Finite Group Databasebeta

← Group #13172188

Character table — Group #13172188

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size1111222222222222444444444444444444444666666668888888888888121212121212121212121212121212121212121212121212121218182424242424242424242424243636363636363636363636727272108108
order122233366666666623336666666666666666644441212121236666666666664444121212121212121212121212121212121212121212122212121212121212121212121244444661212121212121224
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111-11-111111111-1-111111111111111-11-1-11111-1-1-1-1-11-1-1-11111-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111-1-111111111111111111-1111-1-1-1-111-1-111111111111111-1-11-111-1-1-1-11111-1-11-11-1-1-1-1-1-11-11-1-1
χ4111111111111111111111111111111111111111-1-111111111111111111-1-11-1-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-1-111-11-111
χ51111111111111111111111111111111111111-1-111-1-1-1-1111111111111111-111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-11-1-1-1-1-111-11-1-1-1
χ61111111111111111111111111111111111111-1-111-1-1-1-111111111111111-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11111-1-1-1-1-1-11-11-1-1-1-1-1-11-1111
χ71111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111-11-11-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111-111-1-1-1-11111-11-1-1-11111-1-1-1-1-111
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
χ91111111111111111-1111-1-1-1-11111-1-1-1-111111111111111-1-1-1-1-1111-1-1-1-1-11-1-1-1-111-1-1111111-1-11111-1-1-1-111-1-11-111-1-111-1-11-1-1-1111-1-111-1-111-1
χ101111111111111111-1111-1-1-1-11111-1-1-1-111111111111111-1-1-1-1-1111-1-1-1-1-1-1-11-1-111-1-111-1-111-1-11111-1-1-1-1111-1-1111-1-1-1-111-1-111-111-1-1-1-111-1-11
χ111111111111111111-1111-1-1-1-11111-1-1-1-11111111-1-111111-1-1-1-1-1111-1-1-1-111-1-111-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-111-1-1-11111-1-1-11-111-1-111-1-1-111-11
χ121111111111111111-1111-1-1-1-11111-1-1-1-11111111-1-111111-1-1-1-1-1111-1-1-1-11-1-1111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-111-11-1-111-1-111111-1-1-1-111111-1-11-1
χ131111111111111111-1111-1-1-1-11111-1-1-1-111111-1-111-1-1-1-11-1-1-1-1-1111-1-1-1-1-111-1-1-111111111-1-111-1-1-1-11111-1-1-1-11-111-1-111-1-1111-1-1-1-111111-1-1-11
χ141111111111111111-1111-1-1-1-11111-1-1-1-111111-1-111-1-1-1-11-1-1-1-1-1111-1-1-1-1-1-111-1-1111111-1-1-1-111-1-1-1-11111-1-11-1-1111-1-1-1-111-11-111-1-111-1-1-1111-1
χ151111111111111111-1111-1-1-1-11111-1-1-1-111111-1-1-1-1-1-1-1-11-1-1-1-1-1111-1-1-1-1111-111-1-111-1-111-1-111-1-1-1-1111111-111-1-1-11111-1-1-1-111-111-1-1-1-111-11-1
χ161111111111111111-1111-1-1-1-11111-1-1-1-111111-1-1-1-1-1-1-1-11-1-1-1-1-1111-1-1-1-11-11111-1-111-1-1-1-1-1-111-1-1-1-111111111-11-1-111-1-1111-1-1-1111-1-111-1-11-11
χ17222222-12-12-1-1222222-1-122-1-12-1-1-1-1-1-1-122-1-1-12222-1-1-1-1-1222-1-1-1-1-1-1-1-1-12020-1-122-1-1-1-1002222-1-1-1-1-1-1-1-1220200-1-1-1-1000002000-1-1-1-10000000
