Finite Group Databasebeta

← Group #13168563

Character table — Group #13168563

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117
size1111222222222222444444444444444444444666666666688888888888881212121212121212121212121212121212121212121212121218181818242424242424242424242424363636363636363636365454727272108
order122233366666666633346666666661212121212121212444444121212123666121212121212121212244661212121212121212121212121212121212121212224466612121212121212121244446612121212441212124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-11-1-1-11111111111111111111111-1-1-1-1-11-1-111-1-1111-1-1-11111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111-1-111111111111111111111-1111-1-111-1-11111-1-111111111-1-1-1-1111-111-1-111-1-1-111-1-1-1-1-1-1-1-1-111-1-1
χ4111111111111111111111111111111111111111-1-11111111111111111111-1-1-1-1-1-1-111-1-11111-1-111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-1-111
χ51111111111111111111111111111111111111-1-111-1-1-1-1-1-111111111111111111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111111111-1-1-11-1-1-1-111-1-1-1-11-1
χ61111111111111111111111111111111111111-1-111-1-1-1-1-1-11111111111111-11-1-1-111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-111-111-1-1-1-1-1-1-11111-11
χ71111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111111111111111-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111-111-1-111-1-11-1-1-11111-1-111-1-1-11
χ81111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1111-1
χ91111111111111111111-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11-1-11111-1-1-1-11111111111-1-1-1-11111111-1-1-1-1-1-1-111-1-11-111-1-111-1-11-1-11
χ101111111111111111111-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-11-1-111-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-111-1-11111-11-1111-1-1-1-111-111-1
χ111111111111111111111-1111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-111-111-1-1-1-1111111-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-11-111-1-111-1-1111-11-1
χ121111111111111111111-1111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-111-1-1-11111111-1-111-1-1-1-11111-1-1-11-11
χ131111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-11-1-1111111-1-1-1-1-1-111-1-1-1-11111-1-111111-1-1-1-1-1-1-11111-1-1-1-1111111-11-1-1
χ141111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-11-1-11111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111111-111-1-111-1-1-1-11-111
χ151111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-111-111-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-111-1-1-1-1-11-1111-1-1-1-1-1-1-1111
χ161111111111111111111-1111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1-11111111-1-1-1-11-111-1-111111-1-1-1
χ17222222-12-122-122-12-1-122-12-12-1-1-12-1-1-122-1-1-1-1222222-1-1-1-1-1-1-1-1222-1-1-1-1-1-102000-1-122-1-122-1-122-1-1-1-1-1-1-1-12200000200-1-100-1-12000-1-1-1-100000000
