Finite Group Databasebeta

← Group #13167822

Character table — Group #13167822

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99
size112222222224444444444444446666888888888888888881212121212121212121212121212121218181818181818182424242424242424242424242424363636363636484872727272108108
order123334666121233366681212121212122424224436121212242424242424242424242424246666881212121224242424248824242424666612121212242424242424224461261266121224
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111-1-11111111111111111111111-1-111-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111-11-1111111111111111111111-1-11-1-11-1111-1-1-1-1-1-1-1-1-1-1111-1111-1111-1-1-1-1-111-1-111-1-111-1-1
χ4111111111111111111111111111-11-111111111111111111-1-111-1-11-1-11-1111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11-1111-1-1-111-1-1-1-1-1-111-1-111
χ511111111111111111111111111-11-111111111111111111111-1-111-111-11-1-1-111-1-1-1-1-1-1-1-111-1111-11-1-1-111111-1-1-1-11111-1-1-1-1
χ611111111111111111111111111-11-1111111111111111111-1-1-1-111-111-11-1-1-111-1-1-1-1-1-1-1-1-1-1-11-1-1-11-1-1-1111-1-111-1-1-1-1-1-11111
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
χ911111111111111111-1111111-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-11-11111-1-11111-1-1-1-111-1-1-1-1-1-11111-1-111-1-1-1-1-1-11-11-1111-11-11-11-1
χ1011111111111111111-1111111-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-11111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-11-1111-11-11-11-11
χ1111111111111111111-1111111-1-11-11-111111-1-1-1-1-1-1-1-1-1-1-1-11-111-1-1-11-11-11-1-111-1-1111111111-1-1-11-1-1-1-1111-111-1-1-11-1-111-1-11
χ1211111111111111111-1111111-1-11-11-111111-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-11-11-11-1-111-1-1111111-1-11-1111-1-1-1-11111-1-11-1-1-111-1-111-1
χ1311111111111111111-1111111-1-1-11-1111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1111-11-11-111-1-1-1-111111111-11-1-1-11111-1-1-11-1-11-1-11-11-1-11-11
χ1411111111111111111-1111111-1-1-11-1111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-11-11-111-1-1-1-1111111-1-1-1111-11111-1-1-1-111-1-1-1-11-111-11-1
χ1511111111111111111-1111111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1111111-11-11111-1-11-111-1
χ1611111111111111111-1111111-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-11111111-11-111-111-11-1-11
χ1722222-2222-2-22222220-2-2-2-2-2-20022-2-222-2-2-200000000000000222200-2-2-2-20000-22000000002200-2-20000000000-2200000000
χ1822222-2222-2-22222220-2-2-2-2-2-2002-2-2222-2-2-20000000000000022-2-2002-22-200002-2000000002-200-2200000000002-200000000
χ1922222-2222-2-22222220-2-2-2-2-2-200-222-222-2-2-200000000000000-2-22200-22-2200002-200000000-22002-200000000002-200000000
χ2022222-2222-2-22222220-2-2-2-2-2-200-2-22222-2-2-200000000000000-2-2-2-20022220000-2200000000-2-200220000000000-2200000000
χ212222-12-122222-1-12-1-12-1222-1-1220202-1-1-1-1-1222-1-1-1-1-1-1-1-1-122002-102-10200022000000002-10-1-120-1000-1-1-1220000-1-1-1-10000
χ222222-12-122222-1-12-1-12-1222-1-1220202-1-1-1-1-1222-1-1-1-1-1-1-1-1-1-2-2002-102-1020002200000000-210-11-20-1000-1-1-1-2-2000011110000
