Finite Group Databasebeta

← Group #13167782

Character table — Group #13167782

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99
size1122222222244444444444444466668888888888888888899121212121212121212121212121212121818181818242424242424242424242424242436363636363636484872727272108108
order12333466612123336668121212121212242422443612121224242424242424242424242444226666881212121224242424266121266666612122424242424242244824246666121244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111-1-11111111111111111111-1-1-1-11111111111-1-1-1-1111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111-11-111111111111111111-1-1111-11-11-11-11-111-1-1-1-1-1-1-111111-11-1111-1-1-11-11-1-1-1-1111-11-1-1-1
χ4111111111111111111111111111-11-111111111111111111-1-1-1-11-11-11-11-11-111-1-1-1-1-1-1-1-1-1-1-11-11-1111-1-1-1-11-11-1-1-1-1-1-11-1111
χ511111111111111111111111111-11-1111111111111111111-1-111-11-11-11-11-11-1-111-1-1-1-1-11111-11-11-1-1-1111-11-11-1-1-111-11-11-1-1
χ611111111111111111111111111-11-1111111111111111111-1-1-1-1-11-11-11-11-11-1-111-1-1-1-1-1-1-1-1-1-11-11-1-1-11111-11-1-1-1-1-1-11-11-111
χ711111111111111111111111111-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-111
χ811111111111111111111111111-1-1-1-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-11111-1-1
χ911111111111111111-1111111-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1111-11111-1-11111-1-1-1-11111111-1-11111-1-1-1-1-1-11-1-11-1-1-11-11-1-111-1
χ1011111111111111111-1111111-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-111-111111-1-11111-1-1-1-111111-1-1111111-1-1-1-1-1-1-111-1-1-1-1-11-111-1-11
χ1111111111111111111-1111111-1-11-11-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-11-1-111-11-1-1-111-1-1-1-1-111-1-11-11-1-1-1-111111-1-11111-111-1-1-11
χ1211111111111111111-1111111-1-11-11-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11-1-111-11-1-1-111-1-1-1-1-1-1-1111-11-1-1-1-1111-1-111111-11-1-1111-1
χ1311111111111111111-1111111-1-1-11-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-111-1-11-1111-1-1-1-1-1-1-111-1-1-11-11111-1-1-1-1-1111111-1-1-111-11
χ1411111111111111111-1111111-1-1-11-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-11-1111-1-1-1-1-1-1-1-1-111-11-11111-1-1-111-1-1111-1111-1-11-1
χ1511111111111111111-1111111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-111-1-1-1-111111111111-1-1-1-1-1-1111111-111-1-1-1-11-1-111-11-1
χ1611111111111111111-1111111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111-11-1-1-1-111-1-1-1-1111111111-1-111-1-1-1-11111111-1-11-1-1-1-111-1-11-11
χ1722222-2222-2-22222220-2-2-2-2-2-20022-2-222-2-2-2000000000000-2-200222200-2-2-2-20000222-2-2000022-2-2000000000000000000000
χ1822222-2222-2-22222220-2-2-2-2-2-2002-2-2222-2-2-200000000000022002-22-200-22-220000-2-2-22200002-2-22000000000000000000000
χ1922222-2222-2-22222220-2-2-2-2-2-200-222-222-2-2-20000000000002200-22-22002-22-20000-2-2-2220000-222-2000000000000000000000
χ2022222-2222-2-22222220-2-2-2-2-2-200-2-22222-2-2-2000000000000-2-200-2-2-2-20022220000222-2-20000-2-222000000000000000000000
χ212222-1222-1222-1-1-12-122-122-1-1220202-1-1-1-1-1222-1-1-1-1-1-1-1-1-10022020-102020-10022000002-12-10-10-1000-1-1-10202000-1-10-10-100
χ222222-1222-1222-1-1-12-122-122-1-1220202-1-1-1-1-1222-1-1-1-1-1-1-1-1-100-2-2020-102020-1002200000-21-210-10-1000-1-1-10-20-200011010100
