Finite Group Databasebeta

← Group #13137960

Character table — Group #13137960

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11112222224466666666888121212121212121218181818181818181818181824242424242424242424363636363636363636363636727272727272727272
order12223446661212336666664121236661212121222448888888812121212121212121212661212242424242424242422466661212
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
χ92222222222222-12-12-1-12222-1-1-1-12-12-1000022220000-1-122-1-1-1-1-1-10000-1-1-1-1000002000-1-100
χ102222222222222-12-12-1-12222-1-1-1-12-12-10000-2-2-2-20000-1-122-1-1-1-1-1-10000111100000-20001100
χ112222222222222-12-12-1-12-2-2-2-1-1-1-12-12-100002222000011-2-2-1-111110000-1-1-1-100000-20001100
χ122222222222222-12-12-1-12-2-2-2-1-1-1-12-12-10000-2-2-2-2000011-2-2-1-1111100001111000002000-1-100
χ13222222222222-12-12-122-1222-1-1-1-1-12-1200000000222222-1-1-1-1-1-1-1-100000000-1-1-1-10020000-1-1
χ14222222222222-12-12-122-1222-1-1-1-1-12-1200000000-2-2-2-222-1-1-1-1-1-1-1-100000000111100-2000011
χ15222222222222-12-12-122-1-2-2-2-1-1-1-1-12-12000000002222-2-211-1-1111100000000-1-1-1-100-2000011
χ16222222222222-12-12-122-1-2-2-2-1-1-1-1-12-1200000000-2-2-2-2-2-211-1-111110000000011110020000-1-1
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
χ1922-2-22002-2-2002222-2-2-2-200022-2-20000002i−2i−i2−i2i2i222−2−20000000000002i−2i−i2−i2i2i222−2−2000000000
χ2022-2-22002-2-2002222-2-2-2-200022-2-20000002i−2ii2i2−i2−i2−2−2220000000000002i−2ii2i2−i2−i2−2−222000000000
χ2122-2-22002-2-2002222-2-2-2-200022-2-2000000−2i2i−i2−i2i2i2−2−222000000000000−2i2i−i2−i2i2i2−2−222000000000
χ2222-2-22002-2-2002222-2-2-2-200022-2-2000000−2i2ii2i2−i2−i222−2−2000000000000−2i2ii2i2−i2−i222−2−2000000000
χ232-22-222-2-2-222-222-2-222-2-20002-22-222-2-200002i−2i2i−2i000000002-2000000002i−2i2i−2i0000000000000
χ242-22-222-2-2-222-222-2-222-2-20002-22-222-2-20000−2i2i−2i2i000000002-200000000−2i2i−2i2i0000000000000
χ252-22-222-2-2-222-22-1-212-11-2000-11-112-1-2100002i−2i2i−2i00003−300-1133−3−30000−ii−ii000000000−i3i300
χ262-22-222-2-2-222-22-1-212-11-2000-11-112-1-2100002i−2i2i−2i0000−3300-11−3−3330000−ii−ii000000000i3−i300
χ272-22-222-2-2-222-22-1-212-11-2000-11-112-1-210000−2i2i−2i2i00003−300-1133−3−30000i−ii−i000000000i3−i300
χ282-22-222-2-2-222-22-1-212-11-2000-11-112-1-210000−2i2i−2i2i0000−3300-11−3−3330000i−ii−i000000000−i3i300
χ292-22-22-22-2-22-2222-2-222-2-20002-22-2-2-222000000002-22-20000-220000000000002-22-2000000000
χ302-22-22-22-2-22-2222-2-222-2-20002-22-2-2-22200000000-22-220000-22000000000000-22-22000000000
χ312-22-22-22-2-22-22-121-2-12-21000-11-111-2-12000000002-22-2003−31-13−33−300000000-11-1100000003−3
χ322-22-22-22-2-22-22-121-2-12-21000-11-111-2-12000000002-22-200−331-1−33−3300000000-11-110000000−33
χ332-22-22-22-2-22-22-121-2-12-21000-11-111-2-1200000000-22-22003−31-13−33−3000000001-11-10000000−33
χ342-22-22-22-2-22-22-121-2-12-21000-11-111-2-1200000000-22-2200−331-1−33−33000000001-11-100000003−3
