−333−3−333−3000000000000
χ432222-122-2-2-2-2-2-2-1-1-111110022-200i3i3−i3−i32i2i−2i−2i11-1-1-1-111i3i3−i3−i3−i−i−i−iiiii00-1−2i2i00001−i3i3−i3i3ii−i−i−333−3−333−3000000000000
χ442222-122-2-2-2-2-2-2-1-1-111110022-200i3i3−i3−i3−2i−2i2i2i11-1-1-1-111i3i3−i3−i3iiii−i−i−i−i00-12i−2i00001−i3i3−i3i3−i−iii3−3−333−3−33000000000000
χ452222-1-2-222-2-222-1-1-1-1-1-1-100-22-200−i3−i3i3i3222211-1-111-1-1i3i3−i3−i3-1-1-1-1-1-1-1-1001-2-200001i3−i3−i3i31111−i3i3i3−i3i3−i3−i3i3000000000000
χ462222-1-2-222-2-222-1-1-1-1-1-1-100-22-200−i3−i3i3i3-2-2-2-211-1-111-1-1i3i3−i3−i3111111110012200001i3−i3−i3i3-1-1-1-1i3−i3−i3i3−i3i3i3−i3000000000000
χ472222-1-2-222-2-222-1-1-1-1-1-1-100-22-200i3i3−i3−i3222211-1-111-1-1−i3−i3i3i3-1-1-1-1-1-1-1-1001-2-200001−i3i3i3−i31111i3−i3−i3i3−i3i3i3−i3000000000000
χ482222-1-2-222-2-222-1-1-1-1-1-1-100-22-200i3i3−i3−i3-2-2-2-211-1-111-1-1−i3−i3i3i3111111110012200001−i3i3i3−i3-1-1-1-1−i3i3i3−i3i3−i3−i3i3000000000000
χ492222-1-2-222-2-2-2-2-1-1-1-1-1-1-1002-2200−i3−i3i3i3000011111111i3i3−i3−i3−i3−i3i3i3−i3−i3i3i300-1002-2-22-1−i3i3i3−i3i3−i3i3−i3-1-11111-1-1000000000000
χ502222-1-2-222-2-2-2-2-1-1-1-1-1-1-1002-2200−i3−i3i3i3000011111111i3i3−i3−i3i3i3−i3−i3i3i3−i3−i300-100-222-2-1−i3i3i3−i3−i3i3−i3i311-1-1-1-111000000000000
χ512222-1-2-222-2-2-2-2-1-1-1-1-1-1-1002-2200i3i3−i3−i3000011111111−i3−i3i3i3−i3−i3i3i3−i3−i3i3i300-100-222-2-1i3−i3−i3i3i3−i3i3−i311-1-1-1-111000000000000
χ522222-1-2-222-2-2-2-2-1-1-1-1-1-1-1002-2200i3i3−i3−i3000011111111−i3−i3i3i3i3i3−i3−i3i3i3−i3−i300-1002-2-22-1i3−i3−i3i3−i3i3−i3i3-1-11111-1-1000000000000
χ532222-1-2-2-2-22222-1-1-11111222-2-2-2-2-1-1-1-10000-1-11111-1-1111133−3−3−3−333-22-1000000111-1-13−3−333−33−3−33−33000000000000
χ542222-1-2-2-2-22222-1-1-11111222-2-2-2-2-1-1-1-10000-1-11111-1-11111−3−33333−3−3-22-1000000111-1-1−333−3−33−333−33−3000000000000
χ552222-1-2-2-2-22222-1-1-11111-2-22-2-22211110000-1-11111-1-1-1-1-1-133−3−3−3−3332-2-10000001-1-1113−3−33−33−333−33−3000000000000
χ562222-1-2-2-2-22222-1-1-11111-2-22-2-22211110000-1-11111-1-1-1-1-1-1−3−33333−3−32-2-10000001-1-111−333−33−33−3−33−33000000000000
χ572222-1-2-2-2-222-2-2-1-1-1111122-222-2-2-1-1-1-12i2i−2i−2i-1-1-1-111111111−i−i−i−iiiii2-212i−2i2i2i−2i−2i-1-1-111−i−iii−i−i−i−iiiii000000000000
χ582222-1-2-2-2-222-2-2-1-1-1111122-222-2-2-1-1-1-1−2i−2i2i2i-1-1-1-111111111iiii−i−i−i−i2-21−2i2i−2i−2i2i2i-1-1-111ii−i−iiiii−i−i−i−i000000000000
χ592222-1-2-2-2-222-2-2-1-1-11111-2-2-2222211112i2i−2i−2i-1-1-1-11111-1-1-1-1−i−i−i−iiiii-2212i−2i−2i−2i2i2i-111-1-1−i−iiiiiii−i−i−i−i000000000000
χ602222-1-2-2-2-222-2-2-1-1-11111-2-2-222221111−2i−2i2i2i-1-1-1-11111-1-1-1-1iiii−i−i−i−i-221−2i2i2i2i−2i−2i-111-1-1ii−i−i−i−i−i−iiiii000000000000
χ612-22-222i−2i2i−2i2-2002-2-22i2i−2i−2i2-20002i−2i2-22-200002-2002i−2i002i−2i2i−2i00000000000000000000000000000000001+i−1−i1−i−1+i1+i−1−i1−i−1+i0000
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χ642-22-222i−2i2i−2i2-2002-2-22i2i−2i−2i-22000−2i2i-22-2200002-2002i−2i00−2i2i−2i2i0000000000000000000000000000000000−1−i1+i−1+i1−i1+i−1−i1−i−1+i0000
χ652-22-22−2i2i−2i2i2-2002-2-2−2i−2i2i2i2-2000−2i2i2-22-200002-200−2i2i00−2i2i−2i2i00000000000000000000000000000000001−i−1+i1+i−1−i1−i−1+i1+i−1−i0000
