Finite Group Databasebeta

← Group #13167816

Character table — Group #13167816

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99
size112222222224444444444444446666888888888888888881212121212121212121212121212121218181818181818182424242424242424242424242424363636363636484872727272108108
order1233346661212333666812121212121224242244361212122424242424242424242424242466668812121212242424242488242424246666121212122424242424242222612612666624
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111-1-11111111111111111111111-1-111-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111-11-111111111111111111111-11-11-11-11-111-1-1-1-1-1-1-1-1-1-1111-1111-1111-1-1-111-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111-11-111111111111111111-1-11-11-11-11-11-111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11-1111-1-1-1-1-111-1-1-1-1-1-11111
χ511111111111111111111111111-11-111111111111111111111-11-11-11-11-11-1-111-1-1-1-1-1-1-1-111-1111-11-1-1-1111-1-111-1-111-1-111-1-1
χ611111111111111111111111111-11-1111111111111111111-1-1-11-11-11-11-11-1-111-1-1-1-1-1-1-1-1-1-1-11-1-1-11-1-1-111111-1-1-1-1-1-111-1-111
χ711111111111111111111111111-1-1-1-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ811111111111111111111111111-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111-1-1
χ911111111111111111-1111111-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11-11111-1-11111-1-1-1-111-1-1-1-1-1-11111-1-111-1-1-1-1-1-11-11-1111-11-11-1-11
χ1011111111111111111-1111111-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-11111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-11-1111-11-11-111-1
χ1111111111111111111-1111111-1-11-11-111111-1-1-1-1-1-1-1-1-1-1-1-11-11-11-1-111-11-1-1-111-1-1111111111-1-1-11-1-1-1-11111-1-11-1-11-11-1-111-1
χ1211111111111111111-1111111-1-11-11-111111-1-1-1-1-1-1-1-1-1-1-1-1-111-11-1-111-11-1-1-111-1-1111111-1-11-1111-1-1-1-1111-111-1-1-1-11-111-1-11
χ1311111111111111111-1111111-1-1-11-1111111-1-1-1-1-1-1-1-1-1-1-1-11-1-11-111-1-11-1111-1-1-1-111111111-11-1-1-11111-1-1-1-111-1-1-11-1-111-11-1
χ1411111111111111111-1111111-1-1-11-1111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-111-1-11-1111-1-1-1-1111111-1-1-1111-11111-1-1-11-1-11-1-1-111-1-11-11
χ1511111111111111111-1111111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1111111-11-11111-1-11-11-11
χ1611111111111111111-1111111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-11111111-11-111-111-11-11-1
χ1722222-2222-2-22222220-2-2-2-2-2-20022-2-222-2-2-200000000000000222200-2-2-2-20000-22000000002200-2-20000000000-2200000000
χ1822222-2222-2-22222220-2-2-2-2-2-2002-2-2222-2-2-2000000000000002-22-200-22-2200002-2000000002-200-2200000000002-200000000
χ1922222-2222-2-22222220-2-2-2-2-2-200-222-222-2-2-200000000000000-22-22002-22-200002-200000000-22002-200000000002-200000000
χ2022222-2222-2-22222220-2-2-2-2-2-200-2-22222-2-2-200000000000000-2-2-2-20022220000-2200000000-2-200220000000000-2200000000
χ212222-122-12222-1-12-1-122-122-1-1220202-1-1-1-1-1222-1-1-1-1-1-1-1-1-122020-1020-1020022000000002-10-12-10-1000-1-1-1002200-1-100-1-100
χ222222-122-12222-1-12-1-122-122-1-1220202-1-1-1-1-1222-1-1-1-1-1-1-1-1-1-2-2020-1020-102002200000000-210-1-210-1000-1-1-100-2-20011001100