χ18222222-12-12-1-1222222-1-122-1-12-1-1-1-1-1-1-122-1-1-122-2-2-1-1-1-1-1222-1-1-1-1-1-1-1-1-1-202011-2-2-1-111002222-1-1-1-1-1-1-1-1-2-20-200111100000-200011110000000
χ19222222-12-12-1-1222222-1-122-1-12-1-1-1-1-1-1-122-1-1-1-2-2221111-1222-1-1-1-1-1-1-1-1-120-20-1-12211-1-100-2-2-2-211111111-2-20200-1-1-1-100000-200011110000000
χ20222222-12-12-1-1222222-1-122-1-12-1-1-1-1-1-1-122-1-1-1-2-2-2-21111-1222-1-1-1-1-1-1-1-1-1-20-2011-2-2111100-2-2-2-211111111220-2001111000002000-1-1-1-10000000
χ21222222-12-12-1-12222-22-1-1-2-2112-1-1-1111122-1-1-12222-1-1-1-1-1-2-2-211-1-1-11111-20-20112211-1-10022-2-2-1-1-1-11111220-200-1-11100000-2000-1-1110000000
χ22222222-12-12-1-12222-22-1-1-2-2112-1-1-1111122-1-1-122-2-2-1-1-1-1-1-2-2-211-1-1-1111120-20-1-1-2-211110022-2-2-1-1-1-11111-2-2020011-1-100000200011-1-10000000
χ23222222-12-12-1-12222-22-1-1-2-2112-1-1-1111122-1-1-1-2-2221111-1-2-2-211-1-1-11111-20201122-1-1-1-100-2-2221111-1-1-1-1-2-20-200-1-11100000200011-1-10000000
χ24222222-12-12-1-12222-22-1-1-2-2112-1-1-1111122-1-1-1-2-2-2-21111-1-2-2-211-1-1-111112020-1-1-2-2-1-11100-2-2221111-1-1-1-122020011-1-100000-2000-1-1110000000
χ2522222-1222-1222-1-122-12-12222-122-12222-1-1-1-1200220000-1-1-1-1-1-1-1-1-1-1-1-1-1220222-1-10022-1-100000000000000-1-122-1-1-1-1-1-1-1-1200200000-1-10-1000
χ2622222-1222-1222-1-122-12-12222-122-12222-1-1-1-1200220000-1-1-1-1-1-1-1-1-1-1-1-1-12-20-222-1-1002211000000000000001-1-2-2-1-1-1-11111-200-2000001101000
χ2722222-1222-1222-1-122-12-12222-122-12222-1-1-1-1200-2-20000-1-1-1-1-1-1-1-1-1-1-1-1-1-2202-2-21100-2-2-1-100000000000000-11221111-1-1-1-1-200-2000001101000
χ2822222-1222-1222-1-122-12-12222-122-12222-1-1-1-1200-2-20000-1-1-1-1-1-1-1-1-1-1-1-1-1-2-20-2-2-21100-2-2110000000000000011-2-211111111200200000-1-10-1000
χ2922222-1222-1222-1-12-2-12-1-2-2-2-2-122-1-2-2-2-2-1-1-1-1200220000-111111-1-1-11111-220-2-2-2-1-10022-1-100000000000000112-2-1-111-1-111200-200000-1-101000
χ3022222-1222-1222-1-12-2-12-1-2-2-2-2-122-1-2-2-2-2-1-1-1-1200220000-111111-1-1-11111-2-202-2-2-1-100221100000000000000-11-22-1-11111-1-1-200200000110-1000
χ3122222-1222-1222-1-12-2-12-1-2-2-2-2-122-1-2-2-2-2-1-1-1-1200-2-20000-111111-1-1-11111220-2221100-2-2-1-1000000000000001-12-211-1-1-1-111-200200000110-1000
χ3222222-1222-1222-1-12-2-12-1-2-2-2-2-122-1-2-2-2-2-1-1-1-1200-2-20000-111111-1-1-111112-202221100-2-21100000000000000-1-1-2211-1-111-1-1200-200000-1-101000
χ332222-122-12222-122-12-1-12-1-122-1-1-12-1-1-1-1-1-122-122002222-12-1-122-1-1-1-1-1-1-102220000220022-1-1-1-1-1-1-1-1-1-1-1-10020-1-10000-1-1-1-100202000000-10-100
χ342222-122-12222-122-12-1-12-1-122-1-1-12-1-1-1-1-1-122-122002222-12-1-122-1-1-1-1-1-1-10-22-200002200-2-2-1-1-1-1-1-1-1-1-1-1-1-100-20110000111100-20-200000010100
χ352222-122-12222-122-12-1-12-1-122-1-1-12-1-1-1-1-1-122-1-2-200-2-2-2-2-12-1-122-1-1-1-1-1-1-102-220000-2-200221111111111110020-1-10000-1-1-1-100-20-200000010100
χ362222-122-12222-122-12-1-12-1-122-1-1-12-1-1-1-1-1-122-1-2-200-2-2-2-2-12-1-122-1-1-1-1-1-1-10-2-2-20000-2-200-2-211111111111100-20110000111100202000000-10-100
