Finite Group Databasebeta

← Group #13172220

Character table — Group #13172220

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size1111222222222222444444444444444444444666666668888888888888121212121212121212121212121212121212121212121212121218182424242424242424242424243636363636363636363636727272108108
order122233366666666623336666666666666666644441212121236666666666662444661212121212121212121212121212121212121212446661212121212121212124444412121212121212121224
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-11-11111-1-1111111111111111111111-1-1-111-1-1-1-1-1-1-11-111-1-111-1-1-1-1-1
χ3111111111111111111111111111111111111111-1-1-1-1-1-1111111111111111-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-111-1-1-11-1-1-1
χ4111111111111111111111111111111111111111-1-1-1-1-1-111111111111111-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-111-1-1-1-1-1-11-11-1-1-1-1-1-11-1111
χ51111111111111111111111111111111111111-1-11111111111111111111-1111-1-1-1-111-1-111111111111111-1-1-1-1-1111-1-11111-1-11-11-1-1-1-1-1-11-11-1-1
χ61111111111111111111111111111111111111-1-11111111111111111111-1-11-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-111-1-1-11-111
χ71111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111-11-11-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1111-1-11111-1-1-11-111-1-111-1-1-111
χ81111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1
χ91111111111111111-1111-1-1-1-1111-1-1-1-1111111111111111-1-1-1-1-1111-1-1-1-1-11-1-1-1-111-1-111-1-111-1-11111-1-1-1-111-1-1-111-11111-1-1-11-1-1111-1-1-1-1-111-11
χ101111111111111111-1111-1-1-1-1111-1-1-1-1111111111111111-1-1-1-1-1111-1-1-1-1-1-1-11-1-1111111-1-111-1-11111-1-1-1-111-1-1-1-1-1111-1-1111-11-1-11111-1-11-1-11-1
χ111111111111111111-1111-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-11-1-1-1-1-1111-1-1-1-1-111-1-1-111-1-11111-1-111-1-1-1-11111-1-1-1-1-111-11111-1-1-1111-1-1-1-1-11111-11-1
χ121111111111111111-1111-1-1-1-1111-1-1-1-111111111-1-1-1-1-1-11-1-1-1-1-1111-1-1-1-1-1-111-1-111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1111-1-1111-1-111-1-11111-1-11-11
χ131111111111111111-1111-1-1-1-1111-1-1-1-1111111-1-11111111-1-1-1-1-1111-1-1-1-111-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-111111-1-1-111-1-11-1-111-1-11111-1-111-1
χ141111111111111111-1111-1-1-1-1111-1-1-1-1111111-1-11111111-1-1-1-1-1111-1-1-1-11-1-1111-1-111-1-1-1-111-1-11111-1-1-1-1-1-1111-1-11-1-1-1-111-1111-1-1-1-1-11111-1-11
χ151111111111111111-1111-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-1-1-11-1-1-1-1-1111-1-1-1-1111-111-1-1-1-1-1-111-1-111-1-1-1-111111111111-1-1-111-1-11-11-1-11111-1-11-1-1-11
χ161111111111111111-1111-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-1-1-11-1-1-1-1-1111-1-1-1-11-11111-1-111-1-111-1-111-1-1-1-1111111111-1-11-1-1-1-111-11-1-1111-1-1-1-1-1111-1