χ232222-12-122222-1-12-1-12-1222-1-1220-20-2-1-1-1-1-1222-1-1-1-1-1-1-1-1-12200-210-210-2000-2-2000000002-101-1201000111-2-20000-1-1110000
χ242222-12-122222-1-12-1-12-1222-1-1220-20-2-1-1-1-1-1222-1-1-1-1-1-1-1-1-1-2-200-210-210-2000-2-200000000-21011-20100011122000011-1-10000
χ252222-12-122222-1-12-1-1-2-1222-1-1-2-20202-1-1-1-1-1-2-2-21111111112-2002-10-2-102000-2-2000000002-10-11-20-10001112-20000-11-110000
χ262222-12-122222-1-12-1-1-2-1222-1-1-2-20202-1-1-1-1-1-2-2-2111111111-22002-10-2-102000-2-200000000-210-1-120-1000111-2200001-11-10000
χ272222-12-122222-1-12-1-1-2-1222-1-1-2-20-20-2-1-1-1-1-1-2-2-21111111112-200-210210-200022000000002-1011-201000-1-1-1-220000-111-10000
χ282222-12-122222-1-12-1-1-2-1222-1-1-2-20-20-2-1-1-1-1-1-2-2-2111111111-2200-210210-20002200000000-2101-1201000-1-1-12-200001-1-110000
χ29222-1222-12-1-1-1-12-1-12222-1-1-1-1-1-12222-1-12-1-12-1-12-1-122-1-1-1-1002-1-12222-1-12-1-1-1-12222-1-1-1-100-1-100-1-12-1-12-1-10000-1-100000000
χ30222-1222-12-1-1-1-12-1-12222-1-1-1-1-1-12-22-2-1-12-1-12-1-12-1-122-1-1-1-1002-11-22-2-2-112-1-111-2-2-2-2111100-1100-112-1-1-21100001100000000
χ31222-1222-12-1-1-1-12-1-12222-1-1-1-1-1-1-22-22-1-12-1-12-1-12-1-122-1-1-1-100-21-12-2221-1-211-1-1-2-2-2-21111001-1001-1-2112-1-100001100000000
χ32222-1222-12-1-1-1-12-1-12222-1-1-1-1-1-1-2-2-2-2-1-12-1-12-1-12-1-122-1-1-1-100-211-2-2-2-211-211112222-1-1-1-100110011-211-2110000-1-100000000
χ33222-1222-12-1-1-1-12-1-12-222-1-1-1-1112222-1-12-1-1-211-211-2-21111002-1-12-2-22-1-12111122-2-2111100-1-100-1-1-211-2110000-1-100000000
χ34222-1222-12-1-1-1-12-1-12-222-1-1-1-1112-22-2-1-12-1-1-211-211-2-21111002-11-2-22-2-11211-1-1-2-222-1-1-1-100-1100-11-2112-1-100001100000000
χ35222-1222-12-1-1-1-12-1-12-222-1-1-1-111-22-22-1-12-1-1-211-211-2-2111100-21-122-221-1-2-1-111-2-222-1-1-1-1001-1001-12-1-1-21100001100000000
χ36222-1222-12-1-1-1-12-1-12-222-1-1-1-111-2-2-2-2-1-12-1-1-211-211-2-2111100-211-222-211-2-1-1-1-122-2-21111001100112-1-12-1-10000-1-100000000
χ37222-12-22-1211-1-12-1-120-2-211113−322-2-2-1-1-21103−303−30033−3−3002-1-1200-211-23−33−3-220033−3−300-1-1001103−303−300001-100000000
χ38222-12-22-1211-1-12-1-120-2-211113−32-2-22-1-1-21103−303−30033−3−3002-11-20021-1-23−3−332-200−3−33300-11001-103−30−330000-1100000000
χ39222-12-22-1211-1-12-1-120-2-211113−3-222-2-1-1-21103−303−30033−3−300-21-1200-2-112−333−32-200−3−333001-100-110−3303−30000-1100000000
χ40222-12-22-1211-1-12-1-120-2-211113−3-2-222-1-1-21103−303−30033−3−300-211-2002-1-12−33−33-220033−3−3001100-1-10−330−3300001-100000000
χ41222-12-22-1211-1-12-1-120-2-21111−3322-2-2-1-1-2110−330−3300−3−333002-1-1200-211-2−33−33-2200−3−33300-1-100110−330−3300001-100000000
χ42222-12-22-1211-1-12-1-120-2-21111−332-2-22-1-1-2110−330−3300−3−333002-11-20021-1-2−333−32-20033−3−300-11001-10−3303−30000-1100000000
χ43222-12-22-1211-1-12-1-120-2-21111−33-222-2-1-1-2110−330−3300−3−33300-21-1200-2-1123−3−332-20033−3−3001-100-1103−30−330000-1100000000
χ44222-12-22-1211-1-12-1-120-2-21111−33-2-222-1-1-2110−330−3300−3−33300-211-2002-1-123−33−3-2200−3−333001100-1-103−303−300001-100000000