χ18222222-12-122-122-12-1-122-12-12-1-1-12-1-1-122-1-1-1-122-2-222-1-1-1-1-1-1-1-1222-1-1-1-1-1-10-200011221122-1-1-2-2-1-1-1-1-1-1-1-1-2-200000-200110011-2000111100000000
χ19222222-12-122-122-12-1-122-12-12-1-1-12-1-1-122-1-1-1-1-2-222-2-21111-1-1-1-1222-1-1-1-1-1-102000-1-1-2-2-1-1-2-2112211111111-2-200000200-1-100-1-1-2000111100000000
χ20222222-12-122-122-12-1-122-12-12-1-1-12-1-1-122-1-1-1-1-2-2-2-2-2-21111-1-1-1-1222-1-1-1-1-1-10-200011-2-211-2-211-2-2111111112200000-2001100112000-1-1-1-100000000
χ21222222-12-122-122-12-1-12-2-12-12-1-1-12-111-2-211112222-2-21111-1-1-1-1-2-2-21111110-2000-1-1-2-21122-1-122-1-1-1-111112200000-2001100-1-1-2000-1-11100000000
χ22222222-12-122-122-12-1-12-2-12-12-1-1-12-111-2-2111122-2-2-2-21111-1-1-1-1-2-2-21111110200011-2-2-1-122-1-1-2-2-1-1-1-11111-2-200000200-1-10011200011-1-100000000
χ23222222-12-122-122-12-1-12-2-12-12-1-1-12-111-2-21111-2-22222-1-1-1-1-1-1-1-1-2-2-21111110-2000-1-12211-2-211221111-1-1-1-1-2-200000-2001100-1-1200011-1-100000000
χ24222222-12-122-122-12-1-12-2-12-12-1-1-12-111-2-21111-2-2-2-222-1-1-1-1-1-1-1-1-2-2-2111111020001122-1-1-2-211-2-21111-1-1-1-12200000200-1-10011-2000-1-11100000000
χ2522222-12222-12-1-1222-1-122-1-1-12-1-1-1222-1-1-1-1-1-12200222222-1-1-1-12-1-122-1-1-1-12022200-1-100-1-12200-1-1-1-1-1-1-1-10000-1-1-102-100-1-100022000000000-1-100
χ2622222-12222-12-1-1222-1-122-1-1-12-1-1-1222-1-1-1-1-1-12200222222-1-1-1-12-1-122-1-1-1-1-20-2-2-200-1-100-1-12200-1-1-1-1-1-1-1-100001110-210011000-2-20000000001100
χ2722222-12222-12-1-1222-1-122-1-1-12-1-1-1222-1-1-1-1-1-1-2-200-2-2-2-2-2-2-1-1-1-12-1-122-1-1-1-12022200110011-2-200111111110000-1-1-102-100-1-1000-2-20000000001100
χ2822222-12222-12-1-1222-1-122-1-1-12-1-1-1222-1-1-1-1-1-1-2-200-2-2-2-2-2-2-1-1-1-12-1-122-1-1-1-1-20-2-2-200110011-2-2001111111100001110-21001100022000000000-1-100
χ2922222-12222-12-1-1222-1-1-22-1-1-12-1-1-12-2-21111112200-2-2-2-2-2-2-1-1-1-1-211-2-2111120-222001100-1-12200-1-1-1-111110000-1-1-10-210011000-22000000000-1100
χ3022222-12222-12-1-1222-1-1-22-1-1-12-1-1-12-2-21111112200-2-2-2-2-2-2-1-1-1-1-211-2-21111-202-2-2001100-1-12200-1-1-1-11111000011102-100-1-10002-20000000001-100
χ3122222-12222-12-1-1222-1-1-22-1-1-12-1-1-12-2-2111111-2-200222222-1-1-1-1-211-2-2111120-22200-1-10011-2-2001111-1-1-1-10000-1-1-10-2100110002-20000000001-100
χ3222222-12222-12-1-1222-1-1-22-1-1-12-1-1-12-2-2111111-2-200222222-1-1-1-1-211-2-21111-202-2-200-1-10011-2-2001111-1-1-1-1000011102-100-1-1000-22000000000-1100
χ332222-122-12-122222-1-12-12-1-12-1-122-1-1222222220022000000-1-1-1-1-1-1-1-1-1-1-1-1-1222-1-12200220000-1-10000000000222-1-1-1-12-1-1-1-1-1-100020000-1-10000-10
χ342222-122-12-122222-1-12-12-1-12-1-122-1-1222222220022000000-1-1-1-1-1-1-1-1-1-1-1-1-1-22-2112200220000-1-10000000000-2-2-211-11-2-1-111-1-1000-2000011000010
χ352222-122-12-122222-1-12-12-1-12-1-122-1-12222222200-2-2000000-1-1-1-1-1-1-1-1-1-1-1-1-12-22-1-1-2-200-2-20000110000000000-2-22-1-11-1211-1-111000-2000011000010
