Finite Group Databasebeta

← Group #13171654

Character table — Group #13171654

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99
size1122222223344444444444466666666688888888888121212121212121212121212121212121212121616161618181818242424242424242424242424243636363636363636363648727272108108
order12333466644333466612121212122246612121212361212121212121212122246666666812121212121224241212121224121266666612121212242424244666882424612122428
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-111111111-1111111-1-111111111-11-11111111-1-1-11-1-1111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1-111111111111111111-1-11111-1-11-1-1-1-111111111-1-1-1-1111111-1-1-1-1111-11-1-1-1-11-11111-1-1-1-1
χ4111111111111111111111111-1-1-1-11111111111111111-1-1-11111-1-1-1-1-1-1-111-1-11111-1-1-1-1-11-1111-1-1-1-1-1-1-1-1-11-1-1-1-11-1-1-1-11111
χ511111111111111-11111-1-11111111111111-1-11-1-11-1-11-11-1111-1-111-11-1-1111-1-1-11-1-111111-111-1-1-11-1-1-1-1-1-1111-1-1-1-1-1-1111-11-1
χ611111111111111-11111-1-11111111111111-1-11-1-11-1-11-1-1-1111-1-11111-1-111111-11-1-11111-1-1-11-1-1-11-1-1111-1-1-11-1-11111-1-1-11-11
χ711111111111111-11111-1-1111-1-1-1-1111111-1-11-1-11-1-11-111-111-1-1-1-1-1-111-111-1-1-11-1-1-1-1-1-11-111-1-11-111-1-1-111-1-111-11-1-111-11-11
χ811111111111111-11111-1-1111-1-1-1-1111111-1-11-1-11-1-11-1-11-111-1-1-1-11-111-11111-11-1-1-1-1-1-1-1-1-11-1-11-1111111-11-1111-111-1-11-11-1
χ9111111111-1-1111111111111-11111-1-1-1-111111111111-1111-1-1-1-11111111-1-1111111-1-1-1-11-11-1-1-11111111-1-11-1-1-1-11-1-11-111-1-1
χ10111111111-1-1111111111111-11111-1-1-1-111111111111-1-111-1-1-1-111-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-1-1-1-11-111-11-1-111
χ11111111111-1-1111111111111-1-1-1-1-1-1-1-1-111111111111-11-1-1-1-1-1-1-1-11-1-1-1-1-1-111111111111-11-1-1-1-1-1-1-11111-1-1111-1-1-1-11-1-1-111
χ12111111111-1-1111111111111-1-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1111-1-1
χ13111111111-1-1111-11111-1-111-11111-1-1-1-111-1-11-1-11-1-1111-11-1-11111-11-1-11-1-1-1-1-11-1-1-1-1-1-1111-111-11-1-1-1-1-11-11-1111-1111-11-1-11
χ14111111111-1-1111-11111-1-111-11111-1-1-1-111-1-11-1-11-1-111-1-11-1-1111111-1-11-1-111-11-1-1-1-1-1-1-11-1-111-11-1-111111-1-111-11-1-1-11-111-1
χ15111111111-1-1111-11111-1-111-1-1-1-1-1-1-1-1-111-1-11-1-11-1-11111-1-1-111-1-1-1-111-1-1-1-1-1-11-1-11111111-1111-111-1-1-1-1-1-11-1-111111-1-111-1
χ16111111111-1-1111-11111-1-111-1-1-1-1-1-1-1-1-111-1-11-1-11-1-111-11-1-1-111-1-11-111-1-1-111-11-1-11111-11-1-1111-111111-1111-1-1-1-1-1-1-111-1-11
χ1722222-2222222220222-200-2-2-22-22222222200-200-200-20002-2-200220-200-222000-200-2222000-2000-200000000-2000000000000
χ1822222-2222222220222-200-2-2-2-22-2-222222200-200-200-2000-2-2-200-2-20200222000-2002-2-2-2000-20002000000002000000000000