χ232222-122-12222-1-12-1-122-122-1-1220-20-2-1-1-1-1-1222-1-1-1-1-1-1-1-1-1220-2010-2010-200-2-2000000002-1012-10100011100-2-200-1-1001100
χ242222-122-12222-1-12-1-122-122-1-1220-20-2-1-1-1-1-1222-1-1-1-1-1-1-1-1-1-2-20-2010-2010-200-2-200000000-2101-21010001110022001100-1-100
χ252222-122-12222-1-12-1-1-22-122-1-1-2-20202-1-1-1-1-1-2-2-21111111112-2020-10-20-10200-2-2000000002-10-1-210-1000111002-200-1100-1100
χ262222-122-12222-1-12-1-1-22-122-1-1-2-20202-1-1-1-1-1-2-2-2111111111-22020-10-20-10200-2-200000000-210-12-10-100011100-22001-1001-100
χ272222-122-12222-1-12-1-1-22-122-1-1-2-20-20-2-1-1-1-1-1-2-2-21111111112-20-20102010-20022000000002-101-2101000-1-1-100-2200-11001-100
χ282222-122-12222-1-12-1-1-22-122-1-1-2-20-20-2-1-1-1-1-1-2-2-2111111111-220-20102010-2002200000000-21012-101000-1-1-1002-2001-100-1100
χ29222-122-12222-12-1-12-12-12-1-122222020-1-1-1-1-1-1-1-1222-1-1-1-1-1-12220-1020-1020220000000000-12-10-12-10-1-1-1000220000-1-1-1-10000
χ30222-122-12222-12-1-12-12-12-1-122222020-1-1-1-1-1-1-1-1222-1-1-1-1-1-1-2-220-1020-10202200000000001-2-101-2-10-1-1-1000-2-2000011110000
χ31222-122-12222-12-1-12-12-12-1-12222-20-20-1-1-1-1-1-1-1-1222-1-1-1-1-1-122-2010-2010-20-2-20000000000-1210-1210111000-2-20000-1-1110000
χ32222-122-12222-12-1-12-12-12-1-12222-20-20-1-1-1-1-1-1-1-1222-1-1-1-1-1-1-2-2-2010-2010-20-2-200000000001-2101-21011100022000011-1-10000
χ33222-122-12222-12-1-12-1-2-12-1-122-2-22020-1-1-1-1-1111-2-2-21111112-220-10-20-1020-2-20000000000-12-101-2-101110002-20000-11-110000
χ34222-122-12222-12-1-12-1-2-12-1-122-2-22020-1-1-1-1-1111-2-2-2111111-2220-10-20-1020-2-200000000001-2-10-12-10111000-2200001-11-10000
χ35222-122-12222-12-1-12-1-2-12-1-122-2-2-20-20-1-1-1-1-1111-2-2-21111112-2-20102010-20220000000000-12101-210-1-1-1000-220000-111-10000
χ36222-122-12222-12-1-12-1-2-12-1-122-2-2-20-20-1-1-1-1-1111-2-2-2111111-22-20102010-202200000000001-210-1210-1-1-10002-200001-1-110000
χ3722-122222-1-1-1-1-12-1-12222-1-1-1-1-1-12222-1-12-1-12-1-12-1-122-1-1-1-100-1-1222222-1-1-1-1-1-12222-1-1-1-100-1-100-1-12-1-12-1-10000-1-100000000
χ3822-122222-1-1-1-1-12-1-12222-1-1-1-1-1-12-22-2-1-12-1-12-1-12-1-122-1-1-1-100-112-22-22-2-11-1-111-2-2-2-2111100-1100-112-1-1-21100001100000000
χ3922-122222-1-1-1-1-12-1-12222-1-1-1-1-1-1-22-22-1-12-1-12-1-12-1-122-1-1-1-1001-1-22-22-221-111-1-1-2-2-2-21111001-1001-1-2112-1-100001100000000
χ4022-122222-1-1-1-1-12-1-12222-1-1-1-1-1-1-2-2-2-2-1-12-1-12-1-12-1-122-1-1-1-10011-2-2-2-2-2-21111112222-1-1-1-100110011-211-2110000-1-100000000
χ4122-122222-1-1-1-1-12-1-12-222-1-1-1-1112222-1-12-1-1-211-211-2-2111100-1-122-2-222-1-1111122-2-2111100-1-100-1-1-211-2110000-1-100000000
χ4222-122222-1-1-1-1-12-1-12-222-1-1-1-1112-22-2-1-12-1-1-211-211-2-2111100-112-2-222-2-1111-1-1-2-222-1-1-1-100-1100-11-2112-1-100001100000000
χ4322-122222-1-1-1-1-12-1-12-222-1-1-1-111-22-22-1-12-1-1-211-211-2-21111001-1-222-2-221-1-1-111-2-222-1-1-1-1001-1001-12-1-1-21100001100000000
χ4422-122222-1-1-1-1-12-1-12-222-1-1-1-111-2-2-2-2-1-12-1-1-211-211-2-211110011-2-222-2-211-1-1-1-122-2-21111001100112-1-12-1-10000-1-100000000
χ4522-122-222-111-1-12-1-120-2-211113−322-2-2-1-1-21103−303−30033−3−300-1-12200-2-2113−33−3-220033−3−300-1-1001103−303−300001-100000000
χ4622-122-222-111-1-12-1-120-2-211113−32-2-22-1-1-21103−303−30033−3−300-112-200-221-13−3−332-200−3−33300-11001-103−30−330000-1100000000