χ362222-122-12-122222-1-12-12-1-12-1-122-1-12222222200-2-2000000-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-211-2-200-2-2000011000000000022-21111-211111100020000-1-10000-10
χ372222-122-12-122222-1-12-1-2-1-12-1-122-1-1-2-2-2-2-2-2-2-20022000000-1-1-1-11111111112-2-2-1-12200-2-20000-1-10000000000222-1-111-21111-1-1000-20000-1-1000010
χ382222-122-12-122222-1-12-1-2-1-12-1-122-1-1-2-2-2-2-2-2-2-20022000000-1-1-1-1111111111-2-22112200-2-20000-1-10000000000-2-2-2111-1211-1-1-1-100020000110000-10
χ392222-122-12-122222-1-12-1-2-1-12-1-122-1-1-2-2-2-2-2-2-2-200-2-2000000-1-1-1-111111111122-2-1-1-2-200220000110000000000-2-22-1-1-11-2-1-1111100020000110000-10
χ402222-122-12-122222-1-12-1-2-1-12-1-122-1-1-2-2-2-2-2-2-2-200-2-2000000-1-1-1-1111111111-22211-2-20022000011000000000022-211-1-12-1-1-1-111000-20000-1-1000010
χ412-22-2222-22-2-2-22-2-222220-2-222-2-2-2-220000000000002i−2i2i2i−2i−2i2-2-2200000000000000002i−2i0000000000002i2i−2i−2i002-2000000000000000000002-22i−2i0000
χ422-22-2222-22-2-2-22-2-222220-2-222-2-2-2-220000000000002i−2i2i2i−2i−2i2-2-2200000000000000002i−2i0000000000002i2i−2i−2i00-2200000000000000000000-22−2i2i0000
χ432-22-2222-22-2-2-22-2-222220-2-222-2-2-2-22000000000000−2i2i−2i−2i2i2i2-2-220000000000000000−2i2i000000000000−2i−2i2i2i002-2000000000000000000002-2−2i2i0000
χ442-22-2222-22-2-2-22-2-222220-2-222-2-2-2-22000000000000−2i2i−2i−2i2i2i2-2-220000000000000000−2i2i000000000000−2i−2i2i2i00-2200000000000000000000-222i−2i0000
χ452-2-22222-2-2222-2-2-2-22220-2-2-2-222-22-2000000002i−2i2i−2i00000022-2-2000000000000002i−2i00002i−2i2i−2i2i−2i2i2i−2i−2i00002-20000000000002i−2i00002-20000000000
χ462-2-22222-2-2222-2-2-2-22220-2-2-2-222-22-2000000002i−2i−2i2i00000022-2-200000000000000−2i2i00002i−2i2i−2i−2i2i2i2i−2i−2i0000-22000000000000−2i2i0000-220000000000
χ472-2-22222-2-2222-2-2-2-22220-2-2-2-222-22-200000000−2i2i2i−2i00000022-2-2000000000000002i−2i0000−2i2i−2i2i2i−2i−2i−2i2i2i0000-220000000000002i−2i0000-220000000000
χ482-2-22222-2-2222-2-2-2-22220-2-2-2-222-22-200000000−2i2i−2i2i00000022-2-200000000000000−2i2i0000−2i2i−2i2i−2i2i−2i−2i2i2i00002-2000000000000−2i2i00002-20000000000
χ492-2-2222-1-2122-1-2-21-2-1-1201-21-2-1-11213−30033−3−32i−2i2i−2i00−i3i3−i3i3-1-1110003−333−3−300000−ii00−i3i32i−2i−ii2i−2i−i−iii−i3i3−i3i32-200000000−i3i300−ii0000-113−300000000
χ502-2-2222-1-2122-1-2-21-2-1-1201-21-2-1-11213−30033−3−32i−2i−2i2i00−i3i3−i3i3-1-1110003−333−3−300000i−i00i3−i32i−2i−ii−2i2i−i−iii−i3i3−i3i3-2200000000i3−i300i−i00001-1−3300000000
χ512-2-2222-1-2122-1-2-21-2-1-1201-21-2-1-11213−30033−3−3−2i2i2i−2i00i3−i3i3−i3-1-1110003−333−3−300000−ii00−i3i3−2i2ii−i2i−2iii−i−ii3−i3i3−i3-2200000000−i3i300−ii00001-1−3300000000
χ522-2-2222-1-2122-1-2-21-2-1-1201-21-2-1-11213−30033−3−3−2i2i−2i2i00i3−i3i3−i3-1-1110003−333−3−300000i−i00i3−i3−2i2ii−i−2i2iii−i−ii3−i3i3−i32-200000000i3−i300i−i0000-113−300000000
χ532-2-2222-1-2122-1-2-21-2-1-1201-21-2-1-1121−3300−3−3332i−2i2i−2i00i3−i3i3−i3-1-111000−33−3−33300000−ii00i3−i32i−2i−ii2i−2i−i−iiii3−i3i3−i32-200000000i3−i300−ii0000-11−3300000000
