Finite Group Databasebeta

← Group #13138022

Character table — Group #13138022

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11112222224466666666888121212121212121218181818181818181818181824242424242424242424363636363636363636363636727272727272727272
order12223446661212336666664121236661212121244448888888812121212121212121212121212122424242424242424444121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-111
χ31111111111111111111111111111111-1-1-1-11111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-11-111-1-1-1-1
χ41111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-11111-1-11-1-111-1-1
χ511111111111111111111-1-1-111111111111111111111-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1
χ611111111111111111111-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1111111-1-1
χ711111111111111111111-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-11-11-1-11111
χ811111111111111111111-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-111-1-111
χ92222222222222-12-12-12-1222-1-1-1-1-1-12222220000000022-1-1-1-1-1-1-1-1-1-1-1-1000000002000000-1-1
χ102222222222222-12-12-12-1222-1-1-1-1-1-122-2-2-2-20000000022-1-1-1-1-1-1-1-1111100000000-200000011
χ112222222222222-12-12-12-1-2-2-2-1-1-1-1-1-122222200000000-2-211-1-11111-1-1-1-100000000-200000011
χ122222222222222-12-12-12-1-2-2-2-1-1-1-1-1-122-2-2-2-200000000-2-211-1-111111111000000002000000-1-1
χ13222222222222-12-12-12-12222-1-1-1-122-1-1000000002222-1-122-1-1-1-1-1-100000000-1-1-1-100200-1-100
χ14222222222222-12-12-12-12222-1-1-1-122-1-100000000-2-2-2-2-1-122-1-1-1-1-1-100000000111100-2001100
χ15222222222222-12-12-12-12-2-2-2-1-1-1-122-1-100000000222211-2-2-1-1111100000000-1-1-1-100-2001100
χ16222222222222-12-12-12-12-2-2-2-1-1-1-122-1-100000000-2-2-2-211-2-2-1-1111100000000111100200-1-100
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
χ1922222-2-2222-2-22-12-12-12-1000-1-1-1-111-2-222-2-20000000000−i3i311−i3−i3i3i3-1-111000000000000000−i3i3
χ2022222-2-2222-2-22-12-12-12-1000-1-1-1-111-2-222-2-20000000000i3−i311i3i3−i3−i3-1-111000000000000000i3−i3
χ2122222-2-2222-2-22-12-12-12-1000-1-1-1-111-2-2-2-2220000000000−i3i311−i3−i3i3i311-1-1000000000000000i3−i3
χ2222222-2-2222-2-22-12-12-12-1000-1-1-1-111-2-2-2-2220000000000i3−i311i3i3−i3−i311-1-1000000000000000−i3i3
χ2322-2-22002-2-200222-2-22-2-200022-2-200002-20022−2−222−2−200000000002-20022−2−222−2−2000000000
χ2422-2-22002-2-200222-2-22-2-200022-2-200002-200−2−222−2−22200000000002-200−2−222−2−222000000000
χ2522-2-22002-2-200222-2-22-2-200022-2-20000-220022−2−2−2−2220000000000-220022−2−2−2−222000000000
χ2622-2-22002-2-200222-2-22-2-200022-2-20000-2200−2−22222−2−20000000000-2200−2−22222−2−2000000000
χ272-22-2200-22-20022-2-22-2-220002-2-220000002-2−i2i2−i2i2−i2i2−i2i20000000000002-2−i2i2−i2i2−i2i2−i2i2000000000
χ282-22-2200-22-20022-2-22-2-220002-2-220000002-2i2−i2i2−i2i2−i2i2−i20000000000002-2i2−i2i2−i2i2−i2i2−i2000000000
χ292-22-2200-22-20022-2-22-2-220002-2-22000000-22−i2i2−i2i2i2−i2i2−i2000000000000-22−i2i2−i2i2i2−i2i2−i2000000000
χ302-22-2200-22-20022-2-22-2-220002-2-22000000-22i2−i2i2−i2−i2i2−i2i2000000000000-22i2−i2i2−i2−i2i2−i2i2000000000
χ312-2-2222-2-2-222-222-22-2-22-20002-22-22-2-2200002i−2i−2i2i000000002-2000000002i−2i−2i2i0000000000000
χ322-2-2222-2-2-222-222-22-2-22-20002-22-22-2-220000−2i2i2i−2i000000002-200000000−2i2i2i−2i0000000000000
χ332-2-222-22-2-22-2222-22-2-22-20002-22-2-222-2000000002i−2i−2i2i0000-220000000000002i−2i−2i2i000000000
χ342-2-222-22-2-22-2222-22-2-22-20002-22-2-222-200000000−2i2i2i−2i0000-22000000000000−2i2i2i−2i000000000
χ352-2-222-22-2-22-22-12121-2-1-2000-11-11-22-11000000002i−2i−2i2i3−3001-13−33−300000000−iii−i00000−i3i300