χ1922222-2222-2-22220222-200-2-222-222-2-2-2-22200-200-200-200022200220-200-2-2-2000-2002-2-2-20002000-2000000002000000000000
χ2022222-2222-2-22220222-200-2-22-22-2-2-2-2-2-22200-200-200-2000-22200-2-202002-2-2000-200-22220002000200000000-2000000000000
χ212222-122-1222-12-122-1-1-1-1-122222-1-122-1-1-1-122-1-1-1-1-1-1220222-1-1-1-1-10-1-1-12-1-1002-1-1-122-1-1020-1-1-12-1-1-1000200-1-1-10000000000
χ222222-122-1222-12-122-1-1-1-1-1222-2-21122-1-1-1-122-1-1-1-1-1-1220-2-22-1-1-1110111-2-1-1002-1-1-1-2-211020-1-1-1-2111000-2001110000000000
χ232222-122-1222-12-1-22-1-1-11122222-1-122-1-1-1-1-2-2-111-1112-20-222-111-1-10-1112-1-100-2-11122-1-10-20-111-2-111000-200-1110000000000
χ242222-122-1222-12-1-22-1-1-111222-2-21122-1-1-1-1-2-2-111-1112-202-22-1111101-1-1-2-1-100-2-111-2-2110-20-11121-1-10002001-1-10000000000
χ252222-122-12-2-2-12-122-1-1-1-1-122-222-1-1-2-211-1-122-1-1-1-1-1-12-2022-2111-1-10-1-1-1211002-1-1-1-2-2110-201112-1-1-1000-2001110000000000
χ262222-122-12-2-2-12-122-1-1-1-1-122-2-2-211-2-211-1-122-1-1-1-1-1-12-20-2-2-2111110111-211002-1-1-122-1-10-20111-2111000200-1-1-10000000000
χ272222-122-12-2-2-12-1-22-1-1-11122-222-1-1-2-211-1-1-2-2-111-111220-22-21-1-1-1-10-11121100-2-111-2-2110201-1-1-2-1110002001-1-10000000000
χ282222-122-12-2-2-12-1-22-1-1-11122-2-2-211-2-211-1-1-2-2-111-1112202-2-21-1-11101-1-1-21100-2-11122-1-10201-1-121-1-1000-200-1110000000000
χ292222-1-22-1222-12-102-1-11−i3i3-2-2-22-2-1-122-1-1-1-1001−i3i31−i3i3-20002-21−i3i3-1-101−i3i3-2-1-10001−i3i3-22-1-10001−i3i301−i3i30000001−i3i30000000000
χ302222-1-22-1222-12-102-1-11−i3i3-2-2-2-221122-1-1-1-1001−i3i31−i3i3-2000-2-21−i3i3110-1i3−i32-1-10001−i3i32-2110001−i3i30-1i3−i3000000-1i3−i30000000000
χ312222-1-22-1222-12-102-1-11i3−i3-2-2-22-2-1-122-1-1-1-1001i3−i31i3−i3-20002-21i3−i3-1-101i3−i3-2-1-10001i3−i3-22-1-10001i3−i301i3−i30000001i3−i30000000000
χ322222-1-22-1222-12-102-1-11i3−i3-2-2-2-221122-1-1-1-1001i3−i31i3−i3-2000-2-21i3−i3110-1−i3i32-1-10001i3−i32-2110001i3−i30-1−i3i3000000-1−i3i30000000000
χ332222-1-22-12-2-2-12-102-1-11−i3i3-2-222-2-1-1-2-211-1-1001−i3i31−i3i3-200022-1i3−i3-1-101−i3i3-2110001−i3i32-211000-1i3−i301−i3i3000000-1i3−i30000000000
χ342222-1-22-12-2-2-12-102-1-11−i3i3-2-22-2211-2-211-1-1001−i3i31−i3i3-2000-22-1i3−i3110-1i3−i32110001−i3i3-22-1-1000-1i3−i30-1i3−i30000001−i3i30000000000
χ352222-1-22-12-2-2-12-102-1-11i3−i3-2-222-2-1-1-2-211-1-1001i3−i31i3−i3-200022-1−i3i3-1-101i3−i3-2110001i3−i32-211000-1−i3i301i3−i3000000-1−i3i30000000000
χ362222-1-22-12-2-2-12-102-1-11i3−i3-2-22-2211-2-211-1-1001i3−i31i3−i3-2000-22-1−i3i3110-1−i3i32110001i3−i3-22-1-1000-1−i3i30-1−i3i30000001i3−i30000000000