χ4522-122222-122-12-1-12-122-1-1-122222020-1-1-1-1-1-1-1-1222-1-1-1-1-1-122-120020020-1220000000000-12-102-1-10-1-1-1000002200-1-100-1-100
χ4622-122222-122-12-1-12-122-1-1-122222020-1-1-1-1-1-1-1-1222-1-1-1-1-1-1-2-2-120020020-12200000000001-2-10-21-10-1-1-100000-2-20011001100
χ4722-122222-122-12-1-12-122-1-1-12222-20-20-1-1-1-1-1-1-1-1222-1-1-1-1-1-1221-200-200-201-2-20000000000-12102-11011100000-2-200-1-1001100
χ4822-122222-122-12-1-12-122-1-1-12222-20-20-1-1-1-1-1-1-1-1222-1-1-1-1-1-1-2-21-200-200-201-2-200000000001-210-21101110000022001100-1-100
χ4922-122222-122-12-1-12-1-22-1-1-122-2-22020-1-1-1-1-1111-2-2-21111112-2-1200-20020-1-2-20000000000-12-10-21-10111000002-200-1100-1100
χ5022-122222-122-12-1-12-1-22-1-1-122-2-22020-1-1-1-1-1111-2-2-2111111-22-1200-20020-1-2-200000000001-2-102-1-1011100000-22001-1001-100
χ5122-122222-122-12-1-12-1-22-1-1-122-2-2-20-20-1-1-1-1-1111-2-2-21111112-21-200200-201220000000000-1210-2110-1-1-100000-2200-11001-100
χ5222-122222-122-12-1-12-1-22-1-1-122-2-2-20-20-1-1-1-1-1111-2-2-2111111-221-200200-2012200000000001-2102-110-1-1-1000002-2001-100-1100
χ534444-2-4-244-4-44-2-24-2-202-4-4-42200040-4-2-222200000000000000004-20020-40000000000000000-2000200000000000000000000
χ544444-2-4-244-4-44-2-24-2-202-4-4-422000-404-2-22220000000000000000-4200-20400000000000000002000-200000000000000000000
χ55444-2-24-2-24-2-2-21-2-21-24-24-2-211-2-2040411-2114-2-2-211-2-211110000-2-204-20-2000-2-20000000000010001000-21100000000000000
χ56444-2-24-2-24-2-2-21-2-21-24-24-2-211-2-20-40-411-2114-2-2-211-2-211110000220-42020002200000000000-1000-10002-1-100000000000000
χ57444-2-24-2-24-2-2-21-2-21-2-4-24-2-21122040411-211-4222-1-122-1-1-1-10000-2-20-4-20-20002200000000000100010002-1-100000000000000
χ58444-2-24-2-24-2-2-21-2-21-2-4-24-2-211220-40-411-211-4222-1-122-1-1-1-100002204202000-2-200000000000-1000-1000-21100000000000000
χ59444-2-2-4-2-2422-21-2-21-202-422-1-123−23040-4112-1-1023−230−3300−3−3330000-2-20020200023−23000000000001000-10000−3300000000000000
χ60444-2-2-4-2-2422-21-2-21-202-422-1-123−230-404112-1-1023−230−3300−3−33300002200-20-2000−232300000000000-1000100003−300000000000000
χ61444-2-2-4-2-2422-21-2-21-202-422-1-1−2323040-4112-1-10−232303−30033−3−30000-2-200202000−2323000000000001000-100003−300000000000000
χ62444-2-2-4-2-2422-21-2-21-202-422-1-1−23230-404112-1-10−232303−30033−3−300002200-20-200023−2300000000000-100010000−3300000000000000
χ6344-244-444-2-4-4-24-2-24-20-4222-4-40040-40-2-222200000000000000-2400000-40200000000000000-20002000000000000000000000
χ6444-244-444-2-4-4-24-2-24-20-4222-4-400-4040-2-2222000000000000002-40000040-2000000000000002000-2000000000000000000000
χ6544-24-24-24-244-2-21-2-214-2-2-2-2-2-244000011111-2-2-2-2-2-2111111440000000000000000000000-2-200-2-20000000000000011000000
χ6644-24-24-24-244-2-21-2-214-2-2-2-2-2-244000011111-2-2-2-2-2-2111111-4-4000000000000000000000022002200000000000000-1-1000000
χ6744-24-24-24-244-2-21-2-21-4-2-2-2-2-2-2-4-4000011111222222-1-1-1-1-1-14-40000000000000000000000-2-20022000000000000001-1000000
χ6844-24-24-24-244-2-21-2-21-4-2-2-2-2-2-2-4-4000011111222222-1-1-1-1-1-1-4400000000000000000000002200-2-200000000000000-11000000