χ542-2-2222-1-2122-1-2-21-2-1-1201-21-2-1-1121−3300−3−3332i−2i−2i2i00i3−i3i3−i3-1-111000−33−3−33300000i−i00−i3i32i−2i−ii−2i2i−i−iiii3−i3i3−i3-2200000000−i3i300i−i00001-13−300000000
χ552-2-2222-1-2122-1-2-21-2-1-1201-21-2-1-1121−3300−3−333−2i2i2i−2i00−i3i3−i3i3-1-111000−33−3−33300000−ii00i3−i3−2i2ii−i2i−2iii−i−i−i3i3−i3i3-2200000000i3−i300−ii00001-13−300000000
χ562-2-2222-1-2122-1-2-21-2-1-1201-21-2-1-1121−3300−3−333−2i2i−2i2i00−i3i3−i3i3-1-111000−33−3−33300000i−i00−i3i3−2i2ii−i−2i2iii−i−i−i3i3−i3i32-200000000−i3i300i−i0000-11−3300000000
χ5744444-2-24-24-2-2-2-2-24-21-24-2-21-2-211-2-2-2-2-2-21111440044-2-2-2-211114-2-2-2-211110000000-2-200-2-2-2-2001111111100000000000000000000000000000000
χ5844444-2-24-24-2-2-2-2-24-21-24-2-21-2-211-2-2-2-2-2-21111-4-400-4-4222211114-2-2-2-2111100000002200222200-1-1-1-1-1-1-1-100000000000000000000000000000000
χ5944444-2-24-24-2-2-2-2-24-21-2-4-2-21-2-211-2-22222-1-1-1-14400-4-422221111-42222-1-1-1-100000002200-2-2-2-2001111-1-1-1-100000000000000000000000000000000
χ6044444-2-24-24-2-2-2-2-24-21-2-4-2-21-2-211-2-22222-1-1-1-1-4-40044-2-2-2-21111-42222-1-1-1-10000000-2-200222200-1-1-1-1111100000000000000000000000000000000
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χ844-44-444-2-4-2-4-424-424-2-2402-4-24222-4-20000000000004i−4i−2i−2i2i2i-222-200000000000000004i−4i000000000000−2i−2i2i2i00000000000000000000000000000000
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χ884-44-44-2-2-4-2-422-2224-21-20221-22-1-12-200003-3-3300004i−4i−2i−2i2i2i1-1-11000003-3-330000000−2i2i000000003i−3i−3i3iii−i−i00000000000000000000000000000000
χ894-44-44-2-2-4-2-422-2224-21-20221-22-1-12-200003-3-330000−4i4i2i2i−2i−2i1-1-11000003-3-3300000002i−2i00000000−3i3i3i−3i−i−iii00000000000000000000000000000000
χ904-44-44-2-2-4-2-422-2224-21-20221-22-1-12-20000-333-300004i−4i−2i−2i2i2i1-1-1100000-333-30000000−2i2i00000000−3i3i3i−3iii−i−i00000000000000000000000000000000
χ914-44-44-2-2-4-2-422-2224-21-20221-22-1-12-20000-333-30000−4i4i2i2i−2i−2i1-1-1100000-333-300000002i−2i000000003i−3i−3i3i−i−iii00000000000000000000000000000000
χ924-44-4-244242-4-44-4-4-2-24-20224-22-4-42-2000000000000000000-222-20000000000000000000000000000000000004-400000000000000000000-22000000
χ934-44-4-244242-4-44-4-4-2-24-20224-22-4-42-2000000000000000000-222-2000000000000000000000000000000000000-44000000000000000000002-2000000
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χ954-4-444-24-4-44-2422-4-44-2-20-42224-22-2-400000000−4i4i00000000-2-222000000000000000000002i−2i−4i4i002i2i−2i−2i000000000000000000000000000000000000
χ964-4-444-2-2-424-2-2222-4-21-2022-12-21-1-2223−2300−3−3334i−4i0000−2i32i3−2i32i311-1-100023−23−3−33300000000000−2i2i−2i2i00ii−i−ii3−i3i3−i300000000000000000000000000000000
χ974-4-444-2-2-424-2-2222-4-21-2022-12-21-1-2223−2300−3−333−4i4i00002i3−2i32i3−2i311-1-100023−23−3−333000000000002i−2i2i−2i00−i−iii−i3i3−i3i300000000000000000000000000000000
χ984-4-444-2-2-424-2-2222-4-21-2022-12-21-1-22−23230033−3−34i−4i00002i3−2i32i3−2i311-1-1000−232333−3−300000000000−2i2i−2i2i00ii−i−i−i3i3−i3i300000000000000000000000000000000