χ17222222-122-12-122-1222-1-1222222-12222-1-1-1-1-1222000000-1-1-1-1-1-1-1-1-1-1-1-1-122022222-1-1-1-10000000000000000-1-1-12-12-1-1-1-1-1-12200000-1-1000-1000
χ18222222-122-12-122-1222-1-1222222-12222-1-1-1-1-1222000000-1-1-1-1-1-1-1-1-1-1-1-1-12-20-2222211-1-10000000000000000-1-1-1-21-2-1-11111-2-200000110001000
χ19222222-122-12-122-1222-1-1222222-12222-1-1-1-1-12-2-2000000-1-1-1-1-1-1-1-1-1-1-1-1-1-2202-2-2-2-2-1-11100000000000000001112-1211-1-1-1-1-2-200000110001000
χ20222222-122-12-122-1222-1-1222222-12222-1-1-1-1-12-2-2000000-1-1-1-1-1-1-1-1-1-1-1-1-1-2-20-2-2-2-2-211110000000000000000111-21-21111112200000-1-1000-1000
χ21222222-122-12-122-12-22-1-1-2-2-2-222-1-2-2-2-2-1-1-1-1-1222000000-111111-1-1-11111-220-2-2-22211-1-100000000000000001112-1-2-1-1-1-111-220000011000-1000
χ22222222-122-12-122-12-22-1-1-2-2-2-222-1-2-2-2-2-1-1-1-1-1222000000-111111-1-1-11111-2-202-2-222-1-1-1-10000000000000000111-212-1-111-1-12-200000-1-10001000
χ23222222-122-12-122-12-22-1-1-2-2-2-222-1-2-2-2-2-1-1-1-1-12-2-2000000-111111-1-1-11111220-222-2-211110000000000000000-1-1-12-1-211-1-1112-200000-1-10001000
χ24222222-122-12-122-12-22-1-1-2-2-2-222-1-2-2-2-2-1-1-1-1-12-2-2000000-111111-1-1-111112-20222-2-2-1-1110000000000000000-1-1-1-2121111-1-1-220000011000-1000
χ2522222-122-12-122-1222-12-122-1-1-1-12-1-1-1-1-1-122-1-12222-1-1-1-1-1222-1-1-1-1-1-1-1-1-12020-1-1-1-10022-1-12222-1-1-1-1-1-1-1-1222-1-1000-1-1000000020-1-100-1-100000
χ2622222-122-12-122-1222-12-122-1-1-1-12-1-1-1-1-1-122-1-122-2-21111-1222-1-1-1-1-1-1-1-1-120-20-1-1-1-1002211-2-2-2-211111111-2-22-1-1000-1-10000000-2011001100000
χ2722222-122-12-122-1222-12-122-1-1-1-12-1-1-1-1-1-122-1-1-2-222-1-1-1-1-1222-1-1-1-1-1-1-1-1-1-2020111100-2-2-1-12222-1-1-1-1-1-1-1-1-2-2-211000110000000-2011001100000
χ2822222-122-12-122-1222-12-122-1-1-1-12-1-1-1-1-1-122-1-1-2-2-2-21111-1222-1-1-1-1-1-1-1-1-1-20-20111100-2-211-2-2-2-21111111122-21100011000000020-1-100-1-100000
χ2922222-122-12-122-122-2-12-1-2-211-1-121111-1-122-1-12222-1-1-1-1-1-2-2-211-1-1-11111-20-2011-1-100221122-2-2-1-1-1-1111122-211000-1-10000000-20-1-1001100000
χ3022222-122-12-122-122-2-12-1-2-211-1-121111-1-122-1-122-2-21111-1-2-2-211-1-1-11111-202011-1-10022-1-1-2-2221111-1-1-1-1-2-2-211000-1-10000000201100-1-100000
χ3122222-122-12-122-122-2-12-1-2-211-1-121111-1-122-1-1-2-222-1-1-1-1-1-2-2-211-1-1-1111120-20-1-11100-2-21122-2-2-1-1-1-11111-2-22-1-1000110000000201100-1-100000
χ3222222-122-12-122-122-2-12-1-2-211-1-121111-1-122-1-1-2-2-2-21111-1-2-2-211-1-1-111112020-1-11100-2-2-1-1-2-2221111-1-1-1-1222-1-1000110000000-20-1-1001100000
χ332222-122-12222-122-12-1-12-1-122-1-1-1-1-1-1-122-1-12-100222222-12-1-122-1-1-1-1-1-1-102220000220022-1-1-1-1-1-1-1-1-1-1-1-100000-12-100-1-1-1-100202000000-10-100