χ662-22-22−2i2i−2i2i2-2002-2-2−2i−2i2i2i2-2000−2i2i2-22-200002-200−2i2i00−2i2i−2i2i0000000000000000000000000000000000−1+i1−i−1−i1+i−1+i1−i−1−i1+i0000
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χ682-22-22−2i2i−2i2i2-2002-2-2−2i−2i2i2i-220002i−2i-22-2200002-200−2i2i002i−2i2i−2i0000000000000000000000000000000000−1+i1−i−1−i1+i1−i−1+i1+i−1−i0000
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χ744-44-4-24i−4i−4i4i-4400-2222i2i−2i−2i00000002i3−2i3−2i32i300002-200−2i2i00−232323−230000000000000000000000000000000000000000000000
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χ784-44-4-2−4i4i−4i4i4-400-2222i2i−2i−2i-440004i−4i2-22-20000-22002i−2i00−2i2i−2i2i0000000000000000000000000000000000000000000000
χ794-4-4440000004i−4i-44-40000000000000002+2i−2−2i2−2i−2+2i0000004i−4i00002+2i−2−2i2+2i−2−2i2−2i−2+2i2−2i−2+2i00000000000000000000000000000000000000
χ804-4-4440000004i−4i-44-4000000000000000−2−2i2+2i−2+2i2−2i0000004i−4i0000−2−2i2+2i−2−2i2+2i−2+2i2−2i−2+2i2−2i00000000000000000000000000000000000000
χ814-4-444000000−4i4i-44-40000000000000002−2i−2+2i2+2i−2−2i000000−4i4i00002−2i−2+2i2−2i−2+2i2+2i−2−2i2+2i−2−2i00000000000000000000000000000000000000
χ824-4-444000000−4i4i-44-4000000000000000−2+2i2−2i−2−2i2+2i000000−4i4i0000−2+2i2−2i−2+2i2−2i−2−2i2+2i−2−2i2+2i00000000000000000000000000000000000000
χ834-4-44-20000004i−4i2-22−2i32i3−2i32i3000000000002+2i−2−2i2−2i−2+2i0023−2300−2i2i0000−2ζ2+2ζ72ζ2−2ζ7−2ζ10+2ζ112ζ10−2ζ11−2ζ2−2ζ72ζ2+2ζ7−2ζ10−2ζ112ζ10+2ζ1100000000000000000000000000000000000000
χ844-4-44-20000004i−4i2-22−2i32i3−2i32i300000000000−2−2i2+2i−2+2i2−2i0023−2300−2i2i00002ζ2−2ζ7−2ζ2+2ζ72ζ10−2ζ11−2ζ10+2ζ112ζ2+2ζ7−2ζ2−2ζ72ζ10+2ζ11−2ζ10−2ζ1100000000000000000000000000000000000000
χ854-4-44-20000004i−4i2-222i3−2i32i3−2i3000000000002+2i−2−2i2−2i−2+2i00−232300−2i2i0000−2ζ10+2ζ112ζ10−2ζ11−2ζ2+2ζ72ζ2−2ζ7−2ζ10−2ζ112ζ10+2ζ11−2ζ2−2ζ72ζ2+2ζ700000000000000000000000000000000000000
χ864-4-44-20000004i−4i2-222i3−2i32i3−2i300000000000−2−2i2+2i−2+2i2−2i00−232300−2i2i00002ζ10−2ζ11−2ζ10+2ζ112ζ2−2ζ7−2ζ2+2ζ72ζ10+2ζ11−2ζ10−2ζ112ζ2+2ζ7−2ζ2−2ζ700000000000000000000000000000000000000
χ874-4-44-2000000−4i4i2-22−2i32i3−2i32i3000000000002−2i−2+2i2+2i−2−2i00−2323002i−2i0000−2ζ2−2ζ72ζ2+2ζ7−2ζ10−2ζ112ζ10+2ζ11−2ζ2+2ζ72ζ2−2ζ7−2ζ10+2ζ112ζ10−2ζ1100000000000000000000000000000000000000
χ884-4-44-2000000−4i4i2-22−2i32i3−2i32i300000000000−2+2i2−2i−2−2i2+2i00−2323002i−2i00002ζ2+2ζ7−2ζ2−2ζ72ζ10+2ζ11−2ζ10−2ζ112ζ2−2ζ7−2ζ2+2ζ72ζ10−2ζ11−2ζ10+2ζ1100000000000000000000000000000000000000
χ894-4-44-2000000−4i4i2-222i3−2i32i3−2i3000000000002−2i−2+2i2+2i−2−2i0023−23002i−2i0000−2ζ10−2ζ112ζ10+2ζ11−2ζ2−2ζ72ζ2+2ζ7−2ζ10+2ζ112ζ10−2ζ11−2ζ2+2ζ72ζ2−2ζ700000000000000000000000000000000000000
χ904-4-44-2000000−4i4i2-222i3−2i32i3−2i300000000000−2+2i2−2i−2−2i2+2i0023−23002i−2i00002ζ10+2ζ11−2ζ10−2ζ112ζ2+2ζ7−2ζ2−2ζ72ζ10−2ζ11−2ζ10+2ζ112ζ2−2ζ7−2ζ2+2ζ700000000000000000000000000000000000000
χ9188-8-8800000000-8-8800000000000000000000000000000000000000000000000000000000000000000000000000000
χ9288-8-8-40000000044-443−43−43430000000000000000000000000000000000000000000000000000000000000000000000000
χ9388-8-8-40000000044-4−434343−430000000000000000000000000000000000000000000000000000000000000000000000000

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