χ232222-1222-1222-1-1-12-122-122-1-1220-20-2-1-1-1-1-1222-1-1-1-1-1-1-1-1-100220-2010-20-20100-2-2000002-12-101010001110-20-2000-1-1010100
χ242222-1222-1222-1-1-12-122-122-1-1220-20-2-1-1-1-1-1222-1-1-1-1-1-1-1-1-100-2-20-2010-20-20100-2-200000-21-2101010001110202000110-10-100
χ252222-1222-1222-1-1-12-1-22-122-1-1-2-20202-1-1-1-1-1-2-2-2111111111002-2020-10-2020-100-2-2000002-1-210-10-10001110-202000-11010-100
χ262222-1222-1222-1-1-12-1-22-122-1-1-2-20202-1-1-1-1-1-2-2-211111111100-22020-10-2020-100-2-200000-212-10-10-1000111020-20001-10-10100
χ272222-1222-1222-1-1-12-1-22-122-1-1-2-20-20-2-1-1-1-1-1-2-2-2111111111002-20-201020-2010022000002-1-210101000-1-1-1020-2000-110-10100
χ282222-1222-1222-1-1-12-1-22-122-1-1-2-20-20-2-1-1-1-1-1-2-2-211111111100-220-201020-201002200000-212-10101000-1-1-10-2020001-1010-100
χ29222-1222-1222-12-1-1-122-12-1-122222020-1-1-1-1-1-1-1-1222-1-1-1-1-1-1002220-102020-10220000000-12-12-10-10-1-1-10002020000-1-1-10-1000
χ30222-1222-1222-12-1-1-122-12-1-122222020-1-1-1-1-1-1-1-1222-1-1-1-1-1-100-2-220-102020-102200000001-21-2-10-10-1-1-1000-20-2000011101000
χ31222-1222-1222-12-1-1-122-12-1-12222-20-20-1-1-1-1-1-1-1-1222-1-1-1-1-1-10022-2010-20-2010-2-20000000-12-121010111000-20-20000-1-1101000
χ32222-1222-1222-12-1-1-122-12-1-12222-20-20-1-1-1-1-1-1-1-1222-1-1-1-1-1-100-2-2-2010-20-2010-2-200000001-21-21010111000202000011-10-1000
χ33222-1222-1222-12-1-1-12-2-12-1-122-2-22020-1-1-1-1-1111-2-2-2111111002-220-10-2020-10-2-20000000-121-2-10-1011100020-20000-11-101000
χ34222-1222-1222-12-1-1-12-2-12-1-122-2-22020-1-1-1-1-1111-2-2-211111100-2220-10-2020-10-2-200000001-2-12-10-10111000-20200001-110-1000
χ35222-1222-1222-12-1-1-12-2-12-1-122-2-2-20-20-1-1-1-1-1111-2-2-2111111002-2-201020-2010220000000-121-21010-1-1-1000-2020000-1110-1000
χ36222-1222-1222-12-1-1-12-2-12-1-122-2-2-20-20-1-1-1-1-1111-2-2-211111100-22-201020-20102200000001-2-121010-1-1-100020-200001-1-101000
χ3722-1222-122-1-1-1-122-1-1222-1-1-1-1-1-12222-1-12-1-12-1-12-1-122-1-1-1-12200-1-12222-1-122-1-1-1-12-1-1-1-10000-1-1-1-12-1-12-1-100002-1-100000000
χ3822-1222-122-1-1-1-122-1-1222-1-1-1-1-1-12-22-2-1-12-1-12-1-12-1-122-1-1-1-1-2-200-112-22-2-112-2-1-111-211110000-11-112-1-1-2110000-21100000000
χ3922-1222-122-1-1-1-122-1-1222-1-1-1-1-1-1-22-22-1-12-1-12-1-12-1-122-1-1-1-1-2-2001-1-22-221-1-2211-1-1-2111100001-11-1-2112-1-10000-21100000000
χ4022-1222-122-1-1-1-122-1-1222-1-1-1-1-1-1-2-2-2-2-1-12-1-12-1-12-1-122-1-1-1-1220011-2-2-2-211-2-211112-1-1-1-100001111-211-21100002-1-100000000
χ4122-1222-122-1-1-1-122-1-1-222-1-1-1-1112222-1-12-1-1-211-211-2-211112200-1-122-2-2-1-12211112-1-1-1-10000-1-1-1-1-211-2110000-21100000000
χ4222-1222-122-1-1-1-122-1-1-222-1-1-1-1112-22-2-1-12-1-1-211-211-2-21111-2-200-112-2-22-112-211-1-1-211110000-11-11-2112-1-100002-1-100000000
χ4322-1222-122-1-1-1-122-1-1-222-1-1-1-111-22-22-1-12-1-1-211-211-2-21111-2-2001-1-222-21-1-22-1-111-2111100001-11-12-1-1-21100002-1-100000000
χ4422-1222-122-1-1-1-122-1-1-222-1-1-1-111-2-2-2-2-1-12-1-1-211-211-2-21111220011-2-22211-2-2-1-1-1-12-1-1-1-1000011112-1-12-1-10000-21100000000
χ4522-122-2-12211-1-122-1-10-2-211113−322-2-2-1-1-21103−303−30033−3−3-2-200-1-1220011-2-23−33−32-1-1110000-1-11103−303−3000003−300000000
χ4622-122-2-12211-1-122-1-10-2-211113−32-2-22-1-1-21103−303−30033−3−32200-112-2001-1-223−3−33-211-1-10000-111-103−30−3300000−3300000000
χ4722-122-2-12211-1-122-1-10-2-211113−3-222-2-1-1-21103−303−30033−3−322001-1-2200-112-2−333−3-211-1-100001-1-110−3303−300000−3300000000