χ342222-122-12222-122-12-1-12-1-122-1-1-1-1-1-1-122-1-12-100222222-12-1-122-1-1-1-1-1-1-10-22-20000-2-20022-1-1-1-1-1-1-1-1-1-1-1-1000001-2100111100-20-200000010100
χ352222-122-12222-122-12-1-12-1-122-1-1-1-1-1-1-122-1-12-100-2-2-2-2-2-2-12-1-122-1-1-1-1-1-1-102-2200002200-2-211111111111100000-12-100-1-1-1-100-20-200000010100
χ362222-122-12222-122-12-1-12-1-122-1-1-1-1-1-1-122-1-12-100-2-2-2-2-2-2-12-1-122-1-1-1-1-1-1-10-2-2-20000-2-200-2-2111111111111000001-2100111100202000000-10-100
χ372222-122-12222-122-1-2-1-1211-2-2-1-1-1111122-1-12-100222222-1-211-2-2-1-1-1111102-2-20000-2-200-2-2-1-111-1-1-1-1111100000-12100-1-11100-20200000010-100
χ382222-122-12222-122-1-2-1-1211-2-2-1-1-1111122-1-12-100222222-1-211-2-2-1-1-111110-2-2200002200-2-2-1-111-1-1-1-11111000001-2-10011-1-10020-2000000-10100
χ392222-122-12222-122-1-2-1-1211-2-2-1-1-1111122-1-12-100-2-2-2-2-2-2-1-211-2-2-1-1-11111022-20000-2-2002211-1-11111-1-1-1-100000-12100-1-1110020-2000000-10100
χ402222-122-12222-122-1-2-1-1211-2-2-1-1-1111122-1-12-100-2-2-2-2-2-2-1-211-2-2-1-1-111110-222000022002211-1-11111-1-1-1-1000001-2-10011-1-100-20200000010-100
χ412-22-2222-22-2-2-22-22-2022200002-2-20000-2-22-22-22-22i−2i2i2i−2i−2i2000002-2-200000000002-2002-2002i−2i002i2i−2i−2i00002i−2i0000002-20000000002i−2i000000000
χ422-22-2222-22-2-2-22-22-2022200002-2-20000-2-22-22-22-2−2i2i−2i−2i2i2i2000002-2-200000000002-2002-200−2i2i00−2i−2i2i2i0000−2i2i0000002-2000000000−2i2i000000000
χ432-22-2222-22-2-2-22-22-2022200002-2-20000-2-22-22-2-222i−2i2i2i−2i−2i2000002-2-20000000000-2200-22002i−2i002i2i−2i−2i0000−2i2i000000-22000000000−2i2i000000000
χ442-22-2222-22-2-2-22-22-2022200002-2-20000-2-22-22-2-22−2i2i−2i−2i2i2i2000002-2-20000000000-2200-2200−2i2i00−2i−2i2i2i00002i−2i000000-220000000002i−2i000000000
χ452-22-22-12-2-1-21-2212-20-12-100−i3i3-11-2−i3−i3i3i3112-2-112-22i−2i−i−iii-1000−i3i3-111−i3−i3i3i30000−i3i3-11002-23−32i−2i00−i−iii33−3−32i−2i0−i3i3000-11000000000−ii003−300000
χ462-22-22-12-2-1-21-2212-20-12-100−i3i3-11-2−i3−i3i3i3112-2-112-2−2i2iii−i−i-1000−i3i3-111−i3−i3i3i30000−i3i3-11002-2−33−2i2i00ii−i−i−3−333−2i2i0−i3i3000-11000000000i−i00−3300000
χ472-22-22-12-2-1-21-2212-20-12-100−i3i3-11-2−i3−i3i3i3112-2-11-222i−2i−i−iii-1000−i3i3-111−i3−i3i3i30000i3−i31-100-223−32i−2i00−i−iii33−3−3−2i2i0i3−i30001-1000000000i−i00−3300000
χ482-22-22-12-2-1-21-2212-20-12-100−i3i3-11-2−i3−i3i3i3112-2-11-22−2i2iii−i−i-1000−i3i3-111−i3−i3i3i30000i3−i31-100-22−33−2i2i00ii−i−i−3−3332i−2i0i3−i30001-1000000000−ii003−300000
χ492-22-22-12-2-1-21-2212-20-12-100i3−i3-11-2i3i3−i3−i3112-2-112-22i−2i−i−iii-1000i3−i3-111i3i3−i3−i30000i3−i3-11002-2−332i−2i00−i−iii−3−3332i−2i0i3−i3000-11000000000−ii00−3300000
χ502-22-22-12-2-1-21-2212-20-12-100i3−i3-11-2i3i3−i3−i3112-2-112-2−2i2iii−i−i-1000i3−i3-111i3i3−i3−i30000i3−i3-11002-23−3−2i2i00ii−i−i33−3−3−2i2i0i3−i3000-11000000000i−i003−300000