χ352-2-22200-22-20022-2-2-2-2220002-2-2200002-2002−2−222−2−2200000000002-2002−2−222−2−22000000000
χ362-2-22200-22-20022-2-2-2-2220002-2-2200002-200−222−2−222−200000000002-200−222−2−222−2000000000
χ372-2-22200-22-20022-2-2-2-2220002-2-220000-22002−2−22−222−20000000000-22002−2−22−222−2000000000
χ382-2-22200-22-20022-2-2-2-2220002-2-220000-2200−222−22−2−220000000000-2200−222−22−2−22000000000
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
χ4144444-4-4444-4-44-24-24-2-24000-2-2-2-2-42-420000000000000000220000000000000000000000000
χ4244444-4-4444-4-4-24-24-244-2000-2-2-2-22-42-40000000000000000220000000000000000000000000
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
χ4544-4-44004-4-4004-24-2-422-4000-2-22200000000−2i2−2i22i22i2000000000000000000i2i2−i2−i20000000000000
χ4644-4-44004-4-4004-24-2-422-4000-2-222000000002i22i2−2i2−2i2000000000000000000−i2−i2i2i20000000000000
χ4744-4-44004-4-400-24-242-4-42000-2-2220000000000002222−22−22000000000000000000−2−222000000000
χ4844-4-44004-4-400-24-242-4-42000-2-222000000000000−22−22222200000000000000000022−2−2000000000
χ494-44-444-4-4-444-4-242-4-24-42000-22-22-242-40000000000000000-220000000000000000000000000
χ504-44-444-4-4-444-4-2-222-2-2220001-11-1-2-22200000000000023−23001-1−3−333000000000000000000000
χ514-44-444-4-4-444-4-2-222-2-2220001-11-1-2-222000000000000−2323001-133−3−3000000000000000000000
χ524-44-44-44-4-44-444-2-424-22-4000-22-22-424-200000000000000002-20000000000000000000000000
χ534-44-44-44-4-44-44-2-222-2-2220001-11-122-2-20000000000000023−23-11−33−33000000000000000000000
χ544-44-44-44-4-44-44-2-222-2-2220001-11-122-2-200000000000000−2323-113−33−3000000000000000000000
χ554-4-44400-44-4004-2-42-42-24000-222-20000000022−22−2222000000000000000000−222−20000000000000
χ564-4-44400-44-4004-2-42-42-24000-222-200000000−222222−220000000000000000002−2−220000000000000
χ574-4-44400-44-400-242-42-44-2000-222-200000000000022−22−2222000000000000000000−222−2000000000
χ584-4-44400-44-400-242-42-44-2000-222-2000000000000−222222−220000000000000000002−2−22000000000
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
χ6788-8-88008-8-800-4-4-4-4444400022-2-200000000000000000000000000000000000000000000000
χ688-8-88800-88-800-4-44444-4-40002-2-2200000000000000000000000000000000000000000000000
χ691212-12-12-600-666000000000000000000000004i−4i00000000000000000000−2i2i00000000000000000
χ701212-12-12-600-66600000000000000000000000−4i4i000000000000000000002i−2i00000000000000000
χ7112-1212-12-612-1266-6-6600000000000000000000000000000000000000000000000000000000000000
χ7212-1212-12-6-121266-66-600000000000000000000000000000000000000000000000000000000000000
χ7312-12-1212-6006-660000000000000000000004-400000000000000000000-220000000000000000000
χ7412-12-1212-6006-66000000000000000000000-44000000000000000000002-20000000000000000000

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