χ372222-122-12222-122-1-2-1-1211-2-2-1-1-121111-1-122-122002222-1-211-2-2-1-1-1111102-2-20000-2-20022-1-111-1-1-1-1111100-20-110000-1-11100-20200000010-100
χ382222-122-12222-122-1-2-1-1211-2-2-1-1-121111-1-122-122002222-1-211-2-2-1-1-111110-2-220000-2-200-2-2-1-111-1-1-1-1111100201-1000011-1-10020-2000000-10100
χ392222-122-12222-122-1-2-1-1211-2-2-1-1-121111-1-122-1-2-200-2-2-2-2-1-211-2-2-1-1-11111022-2000022002211-1-11111-1-1-1-100-20-110000-1-1110020-2000000-10100
χ402222-122-12222-122-1-2-1-1211-2-2-1-1-121111-1-122-1-2-200-2-2-2-2-1-211-2-2-1-1-111110-22200002200-2-211-1-11111-1-1-1-100201-1000011-1-100-20200000010-100
χ412-22-2222-2-2-22-222-2-202220000-22-2200002-2-2-2-22i−2i2i−2i2i2i−2i−2i2000002-2-200000000002i−2i002i−2i002i−2i002i2i−2i−2i00002-200002i−2i000000000002-2000000000
χ422-22-2222-2-2-22-222-2-202220000-22-2200002-2-2-2-22i−2i−2i2i2i2i−2i−2i2000002-2-20000000000−2i2i00−2i2i002i−2i002i2i−2i−2i0000-220000−2i2i00000000000-22000000000
χ432-22-2222-2-2-22-222-2-202220000-22-2200002-2-2-2-2−2i2i2i−2i−2i−2i2i2i2000002-2-200000000002i−2i002i−2i00−2i2i00−2i−2i2i2i0000-2200002i−2i00000000000-22000000000
χ442-22-2222-2-2-22-222-2-202220000-22-2200002-2-2-2-2−2i2i−2i2i−2i−2i2i2i2000002-2-20000000000−2i2i00−2i2i00−2i2i00−2i−2i2i2i00002-20000−2i2i000000000002-2000000000
χ452-22-222-1-21-2-1122-2-202-1-100−i3i3-2-11-1−i3−i3i3i32-21112i−2i2i−2i−i−iii-1000−i3i3-111−i3−i3i3i300003−32i−2i3−3−ii002i−2i00−i−iii33−3−32-20000−ii3−3000000000-11−i3i30000000
χ462-22-222-1-21-2-1122-2-202-1-100−i3i3-2-11-1−i3−i3i3i32-21112i−2i−2i2i−i−iii-1000−i3i3-111−i3−i3i3i30000−33−2i2i3−3i−i002i−2i00−i−iii33−3−3-220000i−i−330000000001-1i3−i30000000
χ472-22-222-1-21-2-1122-2-202-1-100−i3i3-2-11-1−i3−i3i3i32-2111−2i2i2i−2iii−i−i-1000−i3i3-111−i3−i3i3i300003−32i−2i−33−ii00−2i2i00ii−i−i−3−333-220000−ii3−30000000001-1i3−i30000000
χ482-22-222-1-21-2-1122-2-202-1-100−i3i3-2-11-1−i3−i3i3i32-2111−2i2i−2i2iii−i−i-1000−i3i3-111−i3−i3i3i30000−33−2i2i−33i−i00−2i2i00ii−i−i−3−3332-20000i−i−33000000000-11−i3i30000000
χ492-22-222-1-21-2-1122-2-202-1-100i3−i3-2-11-1i3i3−i3−i32-21112i−2i2i−2i−i−iii-1000i3−i3-111i3i3−i3−i30000−332i−2i−33−ii002i−2i00−i−iii−3−3332-20000−ii−33000000000-11i3−i30000000
χ502-22-222-1-21-2-1122-2-202-1-100i3−i3-2-11-1i3i3−i3−i32-21112i−2i−2i2i−i−iii-1000i3−i3-111i3i3−i3−i300003−3−2i2i−33i−i002i−2i00−i−iii−3−333-220000i−i3−30000000001-1−i3i30000000
χ512-22-222-1-21-2-1122-2-202-1-100i3−i3-2-11-1i3i3−i3−i32-2111−2i2i2i−2iii−i−i-1000i3−i3-111i3i3−i3−i30000−332i−2i3−3−ii00−2i2i00ii−i−i33−3−3-220000−ii−330000000001-1−i3i30000000
χ522-22-222-1-21-2-1122-2-202-1-100i3−i3-2-11-1i3i3−i3−i32-2111−2i2i−2i2iii−i−i-1000i3−i3-111i3i3−i3−i300003−3−2i2i3−3i−i00−2i2i00ii−i−i33−3−32-20000i−i3−3000000000-11i3−i30000000
χ5344444-2-24-2-2-2-24-2-244-2-2144-2-2-2-2-21-2-2-2-2-2-211-2004400001-2-2-21111111114000-2-2-2-200-2-200000000000000000-200111100000000000000000000
χ5444444-2-24-2-2-2-24-2-244-2-2144-2-2-2-2-21-2-2-2-2-2-211-200-4-400001-2-2-2111111111-40002222002200000000000000000200-1-1-1-100000000000000000000
