Finite Group Databasebeta

← Group #13168412

Character table — Group #13168412

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111
size11112222222222224444444444444446666888888888888888812121212121212121212121212121212121212121818181818181818181818182424242424242424242424242424242436363636363636367272108108
order12223336666666663334666666666121222443666121212121212121212121212244466666612121212121212121212444444441212121266666121212121212121212121244121212121212121244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111-11-1111-1-111111111-1-11111-1-111-1-11111-111-1-111-11111-1-111-1-111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111-1-111111111111111111-111111111-1-111-1-111-1-1-1-111-1-1-1-1-1-1-1-1111111-1111-1-111-1-11-1-1-111-1-11-1-1-1
χ4111111111111111111111111111111111-1-11111111111111111-1-1-1111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-111-1-11-1-111-1-1-1-1-1-1-11-1-1-1-111-1111
χ51111111111111111111111111111111-1-1111111111111111111111-1-1-111-1-111-1-1111111-1-1-1-1-1-111-1-1-1-11-1-111-111-1-1111111-11-1-1-1-111-11-1-1
χ61111111111111111111111111111111-1-1111111111111111111-11-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-111-1-1111-1-1-111-1-11-111
χ71111111111111111111111111111111-1-1-1-111111111111111111-11-1-1-111-1-1-1-1-1-1-1-111-1-111-1-111-1-111111-1-111-1-11-1-1-1-111-1-1-1-111-1-1-1-1-1-111
χ81111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1
χ91111111111111111111-1111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-111111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111-1-1-1-1-1-1-1-1-1111-111-1-1111-1-11
χ101111111111111111111-1111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-11111-1-1-1-11111-1-11111-1-1-1-1-1-1-111-1-1-1-11-1-1-1-11111-111111-1-1-111-1
χ111111111111111111111-1111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1111111111-11-1-1-111-1-1-1-111-1-1-1-1-1-1111-1
χ121111111111111111111-1111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-111-1-1-1-11111-1-11111-1-1111111-111-1-1-111-1-11111-1-1-1-1-1-11111-1-1-11
χ131111111111111111111-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-111-1-11111-1-1-1-1111111-1-11111111-1-1111-1-111-1-1-1-111-1-1-1-11111-1-11-1
χ141111111111111111111-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1111111-1-1-1-1-1-11111-1-1-1-1-11-1111-1-1111111-1-1-1-1-1-111-11
χ151111111111111111111-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-11-1-111-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-11-1-11111-11111-1-1-1-1-111111-1-1-11-11
χ161111111111111111111-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1111111111-1-11-111-1-1111-11-1
χ17222222-12-1-12222-122-1-122-1-1-1-12-1-12222200-1-1-1-1-12-1-1-1-122-1-1-1-120222222-1-1002200-1-100002200000000-1-1-1-1-1-102-1-100-1-1002000-1-100-1000
χ18222222-12-1-12222-122-1-122-1-1-1-12-1-12222200-1-1-1-1-12-1-1-1-122-1-1-1-1-20-2222-2-2-1-1002200110000-2-2000000001-1-111-10-2-1-1001100-200011001000
χ19222222-12-1-12222-122-1-122-1-1-1-12-1-1222-2-200-1-1-1-1-12-1-1-1-122-1-1-1-1202-2-2-2221100-2-200-1-10000-2-200000000-111-1-11021100-1-100-200011001000