χ6944-2-2444-2-2-2-21-2-21-2-244-211-2-2-2-2404011-211-2114-2-2-2-2111100-2-200400-20-2-2-2000000000000100010-21100000000000000000
χ7044-2-2444-2-2-2-21-2-21-2-244-211-2-2-2-2-40-4011-211-2114-2-2-2-21111002200-40020222000000000000-1000-102-1-100000000000000000
χ7144-2-2444-2-2-2-21-2-21-2-2-44-211-2-222404011-2112-1-1-42222-1-1-1-100-2-200-400-20-2220000000000001000102-1-100000000000000000
χ7244-2-2444-2-2-2-21-2-21-2-2-44-211-2-222-40-4011-2112-1-1-42222-1-1-1-1002200400202-2-2000000000000-1000-10-21100000000000000000
χ7344-2-24-44-2-2221-2-21-2-20-42-1-12223−2340-40112-1-10−33023−2300−3−33300-2-20000020223−230000000000001000-100−3300000000000000000
χ7444-2-24-44-2-2221-2-21-2-20-42-1-12223−23-4040112-1-10−33023−2300−3−333002200000-20-2−2323000000000000-10001003−300000000000000000
χ7544-2-24-44-2-2221-2-21-2-20-42-1-122−232340-40112-1-103−30−23230033−3−300-2-200000202−23230000000000001000-1003−300000000000000000
χ7644-2-24-44-2-2221-2-21-2-20-42-1-122−2323-4040112-1-103−30−23230033−3−3002200000-20-223−23000000000000-1000100−3300000000000000000
χ774-44440-4-4-400444-4-4-400000000000004-4000000000000000000000000000000000−2i22i2−2i22i2−2i22i20000000000000000000000000000
χ784-44440-4-4-400444-4-4-400000000000004-40000000000000000000000000000000002i2−2i22i2−2i22i2−2i20000000000000000000000000000
χ794-44-240-42-423−23-2-2422-400023−2323−23000000-22023−23000000000000000000000000000000−2i22i22ζ5+2ζ7−2ζ5−2ζ72ζ13+2ζ23−2ζ13−2ζ230000000000000000000000000000
χ804-44-240-42-423−23-2-2422-400023−2323−23000000-22023−230000000000000000000000000000002i2−2i2−2ζ5−2ζ72ζ5+2ζ7−2ζ13−2ζ232ζ13+2ζ230000000000000000000000000000
χ814-44-240-42-4−2323-2-2422-4000−2323−2323000000-220−2323000000000000000000000000000000−2i22i22ζ13+2ζ23−2ζ13−2ζ232ζ5+2ζ7−2ζ5−2ζ70000000000000000000000000000
χ824-44-240-42-4−2323-2-2422-4000−2323−2323000000-220−23230000000000000000000000000000002i2−2i2−2ζ13−2ζ232ζ13+2ζ23−2ζ5−2ζ72ζ5+2ζ70000000000000000000000000000
χ8388-48-4-8-48-4-8-8-4-42-4-42044444400000022-2-2-20000000000000000000000000000000000000000000000000000000000000000
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
χ888-888-404-8-8008-4-4-8440000000000000-440000000000000000000000000000000000000000000000000000000000000000000
χ898-88-4-4044-843−43-42-44-2400043−43−23230000002-20−23230000000000000000000000000000000000000000000000000000000000000000
χ908-88-4-4044-8−4343-42-44-24000−434323−230000002-2023−230000000000000000000000000000000000000000000000000000000000000000
χ918-8-4880-8-8400-48-44-840000000000000-440000000000000000000000000000000000000000000000000000000000000000000
χ928-8-48-404-8400-4-4244-200000000000002-2000000000−3i23i2−3i23i2−3i23i20000000000000000000000000000000000000000000000000000
χ938-8-48-404-8400-4-4244-200000000000002-20000000003i2−3i23i2−3i23i2−3i20000000000000000000000000000000000000000000000000000
χ948-8-4-480-84443−432-4-4-244000−232343−430000002-20−23230000000000000000000000000000000000000000000000000000000000000000
χ958-8-4-480-844−43432-4-4-24400023−23−43430000002-2023−230000000000000000000000000000000000000000000000000000000000000000
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.