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χ522-22-22-12-2-1-21-2212-20-12-100i3−i3-11-2i3i3−i3−i3112-2-11-22−2i2iii−i−i-1000i3−i3-111i3i3−i3−i30000−i3i31-100-223−3−2i2i00ii−i−i33−3−32i−2i0−i3i30001-1000000000−ii00−3300000
χ5344444-2-24-2-2-2-24-2-244-2-2144-2-2-2-2-2-2-2-2-211-2-21-2440000001-2-2-21111111114000-2-2-2-200-2-20000000000000000-2110001100000000000000000000
χ5444444-2-24-2-2-2-24-2-244-2-2144-2-2-2-2-2-2-2-2-211-2-21-2-4-40000001-2-2-2111111111-40002222002200000000000000002-1-1000-1-100000000000000000000
χ5544444-2-24-2-2-2-24-2-24-4-2-21-4-422-2-2-2222211-2-21-2440000001222-1-1111-1-1-1-1-400022-2-200-2-200000000000000002-1-10001100000000000000000000
χ5644444-2-24-2-2-2-24-2-24-4-2-21-4-422-2-2-2222211-2-21-2-4-40000001222-1-1111-1-1-1-14000-2-22200220000000000000000-211000-1-100000000000000000000
χ574444-24-2-24-24-2-24-2-24-21-2-2-244-2-21-2-2-2-2-2-211-2-2000000001-211-2-2111111104040000-2-2000000000000000000000-2-2-20011110000000000000000
χ584444-24-2-24-24-2-24-2-24-21-2-2-244-2-21-2-2-2-2-2-211-2-2000000001-211-2-211111110-40-400002200000000000000000000022200-1-1-1-10000000000000000
χ594444-24-2-24-24-2-24-2-2-4-21-222-4-4-2-212222-2-211-2-20000000012-1-122111-1-1-1-1040-4000022000000000000000000000-2-220011-1-10000000000000000
χ604444-24-2-24-24-2-24-2-2-4-21-222-4-4-2-212222-2-211-2-20000000012-1-122111-1-1-1-10-4040000-2-200000000000000000000022-200-1-1110000000000000000
χ614444-2-24-2-24-24-2-24-241-2-2-2-2-2-211-21111-2-2-2-2-210044-2-2-2-214-2-2-2-21111111004000000000-2-2-2-2-2-211111111000000000000000000000000000000
χ624444-2-24-2-24-24-2-24-241-2-2-2-2-2-211-21111-2-2-2-2-2100-4-4222214-2-2-2-2111111100-4000000000222222-1-1-1-1-1-1-1-1000000000000000000000000000000
χ634444-2-24-2-24-24-2-24-2-41-2-2222211-2-1-1-1-1-2-2-2-2-210044-2-2-2-21-42222111-1-1-1-100-400000000022-2-2221111-1-1-1-1000000000000000000000000000000
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χ7244-4-4-24-2-2-424-22-4220-21-2−2i32i3002-21−2i32i3−2i32i3-22-1-1220000000010i3−i300-11-1i3−i3i3−i30000000023−23000000000000000000000000003i−3i−330000000000000000
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χ7544-4-4-24-2-2-424-22-4220-21-22i3−2i3002-212i3−2i32i3−2i3-22-1-1220000000010−i3i300-11-1−i3i3−i3i300000000−2323000000000000000000000000003i−3i3−30000000000000000
χ7644-4-4-2-24-22-4-2422-4201-2-2−2i32i300-11-2i3−i3i3−i3-22222-1000023−2323−2310−2i32i300-11-1i3−i3i3−i3000000000000000000−33−333i−3i3i−3i000000000000000000000000000000
χ7744-4-4-2-24-22-4-2422-4201-2-2−2i32i300-11-2i3−i3i3−i3-22222-10000−2323−232310−2i32i300-11-1i3−i3i3−i30000000000000000003−33−3−3i3i−3i3i000000000000000000000000000000
χ7844-4-4-2-24-22-4-2422-4201-2-22i3−2i300-11-2−i3i3−i3i3-22222-1000023−2323−23102i3−2i300-11-1−i3i3−i3i3000000000000000000−33−33−3i3i−3i3i000000000000000000000000000000