χ37222-122-122222-1-12-1-12222-1220000-1-122-1-1-12-1-1-1222-12200-12220020000-1-1-1-1-1-1-1-100002-1-1-1-1-100002-1-102000020-1-1-1-10000
χ38222-122-122222-1-12-1-12222-1220000-1-122-1-1-12-1-1-1222-12-200-122200-20000-1-111-1-1-1-10000-2-11-1-1-10000-2110-20000-2011110000
χ39222-122-122222-1-1-2-1-122-2-2-1220000-1-122-1-11-2-1112-2-2-1-2200-12-2-200-20000-1-1111-111000021-1-1110000-211020000-2011-1-10000
χ40222-122-122222-1-1-2-1-122-2-2-1220000-1-122-1-11-2-1112-2-2-1-2-200-12-2-20020000-1-1-1-11-1110000-211-11100002-1-10-2000020-1-1110000
χ41222-122-122-2-22-1-12-1-12222-12-2000011-2-2-1-1-12-1-1-1222-1-22001-2-2-2002000011-1-1-1-1-1-1000021-111100002-1-10-20000-2011-110000
χ42222-122-122-2-22-1-12-1-12222-12-2000011-2-2-1-1-12-1-1-1222-1-2-2001-2-2-200-200001111-1-1-1-10000-2111110000-21102000020-1-11-10000
χ43222-122-122-2-22-1-1-2-1-122-2-2-12-2000011-2-2-1-11-2-1112-2-2-122001-22200-2000011111-11100002-1-11-1-10000-2110-2000020-1-1-110000
χ44222-122-122-2-22-1-1-2-1-122-2-2-12-2000011-2-2-1-11-2-1112-2-2-12-2001-222002000011-1-11-1110000-2-111-1-100002-1-1020000-20111-10000
χ4522-122222-100-1-122-12-12222-1022220000-1-12-1222-1-1-1-1022-10000-1-12222-10022-1-1-1-10000-102000-1-1-1-1-1-1-10020000200-10-1-100
χ4622-122222-100-1-122-12-12222-1022220000-1-12-1222-1-1-1-10-22-10000-1-1-2222-100-2-2-1-1-1-1000010-2000-1-1-1-111100-20000-200101100
χ4722-122222-100-1-122-12-12222-10-2-2-2-20000-1-12-1222-1-1-1-102-210000112-2-2-210022-1-1-1-10000-1020001111-1-1-100-20000-200-101100
χ4822-122222-100-1-122-12-12222-10-2-2-2-20000-1-12-1222-1-1-1-10-2-21000011-2-2-2-2100-2-2-1-1-1-1000010-20001111111002000020010-1-100
χ4922-122222-100-1-12-2-12-12-2-22-1022220000-1-1-212-2-2-111-102-2-10000-1-1-22-2-2-100-2-21-1110000-1020001-1111110020000-200-10-1100
χ5022-122222-100-1-12-2-12-12-2-22-1022220000-1-1-212-2-2-111-10-2-2-10000-1-122-2-2-100221-111000010-20001-111-1-1-100-20000200101-100
χ5122-122222-100-1-12-2-12-12-2-22-10-2-2-2-20000-1-1-212-2-2-111-10221000011-2-222100-2-21-1110000-102000-11-1-111100-20000200-101-100
χ5222-122222-100-1-12-2-12-12-2-22-10-2-2-2-20000-1-1-212-2-2-111-10-2210000112-222100221-111000010-2000-11-1-1-1-1-10020000-20010-1100
χ53444-24-4-244444-2-20-2-24-4002-4-40000-2-244-2-200200-400200002-4000000000-2-2000200000000020000000000000000000000000
χ54444-24-4-244-4-44-2-20-2-24-4002-44000022-4-4-2-200200-40020000-24000000000220002000000000-20000000000000000000000000
χ55444-2-24-2-2444-2-214-21-2-2-2-2-2440000-2-2-2-211-24111-2-2-2-24000-2-2-2-200000001100-211100000-2011100000000000000000000000
χ56444-2-24-2-2444-2-21-4-21-2-222-2440000-2-2-2-2112-41-1-1-222-2-4000-2-2220000000110021-1-100000201-1-100000000000000000000000
χ57444-2-24-2-24-4-4-2-214-21-2-2-2-2-24-40000222211-24111-2-2-2-2-400022220000000-1-100-21110000020-1-1-100000000000000000000000