χ20222222-12-1-12222-122-1-122-1-1-1-12-1-1222-2-200-1-1-1-1-12-1-1-1-122-1-1-1-1-20-2-2-2-2-2-21100-2-20011000022000000001111110-2110011002000-1-100-1000
χ21222222-12-1-12222-122-1-1-22-1-1-1-12-1-12-2-22200-1-1-1-11-21111-2-2111120-2-22222-1-100-2-200110000-2-200000000-1-1-1-1-110-21100110020001100-1000
χ22222222-12-1-12222-122-1-1-22-1-1-1-12-1-12-2-22200-1-1-1-11-21111-2-21111-202-222-2-2-1-100-2-200-1-1000022000000001-1-1111021100-1-100-2000-1-1001000
χ23222222-12-1-12222-122-1-1-22-1-1-1-12-1-12-2-2-2-200-1-1-1-11-21111-2-2111120-22-2-222110022001100002200000000-111-1-1-10-2-1-1001100-2000-1-1001000
χ24222222-12-1-12222-122-1-1-22-1-1-1-12-1-12-2-2-2-200-1-1-1-11-21111-2-21111-2022-2-2-2-211002200-1-10000-2-20000000011111-102-1-100-1-10020001100-1000
χ2522222-12222-12-1-122-12-12-12-12-1-12-1-1-1-12222-1-1-1-12222-1-1-1-1-1-1-1-10202-1-10022-1-1-1-1-1-1002222002200-1-1-1-10-1-100220-1-1-1-100-1-100-1-100000000
χ2622222-12222-12-1-122-12-12-12-12-1-12-1-1-1-122-2-2-1-1-1-12222-1-1-1-1-1-1-1-10-202-1-1002211-1-11100-2-2-2-200-2-20011110-1-1002-20-1-1110011001100000000
χ2722222-12222-12-1-122-12-12-12-12-1-12-1-1-1-1-2-222-1-1-1-12222-1-1-1-1-1-1-1-1020-21100-2-2-1-111-1-10022-2-200-2-200111101100-22011-1-100-1-1001100000000
χ2822222-12222-12-1-122-12-12-12-12-1-12-1-1-1-1-2-2-2-2-1-1-1-12222-1-1-1-1-1-1-1-10-20-21100-2-211111100-2-222002200-1-1-1-101100-2-201111001100-1-100000000
χ2922222-12222-12-1-122-12-1-2-12-12-1-12-1-1112222-1-1-1-1-2-2-2-2111111110-20-2-1-10022-1-111110022-2-200220011110-1-100-2-20111100-1-100-1-100000000
χ3022222-12222-12-1-122-12-1-2-12-12-1-12-1-11122-2-2-1-1-1-1-2-2-2-211111111020-2-1-100221111-1-100-2-22200-2-200-1-1-1-10-1-100-22011-1-10011001100000000
χ3122222-12222-12-1-122-12-1-2-12-12-1-12-1-111-2-222-1-1-1-1-2-2-2-2111111110-2021100-2-2-1-1-1-11100222200-2-200-1-1-1-1011002-20-1-11100-1-1001100000000
χ3222222-12222-12-1-122-12-1-2-12-12-1-12-1-111-2-2-2-2-1-1-1-1-2-2-2-21111111102021100-2-211-1-1-1-100-2-2-2-2002200111101100220-1-1-1-1001100-1-100000000
χ332222-122-1222-1222-1-1-122-1-12-12-1-12-1220022-1-1-1-12-1-1-122-1-1-1-1-1-1222000-1-10022002222-1-1000000220000200-1-10-1-100-1-1-1-1-1-1020000-1-10-100
χ342222-122-1222-1222-1-1-122-1-12-12-1-12-1220022-1-1-1-12-1-1-122-1-1-1-1-1-1-22-20001100220022-2-2-1-1000000-2-20000-200110-1100-1-111-1-10-20000110100
χ352222-122-1222-1222-1-1-122-1-12-12-1-12-12200-2-2-1-1-1-12-1-1-122-1-1-1-1-1-12-22000-1-100-2-200-2-22211000000-2-20000200-1-101-10011-1-1110-20000110100
χ362222-122-1222-1222-1-1-122-1-12-12-1-12-12200-2-2-1-1-1-12-1-1-122-1-1-1-1-1-1-2-2-20001100-2-200-2-2-2-211000000220000-2001101100111111020000-1-10-100
χ372222-122-1222-1222-1-1-12-2-1-12-12-1-12-1-2-20022-1-1-1-1-2111-2-21111112-2-2000-1-1002200-2-2-2-2-1-1000000220000200-1-1011001111-1-10-20000-1-10100
χ382222-122-1222-1222-1-1-12-2-1-12-12-1-12-1-2-20022-1-1-1-1-2111-2-2111111-2-2200011002200-2-222-1-1000000-2-20000-2001101-10011-1-1-1-1020000110-100
χ392222-122-1222-1222-1-1-12-2-1-12-12-1-12-1-2-200-2-2-1-1-1-1-2111-2-211111122-2000-1-100-2-20022-2-211000000-2-20000200-1-10-1100-1-11111020000110-100
χ402222-122-1222-1222-1-1-12-2-1-12-12-1-12-1-2-200-2-2-1-1-1-1-2111-2-2111111-2220001100-2-200222211000000220000-200110-1-100-1-1-1-1110-20000-1-10100