χ4822-122-2-12211-1-122-1-10-2-211113−3-2-222-1-1-21103−303−30033−3−3-2-20011-2-200-1-122−33−332-1-111000011-1-10−330−33000003−300000000
χ4922-122-2-12211-1-122-1-10-2-21111−3322-2-2-1-1-2110−330−3300−3−333-2-200-1-1220011-2-2−33−332-1-1110000-1-1110−330−3300000−3300000000
χ5022-122-2-12211-1-122-1-10-2-21111−332-2-22-1-1-2110−330−3300−3−3332200-112-2001-1-22−333−3-211-1-10000-111-10−3303−3000003−300000000
χ5122-122-2-12211-1-122-1-10-2-21111−33-222-2-1-1-2110−330−3300−3−33322001-1-2200-112-23−3−33-211-1-100001-1-1103−30−33000003−300000000
χ5222-122-2-12211-1-122-1-10-2-21111−33-2-222-1-1-2110−330−3300−3−333-2-20011-2-200-1-1223−33−32-1-111000011-1-103−303−300000−3300000000
χ534444-2-444-2-4-44-2-2-24-20-42-4-42200040-4-2-22220000000000000000040-2000-40200000000000000-202000000000000000000000
χ544444-2-444-2-4-44-2-2-24-20-42-4-422000-404-2-222200000000000000000-40200040-20000000000000020-2000000000000000000000
χ55444-24-44-24-4-4-24-2-2-2402-422-4-40040-40-2-2222000000000000000040-2000-40200000000000000-2020000000000000000000000
χ56444-24-44-24-4-4-24-2-2-2402-422-4-400-4040-2-22220000000000000000-40200040-20000000000000020-20000000000000000000000
χ57444-2-244-2-244-2-211-2-24-2-2-2-2-2-244000011111-2-2-2-2-2-211111100440000000000000000000-2-2-2-20000000000000000011000000
χ58444-2-244-2-244-2-211-2-24-2-2-2-2-2-244000011111-2-2-2-2-2-211111100-4-40000000000000000000222200000000000000000-1-1000000
χ59444-2-244-2-244-2-211-2-2-4-2-2-2-2-2-2-4-4000011111222222-1-1-1-1-1-1004-40000000000000000000-2-222000000000000000001-1000000
χ60444-2-244-2-244-2-211-2-2-4-2-2-2-2-2-2-4-4000011111222222-1-1-1-1-1-100-44000000000000000000022-2-200000000000000000-11000000
χ6144-24-24-24-2-2-2-21-2-2-2144-2-2-211-2-2040411-2114-2-2-211-2-2111100000-20-2040-20-200-2-20000000000101000-211000000000000000
χ6244-24-24-24-2-2-2-21-2-2-2144-2-2-211-2-20-40-411-2114-2-2-211-2-21111000002020-4020200220000000000-10-10002-1-1000000000000000
χ6344-24-24-24-2-2-2-21-2-2-21-44-2-2-21122040411-211-4222-1-122-1-1-1-100000-20-20-40-20-2002200000000001010002-1-1000000000000000
χ6444-24-24-24-2-2-2-21-2-2-21-44-2-2-211220-40-411-211-4222-1-122-1-1-1-10000020204020200-2-20000000000-10-1000-211000000000000000
χ6544-24-2-4-24-222-21-2-2-210-4222-1-123−23040-4112-1-1023−230−3300−3−33300000-20-20002020023−23000000000010-10000−33000000000000000
χ6644-24-2-4-24-222-21-2-2-210-4222-1-123−230-404112-1-1023−230−3300−3−33300000202000-20-200−23230000000000-10100003−3000000000000000
χ6744-24-2-4-24-222-21-2-2-210-4222-1-1−2323040-4112-1-10−232303−30033−3−300000-20-200020200−2323000000000010-100003−3000000000000000
χ6844-24-2-4-24-222-21-2-2-210-4222-1-1−23230-404112-1-10−232303−30033−3−300000202000-20-20023−230000000000-1010000−33000000000000000
χ6944-2-244-2-24-2-21-2-2-21-24-2411-2-2-2-2404011-211-2114-2-2-2-211110000-20-2040-20-20-2-2000000000001010-211000000000000000000
χ7044-2-244-2-24-2-21-2-2-21-24-2411-2-2-2-2-40-4011-211-2114-2-2-2-2111100002020-4020202200000000000-10-102-1-1000000000000000000
χ7144-2-244-2-24-2-21-2-2-21-2-4-2411-2-222404011-2112-1-1-42222-1-1-1-10000-20-20-40-20-20220000000000010102-1-1000000000000000000
χ7244-2-244-2-24-2-21-2-2-21-2-4-2411-2-222-40-4011-2112-1-1-42222-1-1-1-100002020402020-2-200000000000-10-10-211000000000000000000
χ7344-2-24-4-2-24221-2-2-21-202-4-1-12223−2340-40112-1-10−33023−2300−3−3330000-20-2000202023−230000000000010-100−33000000000000000000