χ58444-2-24-2-24-4-4-2-21-4-21-2-222-24-400002222112-41-1-1-222-2400022-2-20000000-1-10021-1-100000-20-11100000000000000000000000
χ59444-2-2-4-2-2444-2-210-21-22−2i32i32-4-40000-2-2-2-21100-1i3−i32−2i32i32000022−2i32i3000000011000-1i3−i30000000-1i3−i300000000000000000000000
χ60444-2-2-4-2-2444-2-210-21-222i3−2i32-4-40000-2-2-2-21100-1−i3i322i3−2i320000222i3−2i3000000011000-1−i3i30000000-1−i3i300000000000000000000000
χ61444-2-2-4-2-24-4-4-2-210-21-22−2i32i32-44000022221100-1i3−i32−2i32i320000-2-22i3−2i30000000-1-1000-1i3−i300000001−i3i300000000000000000000000
χ62444-2-2-4-2-24-4-4-2-210-21-222i3−2i32-44000022221100-1−i3i322i3−2i320000-2-2−2i32i30000000-1-1000-1−i3i300000001i3−i300000000000000000000000
χ6344-244-444-200-2-240-24-2-400-4204-4440000-2-200-4002002000-20000-2-20-400200000200000000000002000000000000000000000
χ6444-244-444-200-2-240-24-2-400-420-44-4-40000-2-200-400200200020000220400-20000020000000000000-2000000000000000000000
χ6544-24-244-2-2001-2-24-2-21-2-2-24-2044-2-20000114-2-2-2-2111-2004-20000110-2-2-2-20000-21110000000000-21110000000000000000000
χ6644-24-244-2-2001-2-24-2-21-2-2-24-20-4-4220000114-2-2-2-2111-200-420000-1-1022220000-211100000000002-1-1-10000000000000000000
χ6744-24-244-2-2001-2-2-4-2-21-2224-2044-2-2000011-42-2221-1-1-200-4-20000110-222-2000021-1-1000000000021-1-10000000000000000000
χ6844-24-244-2-2001-2-2-4-2-21-2224-20-4-422000011-42-2221-1-1-200420000-1-102-2-22000021-1-10000000000-2-1110000000000000000000
χ6944-24-2-44-2-2001-2-20-2-212−2i32i3-4204-4-2-2000011002−2i32i3-1i3−i32000-200001102−2i32i3200000-1i3−i300000000000-1i3−i30000000000000000000
χ7044-24-2-44-2-2001-2-20-2-212−2i32i3-420-4422000011002−2i32i3-1i3−i3200020000-1-10-22i3−2i3-200000-1i3−i3000000000001−i3i30000000000000000000
χ7144-24-2-44-2-2001-2-20-2-2122i3−2i3-4204-4-2-20000110022i3−2i3-1−i3i32000-2000011022i3−2i3200000-1−i3i300000000000-1−i3i30000000000000000000
χ7244-24-2-44-2-2001-2-20-2-2122i3−2i3-420-44220000110022i3−2i3-1−i3i3200020000-1-10-2−2i32i3-200000-1−i3i3000000000001i3−i30000000000000000000
χ7344-2-244-24-200-21-241-2-2444-2-200000000011-2-2-2-2-2-2-2-2104000000004000000-2-211110000-20-20000000-2110000000000100000
χ7444-2-244-24-200-21-241-2-2444-2-200000000011-2-2-2-2-2-2-2-210-400000000-4000000221111000020200000002-1-10000000000-100000
χ7544-2-244-24-200-21-2-41-2-24-4-4-2-20000000001122-222-22210400000000-400000022-11-1-10000-20-200000002-1-10000000000100000
χ7644-2-244-24-200-21-2-41-2-24-4-4-2-20000000001122-222-22210-4000000004000000-2-2-11-1-100002020000000-2110000000000-100000
χ774-44440-4-4-44i−4i4440-4-4-400000000004i−4i4i−4i4-40000000000000000000000004i−4i000000000000000000000000000000000000000