χ994-4-444-2-2-424-2-2222-4-21-2022-12-21-1-22−23230033−3−3−4i4i0000−2i32i3−2i32i311-1-1000−232333−3−3000000000002i−2i2i−2i00−i−iiii3−i3i3−i300000000000000000000000000000000
χ1004-4-44-2442-4-244-4-4-42-24-2022-42-24-4-2200000000004i−4i000000-2-222000000000000004i−4i00000000−2i2i0000000000000000000000−2i2i0000000000000000
χ1014-4-44-2442-4-244-4-4-42-24-2022-42-24-4-220000000000−4i4i000000-2-22200000000000000−4i4i000000002i−2i00000000000000000000002i−2i0000000000000000
χ1024-4-44-24-222-24-2-4-4221-2-20-12221-22-2-123−23002323−23−23004i−4i00000011-1-1000−33−3−33300000−2i2i00−2i32i30000−2i2i000000000000000000i3−i300i−i0000000000000000
χ1034-4-44-24-222-24-2-4-4221-2-20-12221-22-2-123−23002323−23−2300−4i4i00000011-1-1000−33−3−333000002i−2i002i3−2i300002i−2i000000000000000000−i3i300−ii0000000000000000
χ1044-4-44-24-222-24-2-4-4221-2-20-12221-22-2-1−232300−23−232323004i−4i00000011-1-10003−333−3−300000−2i2i002i3−2i30000−2i2i000000000000000000−i3i300i−i0000000000000000
χ1054-4-44-24-222-24-2-4-4221-2-20-12221-22-2-1−232300−23−23232300−4i4i00000011-1-10003−333−3−3000002i−2i00−2i32i300002i−2i000000000000000000i3−i300−ii0000000000000000
χ1068888-4-4-4-4-4-4-4-4-4-4-4-42228222222222-4-4-4-422220000000000-1-1-1-1-42222-1-1-1-1000000000000000000000000000000000000000000000000000000000
χ1078888-4-4-4-4-4-4-4-4-4-4-4-4222-82222222224444-2-2-2-20000000000-1-1-1-14-2-2-2-21111000000000000000000000000000000000000000000000000000000000
χ10888-8-8-48-4-444-84-88-442-4-402-444-24-44-20000000000000000002-22-2000000000000000000000000000000000000000000000000000000000000000000
χ10988-8-8-4-4-4-444444-4-44222022-2-2-2-22-2-20043−43−2323−23230000000000-11-110−2323003−33−3000000000000000000000000000000000000000000000000000000000
χ11088-8-8-4-4-4-444444-4-44222022-2-2-2-22-2-200−434323−2323−230000000000-11-11023−2300−33−33000000000000000000000000000000000000000000000000000000000
χ1118-88-8-48-44-44-848-84-42-4-40-24-4-4-244420000000000000000002-2-22000000000000000000000000000000000000000000000000000000000000000000
χ1128-88-8-4-484844-8-44-8-4-4-4204-2-42444-2-40000000000000000002-2-22000000000000000000000000000000000000000000000000000000000000000000
χ1138-88-8-4-4-44-4444-444-42220-2-222-2-2-2-2200006-6-660000000000-111-100000-333-3000000000000000000000000000000000000000000000000000000000
χ1148-88-8-4-4-44-4444-444-42220-2-222-2-2-2-220000-666-60000000000-111-1000003-3-33000000000000000000000000000000000000000000000000000000000
χ1158-8-88-4-484-8-4-4844-84-4-4204-24-2-4-442400000000000000000022-2-2000000000000000000000000000000000000000000000000000000000000000000
χ1168-8-88-4-4-444-4-4-444442220-2-2-2-222-22-243−4300−23−2323230000000000-1-111000−232333−3−3000000000000000000000000000000000000000000000000000000000
χ1178-8-88-4-4-444-4-4-444442220-2-2-2-222-22-2−4343002323−23−230000000000-1-11100023−23−3−333000000000000000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).