χ5544444-2-24-2-2-2-24-2-24-4-2-21-4-422-2-2-212222-2-211-2004400001222-1-1111-1-1-1-1-400022-2-200-2-20000000000000000020011-1-100000000000000000000
χ5644444-2-24-2-2-2-24-2-24-4-2-21-4-422-2-2-212222-2-211-200-4-400001222-1-1111-1-1-1-14000-2-222002200000000000000000-200-1-11100000000000000000000
χ574444-24-2-2-24-2-2-244-24-21-2-2-2-2-2-211-21111-2-2-2-214400-2-2-2-214-2-2-2-2111111100400000-2-20000-2-2-2-211111111000000000000000000000000000000
χ584444-24-2-2-24-2-2-244-24-21-2-2-2-2-2-211-21111-2-2-2-21-4-400222214-2-2-2-2111111100-4000002200002222-1-1-1-1-1-1-1-1000000000000000000000000000000
χ594444-24-2-2-24-2-2-244-2-4-21-22222-211-2-1-1-1-1-2-2-2-214400-2-2-2-21-42222111-1-1-1-100-400000220000-2-2221111-1-1-1-1000000000000000000000000000000
χ604444-24-2-2-24-2-2-244-2-4-21-22222-211-2-1-1-1-1-2-2-2-21-4-40022221-42222111-1-1-1-100400000-2-2000022-2-2-1-1-1-11111000000000000000000000000000000
χ614444-2-24-24-244-2-2-2-241-2-2-2-2441-2-2-2-2-2-2-211-2-2-2000000001-211-2-21111111040400000000-2-200000000000000-20-2-2000011110000000000000000
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χ7244-4-4-24-2-2-2-4222-4420-21-2−2i32i300-2-112i3−i3i3−i322-22-1000023−2323−2310−2i32i300-11-1i3−i3i3−i3000000000000000000−33−333i−3i3i−3i000000000000000000000000000000
χ7344-4-4-24-2-2-2-4222-4420-21-2−2i32i300-2-112i3−i3i3−i322-22-10000−2323−232310−2i32i300-11-1i3−i3i3−i30000000000000000003−33−3−3i3i−3i3i000000000000000000000000000000
χ7444-4-4-24-2-2-2-4222-4420-21-22i3−2i300-2-112−i3i3−i3i322-22-1000023−2323−23102i3−2i300-11-1−i3i3−i3i3000000000000000000−33−33−3i3i−3i3i000000000000000000000000000000
χ7544-4-4-24-2-2-2-4222-4420-21-22i3−2i300-2-112−i3i3−i3i322-22-10000−2323−2323102i3−2i300-11-1−i3i3−i3i30000000000000000003−33−33i−3i3i−3i000000000000000000000000000000
χ7644-4-4-2-24-242-4-422-2201-2-2−2i32i30012-22−2i32i3−2i32i3-1-1-2220000000010i3−i300-11-1i3−i3i3−i300000000000023−230000000000000000000000−333i−3i0000000000000000
χ7744-4-4-2-24-242-4-422-2201-2-2−2i32i30012-22−2i32i3−2i32i3-1-1-2220000000010i3−i300-11-1i3−i3i3−i3000000000000−232300000000000000000000003−3−3i3i0000000000000000
χ7844-4-4-2-24-242-4-422-2201-2-22i3−2i30012-222i3−2i32i3−2i3-1-1-2220000000010−i3i300-11-1−i3i3−i3i300000000000023−230000000000000000000000−33−3i3i0000000000000000
χ7944-4-4-2-24-242-4-422-2201-2-22i3−2i30012-222i3−2i32i3−2i3-1-1-2220000000010−i3i300-11-1−i3i3−i3i3000000000000−232300000000000000000000003−33i−3i0000000000000000
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χ874-44-4-2442-4-44-4-24-420-2-2400002-2240000-22-4-42−4i4i00−4i−4i4i4i-200000-2220000000000000000002i−2i002i2i−2i−2i0000000000000000000000000000000000
χ884-44-4-24-222-4-22-24-420-21-200−2i32i321-1-2i3i3−i3−i3-2222-14i−4i00−2i−2i2i2i1000−2i32i31-1-1i3i3−i3−i30000000023−230000−2i2i00ii−i−i−3−333000000000000000000000000000000
χ894-44-4-24-222-4-22-24-420-21-200−2i32i321-1-2i3i3−i3−i3-2222-1−4i4i002i2i−2i−2i1000−2i32i31-1-1i3i3−i3−i300000000−232300002i−2i00−i−iii33−3−3000000000000000000000000000000