χ4122-2-2222-2-2-2-222-22-22220-2-22-2-222-2-2002-22i−2i22-2-200000000000000002-2002-22i−2i0000002i−2i00002i−2i00000002-2000000000002i−2i002i−2i00000000
χ4222-2-2222-2-2-2-222-22-22220-2-22-2-222-2-2002-2−2i2i22-2-200000000000000002-2002-2−2i2i000000−2i2i0000−2i2i00000002-200000000000−2i2i00−2i2i00000000
χ4322-2-2222-2-2-2-222-22-22220-2-22-2-222-2-200-222i−2i22-2-20000000000000000-2200-222i−2i0000002i−2i0000−2i2i0000000-22000000000002i−2i00−2i2i00000000
χ4422-2-2222-2-2-2-222-22-22220-2-22-2-222-2-200-22−2i2i22-2-20000000000000000-2200-22−2i2i000000−2i2i00002i−2i0000000-2200000000000−2i2i002i−2i00000000
χ4522-2-22-12-2-2-212-112-2-12-101-2-1-21-12113−32-22i−2i-1-11100003−33−333−3−30000-11002-2−ii3−3−i3i3002i−2i00002i−2i00−i3−i3i3i30-11000003−3−i3i300−ii00−ii00000000
χ4622-2-22-12-2-2-212-112-2-12-101-2-1-21-12113−32-2−2i2i-1-11100003−33−333−3−30000-11002-2i−i3−3i3−i300−2i2i0000−2i2i00i3i3−i3−i30-11000003−3i3−i300i−i00i−i00000000
χ4722-2-22-12-2-2-212-112-2-12-101-2-1-21-12113−3-222i−2i-1-11100003−33−333−3−300001-100-22−ii−33−i3i3002i−2i0000−2i2i00i3i3−i3−i301-100000−33−i3i300−ii00i−i00000000
χ4822-2-22-12-2-2-212-112-2-12-101-2-1-21-12113−3-22−2i2i-1-11100003−33−333−3−300001-100-22i−i−33i3−i300−2i2i00002i−2i00−i3−i3i3i301-100000−33i3−i300i−i00−ii00000000
χ4922-2-22-12-2-2-212-112-2-12-101-2-1-21-1211−332-22i−2i-1-1110000−33−33−3−3330000-11002-2−ii−33i3−i3002i−2i00002i−2i00i3i3−i3−i30-1100000−33i3−i300−ii00−ii00000000
χ5022-2-22-12-2-2-212-112-2-12-101-2-1-21-1211−332-2−2i2i-1-1110000−33−33−3−3330000-11002-2i−i−33−i3i300−2i2i0000−2i2i00−i3−i3i3i30-1100000−33−i3i300i−i00i−i00000000
χ5122-2-22-12-2-2-212-112-2-12-101-2-1-21-1211−33-222i−2i-1-1110000−33−33−3−33300001-100-22−ii3−3i3−i3002i−2i0000−2i2i00−i3−i3i3i301-1000003−3i3−i300−ii00i−i00000000
χ5222-2-22-12-2-2-212-112-2-12-101-2-1-21-1211−33-22−2i2i-1-1110000−33−33−3−33300001-100-22i−i3−3−i3i300−2i2i00002i−2i00i3i3−i3−i301-1000003−3−i3i300i−i00−ii00000000
χ532-2-22222-22-22-2-2-2-222220-2-2-222-2-2-220000002-2-22000000000000000000000000000000002i−2i2i−2i002-22i−2i2i−2i000000000000000000002i−2i2-20000
χ542-2-22222-22-22-2-2-2-222220-2-2-222-2-2-220000002-2-22000000000000000000000000000000002i−2i−2i2i00-222i−2i2i−2i00000000000000000000−2i2i-220000
χ552-2-22222-22-22-2-2-2-222220-2-2-222-2-2-220000002-2-2200000000000000000000000000000000−2i2i2i−2i00-22−2i2i−2i2i000000000000000000002i−2i-220000
χ562-2-22222-22-22-2-2-2-222220-2-2-222-2-2-220000002-2-2200000000000000000000000000000000−2i2i−2i2i002-2−2i2i−2i2i00000000000000000000−2i2i2-20000
χ5744444-2-24-2-2-24-2-2-24-2-214-2-21-21-2-21-2-2-244001111-24-2-211-2-211110004-2-200-2-200-2-200000000000000000001100-20011000000000000000000
χ5844444-2-24-2-2-24-2-2-24-2-214-2-21-21-2-21-2-2-2-4-4001111-24-2-211-2-21111000-422002200220000000000000000000-1-100200-1-1000000000000000000
χ5944444-2-24-2-2-24-2-2-24-2-21-4-2-21-21-2-21-222440011112-422-1-122-1-1-1-1000-4-2-200-2-2002200000000000000000001100200-1-1000000000000000000
χ6044444-2-24-2-2-24-2-2-24-2-21-4-2-21-21-2-21-222-4-40011112-422-1-122-1-1-1-1000422002200-2-20000000000000000000-1-100-20011000000000000000000
χ614444-24-2-2-2-24-244-2-2-21-24-21-21-2-21-2-24400001111-2-211-2-2-2-21111404000-2-200000000-2-200000000000000-2001100-200001100000000000000