χ362-2-222-22-2-22-22-12121-2-1-2000-11-11-22-11000000002i−2i−2i2i−33001-1−33−3300000000−iii−i00000i3−i300
χ372-2-222-22-2-22-22-12121-2-1-2000-11-11-22-1100000000−2i2i2i−2i3−3001-13−33−300000000i−i−ii00000i3−i300
χ382-2-222-22-2-22-22-12121-2-1-2000-11-11-22-1100000000−2i2i2i−2i−33001-1−33−3300000000i−i−ii00000−i3i300
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
χ4144444-4-4444-4-4-24-24-24-24000-2-2-2-2-4-4220000000000000000220000000000000000000000000
χ4244444-4-4444-4-4-2-2-2-2-2-2-2-20001111222200000000000000−2i32i3-1-1i3i3−i3−i3000000000000000000000
χ4344444-4-4444-4-4-2-2-2-2-2-2-2-200011112222000000000000002i3−2i3-1-1−i3−i3i3i3000000000000000000000
χ4444-4-44004-4-4004-242-4-2-42000-2-22200004-400000000000000000000-220000000000000000000
χ4544-4-44004-4-4004-242-4-2-42000-2-2220000-44000000000000000000002-20000000000000000000
χ4644-4-44004-4-400-24-2-4242-4000-2-2220000000000002222−22−22000000000000000000−2−222000000000
χ4744-4-44004-4-400-24-2-4242-4000-2-222000000000000−22−22222200000000000000000022−2−2000000000
χ484-44-4400-44-4004-2-4242-4-2000-222-20000004-400000000000000000000-2200000000000000000
χ494-44-4400-44-4004-2-4242-4-2000-222-2000000-44000000000000000000002-200000000000000000
χ504-44-4400-44-400-242-4-2-424000-222-2000000000000−2i22i2−2i22i2000000000000000000i2−i2i2−i2000000000
χ514-44-4400-44-400-242-4-2-424000-222-20000000000002i2−2i22i2−2i2000000000000000000−i2i2−i2i2000000000
χ524-4-4444-4-4-444-44-2-4-2-4242000-22-22-22-440000000000000000-220000000000000000000000000
χ534-4-4444-4-4-444-4-24242-4-2-4000-22-224-42-20000000000000000-220000000000000000000000000
χ544-4-4444-4-4-444-4-2-22-222-220001-11-1-222-200000000000000001-13i−3i−3i3i000000000000000000000
χ554-4-4444-4-4-444-4-2-22-222-220001-11-1-222-200000000000000001-1−3i3i3i−3i000000000000000000000
χ564-4-444-44-4-44-444-2-4-2-4242000-22-222-24-400000000000000002-20000000000000000000000000
χ574-4-444-44-4-44-44-2-22-222-220001-11-12-2-2200000000000023−2300-11−33−33000000000000000000000
χ584-4-444-44-4-44-44-2-22-222-220001-11-12-2-22000000000000−232300-113−33−3000000000000000000000
χ596666-366-3-3-3-3-3000000006-3-30000000000002222000000000000000000-1-1-1-10000020-1-10000
χ606666-366-3-3-3-3-3000000006-3-3000000000000-2-2-2-2000000000000000000111100000-20110000
χ616666-366-3-3-3-3-300000000-6330000000000002222000000000000000000-1-1-1-100000-20110000
χ626666-366-3-3-3-3-300000000-633000000000000-2-2-2-200000000000000000011110000020-1-10000
χ636-6-66-36-633-3-3300000000033−330000000000002i−2i−2i2i000000000000000000−iii−i0000000−i3i30000
χ646-6-66-36-633-3-3300000000033−33000000000000−2i2i2i−2i000000000000000000i−i−ii0000000i3−i30000
χ656-6-66-36-633-3-33000000000−33330000000000002i−2i−2i2i000000000000000000−iii−i0000000i3−i30000
χ666-6-66-36-633-3-33000000000−3333000000000000−2i2i2i−2i000000000000000000i−i−ii0000000−i3i30000
χ6788-8-88008-8-800-4-4-444-44400022-2-200000000000000000000000000000000000000000000000
χ688-88-8800-88-800-4-444-444-40002-2-2200000000000000000000000000000000000000000000000
χ6912121212-6-12-12-6-6-66600000000000000000000000000000000000000000000000000000000000000
χ701212-12-12-600-66600000000000000000000000002222−22−22000000000000000000−2−2220000000000000
χ711212-12-12-600-6660000000000000000000000000−22−22222200000000000000000022−2−20000000000000
χ7212-1212-12-6006-660000000000000000000000000−2i22i2−2i22i2000000000000000000i2−i2i2−i20000000000000
χ7312-1212-12-6006-6600000000000000000000000002i2−2i22i2−2i2000000000000000000−i2i2−i2i20000000000000
χ7412-12-1212-6-121266-66-600000000000000000000000000000000000000000000000000000000000000

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