χ7944-4-4-2-24-22-4-2422-4201-2-22i3−2i300-11-2−i3i3−i3i3-22222-10000−2323−2323102i3−2i300-11-1−i3i3−i3i30000000000000000003−33−33i−3i3i−3i000000000000000000000000000000
χ804-44-444-2-442-424-4-2-404-2-200004-42000022-22-2-44-4000000-200000-22200000000004-400-220000000000000000000000-2200000000000000000000
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χ884-44-4-2-242-2-42-4-224201-2-200−2i32i31-12i3i3−i3−i322-22-2-1004i−4i−2i−2i2i2i1000−2i32i31-1-1i3i3−i3−i300000000000023−23−2i2i00ii−i−i−3−333000000000000000000000000000000
χ894-44-4-2-242-2-42-4-224201-2-200−2i32i31-12i3i3−i3−i322-22-2-100−4i4i2i2i−2i−2i1000−2i32i31-1-1i3i3−i3−i3000000000000−23232i−2i00−i−iii33−3−3000000000000000000000000000000
χ904-44-4-2-242-2-42-4-224201-2-2002i3−2i31-12−i3−i3i3i322-22-2-1004i−4i−2i−2i2i2i10002i3−2i31-1-1−i3−i3i3i3000000000000−2323−2i2i00ii−i−i33−3−3000000000000000000000000000000
χ914-44-4-2-242-2-42-4-224201-2-2002i3−2i31-12−i3−i3i3i322-22-2-100−4i4i2i2i−2i−2i10002i3−2i31-1-1−i3−i3i3i300000000000023−232i−2i00−i−iii−3−333000000000000000000000000000000
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χ1014-4-44-2-242242-42-2-4-201-2-20000-1-12-333-32-22-2210000−2i32i32i3−2i3100000-1-11-333-300000000000000002i3−2i3i3−i3−i3i3−i3i3i3−i3000000000000000000000000000000
χ1024-4-44-2-242242-42-2-4-201-2-20000-1-12-333-32-22-22100002i3−2i3−2i32i3100000-1-11-333-30000000000000000−2i32i3−i3i3i3−i3i3−i3−i3i3000000000000000000000000000000
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χ10688-8-8-4-4-4-444-4-444440222−4i34i300-2222i3−2i32i3−2i32-2-2-2-2-200000000-102i3−2i3001-11−i3i3−i3i300000000000000000000000000000000000000000000000000000000
χ10788-8-8-4-4-4-444-4-4444402224i3−4i300-222−2i32i3−2i32i32-2-2-2-2-200000000-10−2i32i3001-11i3−i3i3−i300000000000000000000000000000000000000000000000000000000
χ1088-88-8-48-4484-84-4-8-440-42-40000-44-20000442-2-44000000002000002-2-2000000000000000000000000000000000000000000000000000000000000
χ1098-88-8-4-4-44-4444-44-44022200−4i34i32-2-22i32i3−2i3−2i3-2-22-22-200000000-10002i3−2i3-111−i3−i3i3i300000000000000000000000000000000000000000000000000000000
χ1108-88-8-4-4-44-4444-44-440222004i3−4i32-2-2−2i3−2i32i32i3-2-22-22-200000000-1000−2i32i3-111i3i3−i3−i300000000000000000000000000000000000000000000000000000000
χ1118-8-888-4-4-84-444-8-4480-4-4200004440000-224-4-2-400000000200000-2-22000000000000000000000000000000000000000000000000000000000000
χ1128-8-88-48-44-8-4-84484-40-42-4000044-200004-4-224-400000000200000-2-22000000000000000000000000000000000000000000000000000000000000
χ1138-8-88-4-4-444-4444-44-402220000-2-2-26-6-66-22-22-2200000000-10000011-1-333-300000000000000000000000000000000000000000000000000000000
χ1148-8-88-4-4-444-4444-44-402220000-2-2-2-666-6-22-22-2200000000-10000011-13-3-3300000000000000000000000000000000000000000000000000000000

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