χ624444-24-2-2-2-24-244-2-2-21-24-21-21-2-21-2-24400001111-2-211-2-2-2-21111-40-400022000000002200000000000000200-1-10020000-1-100000000000000
χ634444-24-2-2-2-24-244-2-2-21-2-4-21-21-2-21-2-2-4-40000111122-1-12222-1-1-1-140-4000-2-2000000002200000000000000-200110020000-1-100000000000000
χ644444-24-2-2-2-24-244-2-2-21-2-4-21-21-2-21-2-2-4-40000111122-1-12222-1-1-1-1-4040002200000000-2-200000000000000200-1-100-200001100000000000000
χ654444-2-24-244-2-2-2-24-21-2-241-2-2-2-21-2-21-2-2004411114-2-2-2-2-21111110400000000-2-200-2-200-2-2000000000000000000-2000110011000000000000
χ664444-2-24-244-2-2-2-24-21-2-241-2-2-2-21-2-21-2-200-4-411114-2-2-2-2-21111110-40000000022002200220000000000000000002000-1-100-1-1000000000000
χ674444-2-24-244-2-2-2-24-21-2-2-41-2-2-2-21-2-212200441111-422222-1-1-1-1-1-10-400000000-2-2002200-2-20000000000000000002000-1-10011000000000000
χ684444-2-24-244-2-2-2-24-21-2-2-41-2-2-2-21-2-212200-4-41111-422222-1-1-1-1-1-104000000002200-2-20022000000000000000000-20001100-1-1000000000000
χ6944-4-444-2-422-444-4-2-44-2-20-42-2224-22-4004-400-2-22200000000000000004-400-2200000000000000000000000-220000000000000000000000000
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χ7344-4-44-2-2-42224-22-2-4-2-2102212-1-2-2-12−23234-40011-1-100003−3−232333−3−30000-2200-2200−232300000000000000000001-1000003−3000000000000000000
χ7444-4-44-2-2-42224-22-2-4-2-2102212-1-2-2-12−2323-440011-1-100003−3−232333−3−300002-2002-20023−230000000000000000000-1100000−33000000000000000000
χ7544-4-4-2442-4-4-4-24-442-2-2402242-4-2-2-4200004i−4i-2-22200000000000000000000004i−4i000000−2i2i00000000000000000000000000−2i2i000000000000
χ7644-4-4-2442-4-4-4-24-442-2-2402242-4-2-2-420000−4i4i-2-2220000000000000000000000−4i4i0000002i−2i000000000000000000000000002i−2i000000000000
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χ7844-4-4-2-242-4-42-2-22421-2-20-12-2221-22-123−2300−4i4i11-1-1000023−23−33−3−33300000000002i−2i002i3−2i3002i−2i0000000000000000000000−i3i300−ii000000000000
χ7944-4-4-2-242-4-42-2-22421-2-20-12-2221-22-1−2323004i−4i11-1-10000−23233−333−3−30000000000−2i2i002i3−2i300−2i2i0000000000000000000000−i3i300i−i000000000000
χ8044-4-4-2-242-4-42-2-22421-2-20-12-2221-22-1−232300−4i4i11-1-10000−23233−333−3−300000000002i−2i00−2i32i3002i−2i0000000000000000000000i3−i300−ii000000000000
χ814-44-44444-44-4-4-44-4-4444044-4-4-4-4-44-40000004-44-4000000000000000000000000000000000000000000000000000000000000000000000000
χ824-44-444-242-2-4-4-442-44-2-204-2222-42-2-4000000-22-22000000000000000000000000000023−230000000000000000000000000023−2300000000000000
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χ864-44-4-244-2-44-42-44-42-2-240-2-2-42-42242000000-22-22000000000000000000−2i32i3000000000000000000000000000−2i32i300000000000000000000000
χ874-44-4-244-2-44-42-44-42-2-240-2-2-42-42242000000-22-220000000000000000002i3−2i30000000000000000000000000002i3−2i300000000000000000000000
χ884-44-4-24-2-22-2-42-4422-21-20-212-122-1-220000001-11-1003i−3i00003i−3i3i−3i000000−2i32i30000000023−2300000000000000000i3−i30000000−3300000000000000
