Finite Group Databasebeta

← Group #13137875

Character table — Group #13137875

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11112222224466666666888121212121212121218181818181818181818181824242424242424242424363636363636363636363636727272727272727272
order12223446661212336666664121236661212121244448888888812121212121212121212121212122424242424242424444121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-11-1-111-1-1-1-1
χ31111111111111111111111111111111-1-1-1-11111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-11-1-1-111-1-1
χ41111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-11111-1-11-1-1-1-111
χ511111111111111111111-1-1-111111111111111111111-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1
χ611111111111111111111-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-111-1-11111
χ711111111111111111111-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11-1111-1-111
χ811111111111111111111-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-11111-1-1
χ92222222222222-12-12-12-1222-1-1-1-12-12-100000000222222-1-1-1-1-1-1-1-100000000-1-1-1-10020000-1-1
χ102222222222222-12-12-12-1222-1-1-1-12-12-100000000-2-2-2-222-1-1-1-1-1-1-1-100000000111100-2000011
χ112222222222222-12-12-12-1-2-2-2-1-1-1-12-12-1000000002222-2-211-1-1111100000000-1-1-1-100-2000011
χ122222222222222-12-12-12-1-2-2-2-1-1-1-12-12-100000000-2-2-2-2-2-211-1-111110000000011110020000-1-1
χ13222222222222-12-12-12-12222-1-1-1-1-12-12000022220000-1-122-1-1-1-1-1-10000-1-1-1-1000002000-1-100
χ14222222222222-12-12-12-12222-1-1-1-1-12-120000-2-2-2-20000-1-122-1-1-1-1-1-10000111100000-20001100
χ15222222222222-12-12-12-12-2-2-2-1-1-1-1-12-1200002222000011-2-2-1-111110000-1-1-1-100000-20001100
χ16222222222222-12-12-12-12-2-2-2-1-1-1-1-12-120000-2-2-2-2000011-2-2-1-1111100001111000002000-1-100
χ1722222-2-2222-2-2222222220002222-2-2-2-222-2-2000000000000-2-2000022-2-200000000000000000
χ1822222-2-2222-2-2222222220002222-2-2-2-2-2-222000000000000-2-20000-2-22200000000000000000
χ1922-2-2200-22-2002222-2-2-2-200022-2-200002-20022−2−222−2−200000000002-20022−2−222−2−2000000000
χ2022-2-2200-22-2002222-2-2-2-200022-2-200002-200−2−222−2−22200000000002-200−2−222−2−222000000000
χ2122-2-2200-22-2002222-2-2-2-200022-2-20000-220022−2−2−2−2220000000000-220022−2−2−2−222000000000
χ2222-2-2200-22-2002222-2-2-2-200022-2-20000-2200−2−22222−2−20000000000-2200−2−22222−2−2000000000
χ232-22-2200-2-220022-2-222-2-20002-2-220000002-2−i2i2−i2i2−i2i2−i2i20000000000002-2−i2i2−i2i2−i2i2−i2i2000000000
χ242-22-2200-2-220022-2-222-2-20002-2-220000002-2i2−i2i2−i2i2−i2i2−i20000000000002-2i2−i2i2−i2i2−i2i2−i2000000000
χ252-22-2200-2-220022-2-222-2-20002-2-22000000-22−i2i2−i2i2i2−i2i2−i2000000000000-22−i2i2−i2i2i2−i2i2−i2000000000
χ262-22-2200-2-220022-2-222-2-20002-2-22000000-22i2−i2i2−i2−i2i2−i2i2000000000000-22i2−i2i2−i2−i2i2−i2i2000000000
χ272-2-2222-22-2-22-222-2-2-2-2220002-22-22-2-2200002i−2i−2i2i000000002-2000000002i−2i−2i2i0000000000000
χ282-2-2222-22-2-22-222-2-2-2-2220002-22-22-2-220000−2i2i2i−2i000000002-200000000−2i2i2i−2i0000000000000
χ292-2-2222-22-2-22-2-121-21-2-12000-11-11-1-21200002i−2i−2i2i00003−300-1133−3−30000−iii−i000000000−i3i300
χ302-2-2222-22-2-22-2-121-21-2-12000-11-11-1-21200002i−2i−2i2i0000−3300-11−3−3330000−iii−i000000000i3−i300
χ312-2-2222-22-2-22-2-121-21-2-12000-11-11-1-2120000−2i2i2i−2i00003−300-1133−3−30000i−i−ii000000000i3−i300
χ322-2-2222-22-2-22-2-121-21-2-12000-11-11-1-2120000−2i2i2i−2i0000−3300-11−3−3330000i−i−ii000000000−i3i300
χ332-2-222-222-2-2-2222-2-2-2-2220002-22-2-222-2000000002i−2i−2i2i0000-220000000000002i−2i−2i2i000000000
χ342-2-222-222-2-2-2222-2-2-2-2220002-22-2-222-200000000−2i2i2i−2i0000-22000000000000−2i2i2i−2i000000000
χ352-2-222-222-2-2-222-1-21-212-1000-11-11-2-121000000002i−2i−2i2i003−31-13−33−300000000−iii−i0000000−i3i3