χ7444-2-24-4-2-24221-2-2-21-202-4-1-12223−23-4040112-1-10−33023−2300−3−3330000202000-20-20−232300000000000-101003−3000000000000000000
χ7544-2-24-4-2-24221-2-2-21-202-4-1-122−232340-40112-1-103−30−23230033−3−30000-20-20002020−23230000000000010-1003−3000000000000000000
χ7644-2-24-4-2-24221-2-2-21-202-4-1-122−2323-4040112-1-103−30−23230033−3−30000202000-20-2023−2300000000000-10100−33000000000000000000
χ774-44440-4-4-400444-4-4-400000000000004-40000000000000004i−4i00000000000000000004i−4i00000000000000000000000000000
χ784-44440-4-4-400444-4-4-400000000000004-4000000000000000−4i4i0000000000000000000−4i4i00000000000000000000000000000
χ794-4-24402-4-423−23-2-24-42200023−2323−23000000-22023−230000000000004i−4i00000000000000000−2i32i3−2i2i00000000000000000000000000000
χ804-4-24402-4-423−23-2-24-42200023−2323−23000000-22023−23000000000000−4i4i000000000000000002i3−2i32i−2i00000000000000000000000000000
χ814-4-24402-4-4−2323-2-24-422000−2323−2323000000-220−23230000000000004i−4i000000000000000002i3−2i3−2i2i00000000000000000000000000000
χ824-4-24402-4-4−2323-2-24-422000−2323−2323000000-220−2323000000000000−4i4i00000000000000000−2i32i32i−2i00000000000000000000000000000
χ83888-4-4-88-4-4-8-8-4-422-4-4044444400000022-2-2-20000000000000000000000000000000000000000000000000000000000000000
χ8488-4-4-48-4-4-4-4-42222228-4-42222-4-40000-1-12-1-1-422-42222-1-1-1-10000000000000000000000000000000000000000000000000000
χ8588-4-4-48-4-4-4-4-4222222-8-4-42222440000-1-12-1-14-2-24-2-2-2-211110000000000000000000000000000000000000000000000000000
χ8688-4-4-4-8-4-4-444222222044-2-2-2-243−430000-1-1-2110−23230−23230033−3−30000000000000000000000000000000000000000000000000000
χ8788-4-4-4-8-4-4-444222222044-2-2-2-2−43430000-1-1-211023−23023−2300−3−3330000000000000000000000000000000000000000000000000000
χ888-888-40-8-84008-4-44-840000000000000-440000000000000000000000000000000000000000000000000000000000000000000
χ898-88-480-84-800-48-444-80000000000000-440000000000000000000000000000000000000000000000000000000000000000000
χ908-88-4-40-84400-4-42-24400000000000002-200000000032−3232−3232−320000000000000000000000000000000000000000000000000000
χ918-88-4-40-84400-4-42-24400000000000002-2000000000−3232−3232−32320000000000000000000000000000000000000000000000000000
χ928-8-48-404-8443−43-42-444-200043−43−23230000002-20−23230000000000000000000000000000000000000000000000000000000000000000
χ938-8-48-404-84−4343-42-444-2000−434323−230000002-2023−230000000000000000000000000000000000000000000000000000000000000000
χ948-8-4-48044-843−432-4-44-24000−232343−430000002-20−23230000000000000000000000000000000000000000000000000000000000000000
χ958-8-4-48044-8−43432-4-44-2400023−23−43430000002-2023−230000000000000000000000000000000000000000000000000000000000000000
χ968-8-4-4-4044443−43222-2-2-2000−2323−2323000000-1103−300000032−323ζ13−3ζ23−3ζ13+3ζ233ζ5−3ζ7−3ζ5+3ζ70000000000000000000000000000000000000000000000000000
χ978-8-4-4-4044443−43222-2-2-2000−2323−2323000000-1103−3000000−3232−3ζ13+3ζ233ζ13−3ζ23−3ζ5+3ζ73ζ5−3ζ70000000000000000000000000000000000000000000000000000
χ988-8-4-4-40444−4343222-2-2-200023−2323−23000000-110−3300000032−323ζ5−3ζ7−3ζ5+3ζ73ζ13−3ζ23−3ζ13+3ζ230000000000000000000000000000000000000000000000000000
χ998-8-4-4-40444−4343222-2-2-200023−2323−23000000-110−33000000−3232−3ζ5+3ζ73ζ5−3ζ7−3ζ13+3ζ233ζ13−3ζ230000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.