χ894-44-4-24-2-22-2-42-4422-21-20-212-122-1-220000001-11-1003i−3i00003i−3i3i−3i0000002i3−2i300000000−232300000000000000000−i3i300000003−300000000000000
χ904-44-4-24-2-22-2-42-4422-21-20-212-122-1-220000001-11-100−3i3i0000−3i3i−3i3i000000−2i32i300000000−232300000000000000000i3−i300000003−300000000000000
χ914-44-4-24-2-22-2-42-4422-21-20-212-122-1-220000001-11-100−3i3i0000−3i3i−3i3i0000002i3−2i30000000023−2300000000000000000−i3i30000000−3300000000000000
χ924-4-4444-2-4-224-4-4-4244-2-20-422-2-2-4224000000-222-200000000000000000000000000000000004i−4i0000000000000000000000000000−2i2i000000
χ934-4-4444-2-4-224-4-4-4244-2-20-422-2-2-4224000000-222-20000000000000000000000000000000000−4i4i00000000000000000000000000002i−2i000000
χ944-4-444-24-44-4-2-422-44-24-202-424-22-42-2000000-222-2000000000000000000000000000000004i−4i000000−2i2i−2i2i0000000000000000000000000000
χ954-4-444-24-44-4-2-422-44-24-202-424-22-42-2000000-222-200000000000000000000000000000000−4i4i0000002i−2i2i−2i0000000000000000000000000000
χ964-4-44-24424-442-4-4-4-2-2-24022-4-2422-4-2000000-222-2000000000000000000000000000000000000004-400000000000000000000000000-220000
χ974-4-44-24424-442-4-4-4-2-2-24022-4-2422-4-2000000-222-200000000000000000000000000000000000000-44000000000000000000000000002-20000
χ988888-4-4-4-4-4-4-4-4-4-4-4-42228222222222-4-40000-1-1-1-1-4-4222222-1-1-1-1000000000000000000000000000000000000000000000000000000000000
χ998888-4-4-4-4-4-4-4-4-4-4-4-4222-8222222222440000-1-1-1-144-2-2-2-2-2-21111000000000000000000000000000000000000000000000000000000000000
χ10088-8-8-48-4444-8-48-8-44-42-404-2-4-24-424400000022-2-2000000000000000000000000000000000000000000000000000000000000000000000000
χ10188-8-8-4-4-44444-4-44-442220-2-22-2-222-2-243−430000-1-1110000−2323−232333−3−3000000000000000000000000000000000000000000000000000000000000
χ10288-8-8-4-4-44444-4-44-442220-2-22-2-222-2-2−43430000-1-111000023−2323−23−3−333000000000000000000000000000000000000000000000000000000000000
χ1038-88-88-4-484-44-84-44-8-4-420-4-4-24-244240000002-22-2000000000000000000000000000000000000000000000000000000000000000000000000
χ1048-88-8-4-48-4-88444-4-842-4-402-4444-24-4-20000002-22-2000000000000000000000000000000000000000000000000000000000000000000000000
χ1058-88-8-4-4-4-44-4444-444222022-2-2-2-2-22-2000000-11-11006i−6i0000−3i3i−3i3i000000000000000000000000000000000000000000000000000000000000
χ1068-88-8-4-4-4-44-4444-444222022-2-2-2-2-22-2000000-11-1100−6i6i00003i−3i3i−3i000000000000000000000000000000000000000000000000000000000000
χ1078-8-888-4-4-8-44-4-84448-4-42044-2-4244-2-40000002-2-22000000000000000000000000000000000000000000000000000000000000000000000000
χ1088-8-88-48-44-4484-8-84-4-42-404-242-44-24-40000002-2-22000000000000000000000000000000000000000000000000000000000000000000000000
χ1098-8-88-4-4848-8-4444-8-42-4-40-244-4-4-24420000002-2-22000000000000000000000000000000000000000000000000000000000000000000000000
χ1108-8-88-4-4-44-44-44444-42220-2-2-222-2-2-22000000-111-100000000−3i33i33i3−3i3000000000000000000000000000000000000000000000000000000000000
χ1118-8-88-4-4-44-44-44444-42220-2-2-222-2-2-22000000-111-1000000003i3−3i3−3i33i3000000000000000000000000000000000000000000000000000000000000

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