χ362-2-222-222-2-2-222-1-21-212-1000-11-11-2-121000000002i−2i−2i2i00−331-1−33−3300000000−iii−i0000000i3−i3
χ372-2-222-222-2-2-222-1-21-212-1000-11-11-2-12100000000−2i2i2i−2i003−31-13−33−300000000i−i−ii0000000i3−i3
χ382-2-222-222-2-2-222-1-21-212-1000-11-11-2-12100000000−2i2i2i−2i00−331-1−33−3300000000i−i−ii0000000−i3i3
χ39444444444444-2-2-2-2-2-2-2-24441111-2-2-2-2000000000000-2-2-2-2111111000000000000000000000
χ40444444444444-2-2-2-2-2-2-2-2-4-4-41111-2-2-2-2000000000000222211-1-1-1-1000000000000000000000
χ4144444-4-4444-4-44-24-24-24-2000-2-2-2-2-42-420000000000000000220000000000000000000000000
χ4244444-4-4444-4-4-24-24-24-24000-2-2-2-22-42-40000000000000000220000000000000000000000000
χ4344444-4-4444-4-4-2-2-2-2-2-2-2-2000111122220000000000000000-1-13-3-33000000000000000000000
χ4444444-4-4444-4-4-2-2-2-2-2-2-2-2000111122220000000000000000-1-1-333-3000000000000000000000
χ4544-4-4400-44-4004-24-2-42-42000-2-2220000000000002222−22−22000000000000000000−2−222000000000
χ4644-4-4400-44-4004-24-2-42-42000-2-222000000000000−22−22222200000000000000000022−2−2000000000
χ4744-4-4400-44-400-24-242-42-4000-2-222000000002222−22−22000000000000000000−2−2220000000000000
χ4844-4-4400-44-400-24-242-42-4000-2-22200000000−22−22222200000000000000000022−2−20000000000000
χ494-44-4400-4-44004-2-424-2-42000-222-2000000000000−2i22i2−2i22i2000000000000000000i2−i2i2−i2000000000
χ504-44-4400-4-44004-2-424-2-42000-222-20000000000002i2−2i22i2−2i2000000000000000000−i2i2−i2i2000000000
χ514-44-4400-4-4400-242-4-242-4000-222-200000000−2i22i2−2i22i2000000000000000000i2−i2i2−i20000000000000
χ524-44-4400-4-4400-242-4-242-4000-222-2000000002i2−2i22i2−2i2000000000000000000−i2i2−i2i20000000000000
χ534-4-4444-44-4-44-44-2-42-424-2000-22-2242-4-20000000000000000-220000000000000000000000000
χ544-4-4444-44-4-44-4-2-22222-2-20001-11-1-222-200000000000023−23001-1−3−333000000000000000000000
χ554-4-4444-44-4-44-4-2-22222-2-20001-11-1-222-2000000000000−2323001-133−3−3000000000000000000000
χ564-4-444-444-4-4-44-242-42-4-24000-22-2224-2-400000000000000002-20000000000000000000000000
χ574-4-444-444-4-4-44-2-22222-2-20001-11-12-2-220000000000000023−23-11−33−33000000000000000000000
χ584-4-444-444-4-4-44-2-22222-2-20001-11-12-2-2200000000000000−2323-113−33−3000000000000000000000
χ596666-366-3-3-3-3-3000000006-3-3000000002222000000000000000000-1-1-1-100000000200-1-10000
χ606666-366-3-3-3-3-3000000006-3-300000000-2-2-2-2000000000000000000111100000000-200110000
χ616666-366-3-3-3-3-300000000-633000000002222000000000000000000-1-1-1-100000000-200110000
χ626666-366-3-3-3-3-300000000-63300000000-2-2-2-2000000000000000000111100000000200-1-10000
χ636666-3-6-6-3-3-333000000000−3i33i30000000022-2-2000000000000000000-1-11100000000000−i3i30000
χ646666-3-6-6-3-3-333000000000−3i33i300000000-2-22200000000000000000011-1-100000000000i3−i30000
χ656666-3-6-6-3-3-3330000000003i3−3i30000000022-2-2000000000000000000-1-11100000000000i3−i30000
χ666666-3-6-6-3-3-3330000000003i3−3i300000000-2-22200000000000000000011-1-100000000000−i3i30000
χ6788-8-8800-88-800-4-4-4-4444400022-2-200000000000000000000000000000000000000000000000
χ688-88-8800-8-8800-4-444-4-4440002-2-2200000000000000000000000000000000000000000000000
χ691212-12-12-6006-660000000000000000000004-400000000000000000000-220000000000000000000
χ701212-12-12-6006-66000000000000000000000-44000000000000000000002-20000000000000000000
χ7112-1212-12-60066-6000000000000000000000004-400000000000000000000-2200000000000000000
χ7212-1212-12-60066-600000000000000000000000-44000000000000000000002-200000000000000000
χ7312-12-1212-612-12-666-6600000000000000000000000000000000000000000000000000000000000000
χ7412-12-1212-6-1212-6666-600000000000000000000000000000000000000000000000000000000000000

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