χ904-44-4-24-222-4-22-24-420-21-2002i3−2i321-1-2−i3−i3i3i3-2222-14i−4i00−2i−2i2i2i10002i3−2i31-1-1−i3−i3i3i300000000−23230000−2i2i00ii−i−i33−3−3000000000000000000000000000000
χ914-44-4-24-222-4-22-24-420-21-2002i3−2i321-1-2−i3−i3i3i3-2222-1−4i4i002i2i−2i−2i10002i3−2i31-1-1−i3−i3i3i30000000023−2300002i−2i00−i−iii−3−333000000000000000000000000000000
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χ984-4-44-2442-44-442-4-4-20-2-240000222-400002-2-44-200000000-20000022-2000000000000000000002i3−2i300002i3−2i3−2i32i3000000000000000000000000000000
χ994-4-44-24-22242-22-4-4-20-21-200002-1-123-3-332-22-210000−2i32i32i3−2i3100000-1-113-3-330000000000000000−2i32i3i3−i3−i3i3i3−i3−i3i3000000000000000000000000000000
χ1004-4-44-24-22242-22-4-4-20-21-200002-1-123-3-332-22-2100002i3−2i3−2i32i3100000-1-113-3-3300000000000000002i3−2i3−i3i3i3−i3−i3i3i3−i3000000000000000000000000000000
χ1014-4-44-24-22242-22-4-4-20-21-200002-1-12-333-32-22-210000−2i32i32i3−2i3100000-1-11-333-300000000000000002i3−2i3i3−i3−i3i3−i3i3i3−i3000000000000000000000000000000
χ1024-4-44-24-22242-22-4-4-20-21-200002-1-12-333-32-22-2100002i3−2i3−2i32i3100000-1-11-333-30000000000000000−2i32i3−i3i3i3−i3i3−i3−i3i3000000000000000000000000000000
χ1038888-4-4-4-4-4-4-4-4-4-4-4-48222-4-4-4-4222222222222200000000-1-42222-1-1-1-1-1-1-100000000000000000000000000000000000000000000000000000000
χ1048888-4-4-4-4-4-4-4-4-4-4-4-4-822244442222-2-2-2-22222200000000-14-2-2-2-2-1-1-1111100000000000000000000000000000000000000000000000000000000
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χ10688-8-8-4-4-4-4-444444-440222−4i34i3002-22-22i3−2i32i3−2i3-2-22-2-200000000-102i3−2i3001-11−i3i3−i3i300000000000000000000000000000000000000000000000000000000
χ10788-8-8-4-4-4-4-444444-4402224i3−4i3002-22-2−2i32i3−2i32i3-2-22-2-200000000-10−2i32i3001-11i3−i3i3−i300000000000000000000000000000000000000000000000000000000
χ1088-88-8-4-484-848-8-4-44402-4-40000-2-44-400002-2444000000002000002-2-2000000000000000000000000000000000000000000000000000000000000
χ1098-88-8-4-4-4444-44-4-444022200−4i34i3-22-222i32i3−2i3−2i32-2-2-2-200000000-10002i3−2i3-111−i3−i3i3i300000000000000000000000000000000000000000000000000000000
χ1108-88-8-4-4-4444-44-4-4440222004i3−4i3-22-22−2i3−2i32i32i32-2-2-2-200000000-1000−2i32i3-111i3i3−i3−i300000000000000000000000000000000000000000000000000000000
χ1118-8-888-4-4-84-44-4-84480-4-420000444-200004-4-22-400000000200000-2-22000000000000000000000000000000000000000000000000000000000000
χ1128-8-88-4-484-8-4-88444-402-4-40000-24440000-224-4-400000000200000-2-22000000000000000000000000000000000000000000000000000000000000
χ1138-8-88-4-4-444-44-4444-402220000-2-2-2-26-6-66-22-22200000000-10000011-1-333-300000000000000000000000000000000000000000000000000000000
χ1148-8-88-4-4-444-44-4444-402220000-2-2-2-2-666-6-22-22200000000-10000011-13-3-3300000000000000000000000000000000000000000000000000000000

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