χ784-44440-4-4-4−4i4i4440-4-4-40000000000−4i4i−4i4i4-4000000000000000000000000−4i4i000000000000000000000000000000000000000
χ794-444-20-42-44i−4i-24-20-42200000000−2i32i34i−4i−2i2i-2200000000000000000−2i32i300000−2i2i0000000023−2300000000000000000000000000000
χ804-444-20-42-44i−4i-24-20-422000000002i3−2i34i−4i−2i2i-22000000000000000002i3−2i300000−2i2i00000000−232300000000000000000000000000000
χ814-444-20-42-4−4i4i-24-20-42200000000−2i32i3−4i4i2i−2i-2200000000000000000−2i32i3000002i−2i00000000−232300000000000000000000000000000
χ824-444-20-42-4−4i4i-24-20-422000000002i3−2i3−4i4i2i−2i-22000000000000000002i3−2i3000002i−2i0000000023−2300000000000000000000000000000
χ834-44-2402-4-44i−4i4-2-2022-40000000000−2i2i4i−4i-22000000000000000000000000−2i2i6−600000000000000000006−600000000i6−i6000000
χ844-44-2402-4-44i−4i4-2-2022-40000000000−2i2i4i−4i-22000000000000000000000000−2i2i−660000000000000000000−6600000000−i6i6000000
χ854-44-2402-4-4−4i4i4-2-2022-400000000002i−2i−4i4i-220000000000000000000000002i−2i6−600000000000000000006−600000000−i6i6000000
χ864-44-2402-4-4−4i4i4-2-2022-400000000002i−2i−4i4i-220000000000000000000000002i−2i−660000000000000000000−6600000000i6−i6000000
χ8788-4-48-8-48-400-42-402-4-4-800440000000002200400400-200000000000000000000-200000000000000000000000000000000000
χ8888-4-4-48-4-4-4002228222-4-4-4-4-4000000000-1-1-4-4222222200000000000000000002-1-1-1000000000000000000000000000000000
χ8988-4-4-48-4-4-400222-8222-444-4-4000000000-1-1442-2-22-2-220000000000000000000-2-111000000000000000000000000000000000
χ9088-4-4-4-8-4-4-40022202224−4i34i344000000000-1-100-22i3−2i3-22i3−2i3-2000000000000000000001−i3i3000000000000000000000000000000000
χ9188-4-4-4-8-4-4-400222022244i3−4i344000000000-1-100-2−2i32i3-2−2i32i3-2000000000000000000001i3−i3000000000000000000000000000000000
χ928-88-4-4044-88i−8i-4-4204-240000000000−4i4i−4i4i2-20000000000000000000000002i−2i000000000000000000000000000000000000000
χ938-88-4-4044-8−8i8i-4-4204-2400000000004i−4i4i−4i2-2000000000000000000000000−2i2i000000000000000000000000000000000000000
χ948-8-4880-8-8400-4-4804-8400000000000000-4400000000000000000000000000000000000000000000000000000000000000000
χ958-8-48-40-844002-4-4044-200000000−4i34i300002-2000000000000000002i3−2i30000000000000000000000000000000000000000000000
χ968-8-48-40-844002-4-4044-2000000004i3−4i300002-200000000000000000−2i32i30000000000000000000000000000000000000000000000
χ978-8-4-4804-8400-42-40-244000000000000002-20000000000000000000000000026−260000000000000000000−660000000000000000
χ988-8-4-4804-8400-42-40-244000000000000002-200000000000000000000000000−262600000000000000000006−60000000000000000
χ9916-16-8-8-80888004440-4-4-400000000000000-2200000000000000000000000000000000000000000000000000000000000000000

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