χ4722-122-222-111-1-12-1-120-2-211113−3-222-2-1-1-21103−303−30033−3−3001-1-22002-2-11−333−32-200−3−333001-100-110−3303−30000-1100000000
χ4822-122-222-111-1-12-1-120-2-211113−3-2-222-1-1-21103−303−30033−3−30011-2-20022-1-1−33−33-220033−3−3001100-1-10−330−3300001-100000000
χ4922-122-222-111-1-12-1-120-2-21111−3322-2-2-1-1-2110−330−3300−3−33300-1-12200-2-211−33−33-2200−3−33300-1-100110−330−3300001-100000000
χ5022-122-222-111-1-12-1-120-2-21111−332-2-22-1-1-2110−330−3300−3−33300-112-200-221-1−333−32-20033−3−300-11001-10−3303−30000-1100000000
χ5122-122-222-111-1-12-1-120-2-21111−33-222-2-1-1-2110−330−3300−3−333001-1-22002-2-113−3−332-20033−3−3001-100-1103−30−330000-1100000000
χ5222-122-222-111-1-12-1-120-2-21111−33-2-222-1-1-2110−330−3300−3−3330011-2-20022-1-13−33−3-2200−3−333001100-1-103−303−300001-100000000
χ534444-2-44-24-4-44-2-24-2-20-42-4-42200040-4-2-222200000000000000040-200020-4000000000000000-2000200000000000000000000
χ544444-2-44-24-4-44-2-24-2-20-42-4-422000-404-2-2222000000000000000-402000-2040000000000000002000-200000000000000000000
χ55444-24-4-244-4-4-24-2-24-202-422-4-40040-40-2-22220000000000000040-200020-4000000000000000-20002000000000000000000000
χ56444-24-4-244-4-4-24-2-24-202-422-4-400-4040-2-222200000000000000-402000-2040000000000000002000-2000000000000000000000
χ57444-2-24-2-2444-2-21-2-214-2-2-2-2-2-244000011111-2-2-2-2-2-2111111440000000000000000000000-2-200-2-20000000000000011000000
χ58444-2-24-2-2444-2-21-2-214-2-2-2-2-2-244000011111-2-2-2-2-2-2111111-4-4000000000000000000000022002200000000000000-1-1000000
χ59444-2-24-2-2444-2-21-2-21-4-2-2-2-2-2-2-4-4000011111222222-1-1-1-1-1-14-40000000000000000000000-2-20022000000000000001-1000000
χ60444-2-24-2-2444-2-21-2-21-4-2-2-2-2-2-2-4-4000011111222222-1-1-1-1-1-1-4400000000000000000000002200-2-200000000000000-11000000
χ6144-24-244-2-2-2-2-21-2-21-244-2-2-211-2-2040411-2114-2-2-211-2-21111000-20-2040-20-200-2-20000000000010001000-21100000000000000
χ6244-24-244-2-2-2-2-21-2-21-244-2-2-211-2-20-40-411-2114-2-2-211-2-211110002020-40202002200000000000-1000-10002-1-100000000000000
χ6344-24-244-2-2-2-2-21-2-21-2-44-2-2-21122040411-211-4222-1-122-1-1-1-1000-20-20-40-20-2002200000000000100010002-1-100000000000000
χ6444-24-244-2-2-2-2-21-2-21-2-44-2-2-211220-40-411-211-4222-1-122-1-1-1-100020204020200-2-200000000000-1000-1000-21100000000000000
χ6544-24-2-44-2-222-21-2-21-20-4222-1-123−23040-4112-1-1023−230−3300−3−333000-20-20002020023−23000000000001000-10000−3300000000000000
χ6644-24-2-44-2-222-21-2-21-20-4222-1-123−230-404112-1-1023−230−3300−3−333000202000-20-200−232300000000000-1000100003−300000000000000
χ6744-24-2-44-2-222-21-2-21-20-4222-1-1−2323040-4112-1-10−232303−30033−3−3000-20-200020200−2323000000000001000-100003−300000000000000
χ6844-24-2-44-2-222-21-2-21-20-4222-1-1−23230-404112-1-10−232303−30033−3−3000202000-20-20023−2300000000000-100010000−3300000000000000
χ6944-2-244-24-2-2-21-2-21-2-24-2411-2-2-2-2404011-211-2114-2-2-2-2111100-20-2040-20-20-2-2000000000000100010-21100000000000000000
χ7044-2-244-24-2-2-21-2-21-2-24-2411-2-2-2-2-40-4011-211-2114-2-2-2-21111002020-40202022000000000000-1000-102-1-100000000000000000
χ7144-2-244-24-2-2-21-2-21-2-2-4-2411-2-222404011-2112-1-1-42222-1-1-1-100-20-20-40-20-20220000000000001000102-1-100000000000000000
χ7244-2-244-24-2-2-21-2-21-2-2-4-2411-2-222-40-4011-2112-1-1-42222-1-1-1-1002020402020-2-2000000000000-1000-10-21100000000000000000
χ7344-2-24-4-24-2221-2-21-2-202-4-1-12223−2340-40112-1-10−33023−2300−3−33300-20-2000202023−230000000000001000-100−3300000000000000000
χ7444-2-24-4-24-2221-2-21-2-202-4-1-12223−23-4040112-1-10−33023−2300−3−33300202000-20-20−2323000000000000-10001003−300000000000000000
χ7544-2-24-4-24-2221-2-21-2-202-4-1-122−232340-40112-1-103−30−23230033−3−300-20-20002020−23230000000000001000-1003−300000000000000000
χ7644-2-24-4-24-2221-2-21-2-202-4-1-122−2323-4040112-1-103−30−23230033−3−300202000-20-2023−23000000000000-1000100−3300000000000000000
χ774-44440-4-4-400444-4-4-400000000000004-400000000000000000000000000000000022−2222−2222−220000000000000000000000000000
χ784-44440-4-4-400444-4-4-400000000000004-4000000000000000000000000000000000−2222−2222−22220000000000000000000000000000
χ794-4-2440-4-4223−23-2-2422-400023−2323−23000000-22023−2300000000000000000000000000000022−222ζ5−2ζ7−2ζ5+2ζ72ζ13−2ζ23−2ζ13+2ζ230000000000000000000000000000
χ804-4-2440-4-4223−23-2-2422-400023−2323−23000000-22023−23000000000000000000000000000000−2222−2ζ5+2ζ72ζ5−2ζ7−2ζ13+2ζ232ζ13−2ζ230000000000000000000000000000
χ814-4-2440-4-42−2323-2-2422-4000−2323−2323000000-220−232300000000000000000000000000000022−222ζ13−2ζ23−2ζ13+2ζ232ζ5−2ζ7−2ζ5+2ζ70000000000000000000000000000
χ824-4-2440-4-42−2323-2-2422-4000−2323−2323000000-220−2323000000000000000000000000000000−2222−2ζ13+2ζ232ζ13−2ζ23−2ζ5+2ζ72ζ5−2ζ70000000000000000000000000000
χ83888-4-4-8-4-48-8-8-4-42-4-42044444400000022-2-2-20000000000000000000000000000000000000000000000000000000000000000
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
χ888-888-40-84-8008-4-4-8440000000000000-440000000000000000000000000000000000000000000000000000000000000000000
χ898-88-4804-8-800-48-44-840000000000000-440000000000000000000000000000000000000000000000000000000000000000000
χ908-88-4-4044-800-4-4244-200000000000002-2000000000−3i23i2−3i23i2−3i23i20000000000000000000000000000000000000000000000000000
χ918-88-4-4044-800-4-4244-200000000000002-20000000003i2−3i23i2−3i23i2−3i20000000000000000000000000000000000000000000000000000
χ928-8-48-40-84443−43-42-44-2400043−43−23230000002-20−23230000000000000000000000000000000000000000000000000000000000000000
χ938-8-48-40-844−4343-42-44-24000−434323−230000002-2023−230000000000000000000000000000000000000000000000000000000000000000
χ948-8-4-4804-8443−432-4-4-244000−232343−430000002-20−23230000000000000000000000000000000000000000000000000000000000000000
χ958-8-4-4804-84−43432-4-4-24400023−23−43430000002-2023−230000000000000000000000000000000000000000000000000000000000000000
χ968-8-4-4-4044443−43222-2-2-2000−2323−2323000000-1103−3000000−3i23i23ζ13+3ζ23−3ζ13−3ζ233ζ5+3ζ7−3ζ5−3ζ70000000000000000000000000000000000000000000000000000
χ978-8-4-4-4044443−43222-2-2-2000−2323−2323000000-1103−30000003i2−3i2−3ζ13−3ζ233ζ13+3ζ23−3ζ5−3ζ73ζ5+3ζ70000000000000000000000000000000000000000000000000000
χ988-8-4-4-40444−4343222-2-2-200023−2323−23000000-110−33000000−3i23i23ζ5+3ζ7−3ζ5−3ζ73ζ13+3ζ23−3ζ13−3ζ230000000000000000000000000000000000000000000000000000
χ998-8-4-4-40444−4343222-2-2-200023−2323−23000000-110−330000003i2−3i2−3ζ5−3ζ73ζ5+3ζ7−3ζ13−3ζ233ζ13+3ζ230000000000000000000000000000000000000000000000000000

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