Finite Group Databasebeta

← Group #13140621

Character table — Group #13140621

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11112222224466666666888121212121212121218181818181818181818181824242424242424242424363636363636363636363636727272727272727272
order12223446661212336666662663666121212124444888888886666666612121212121224242424242424242446612121212
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
χ511111111111111111111-1-1-111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1
χ611111111111111111111-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-111-1-11111
χ711111111111111111111-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11-1111-1-111
χ811111111111111111111-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-11111-1-1
χ92222222222222-122-1-1-12222-1-1-1-1-1-12222220000000022-1-1-1-1-1-1-1-1-1-1-1-100000000200-1-10000
χ102222222222222-122-1-1-12222-1-1-1-1-1-122-2-2-2-20000000022-1-1-1-1-1-1-1-1111100000000-200110000
χ112222222222222-122-1-1-12-2-2-2-1-1-1-1-1-122222200000000-2-2111111-1-1-1-1-1-100000000-200110000
χ122222222222222-122-1-1-12-2-2-2-1-1-1-1-1-122-2-2-2-200000000-2-2111111-1-1111100000000200-1-10000
χ13222222222222-12-1-1222-1222-1-1-1-122-1-1000000002222-1-122-1-1-1-1-1-100000000-1-1-1-10020000-1-1
χ14222222222222-12-1-1222-1222-1-1-1-122-1-100000000-2-2-2-2-1-122-1-1-1-1-1-100000000111100-2000011
χ15222222222222-12-1-1222-1-2-2-2-1-1-1-122-1-100000000222211-2-21111-1-100000000-1-1-1-100-2000011
χ16222222222222-12-1-1222-1-2-2-2-1-1-1-122-1-100000000-2-2-2-211-2-21111-1-10000000011110020000-1-1
χ1722222-2-2222-2-2222222220002222-2-2-2-222-2-20000000000000000-2-222-2-200000000000000000
χ1822222-2-2222-2-2222222220002222-2-2-2-2-2-2220000000000000000-2-2-2-22200000000000000000
χ1922222-2-2222-2-22-122-1-1-12000-1-1-1-111-2-222-2-20000000000−i3i3−i3−i3i3i311-1-11100000000000−i3i30000
χ2022222-2-2222-2-22-122-1-1-12000-1-1-1-111-2-222-2-20000000000i3−i3i3i3−i3−i311-1-11100000000000i3−i30000
χ2122222-2-2222-2-22-122-1-1-12000-1-1-1-111-2-2-2-2220000000000−i3i3−i3−i3i3i31111-1-100000000000i3−i30000
χ2222222-2-2222-2-22-122-1-1-12000-1-1-1-111-2-2-2-2220000000000i3−i3i3i3−i3−i31111-1-100000000000−i3i30000
χ2322-2-22002-2-200222-2-22-2-200022-2-20000002-2−i2−i2i2i2−i2−i2i2i20000000000002-2−i2−i2i2i2−i2−i2i2i2000000000
χ2422-2-22002-2-200222-2-22-2-200022-2-20000002-2i2i2−i2−i2i2i2−i2−i20000000000002-2i2i2−i2−i2i2i2−i2−i2000000000
χ2522-2-22002-2-200222-2-22-2-200022-2-2000000-22−i2−i2i2i2i2i2−i2−i2000000000000-22−i2−i2i2i2i2i2−i2−i2000000000
χ2622-2-22002-2-200222-2-22-2-200022-2-2000000-22i2i2−i2−i2−i2−i2i2i2000000000000-22i2i2−i2−i2−i2−i2i2i2000000000
χ272-22-2200-22-20022-22-2-22-20002-22-200002-200−i2i2−i2i2−i2i2−i2i200000000002-200−i2i2−i2i2−i2i2−i2i2000000000
χ282-22-2200-22-20022-22-2-22-20002-22-200002-200i2−i2i2−i2i2−i2i2−i200000000002-200i2−i2i2−i2i2−i2i2−i2000000000
χ292-22-2200-22-20022-22-2-22-20002-22-20000-2200−i2i2−i2i2i2−i2i2−i20000000000-2200−i2i2−i2i2i2−i2i2−i2000000000
χ302-22-2200-22-20022-22-2-22-20002-22-20000-2200i2−i2i2−i2−i2i2−i2i20000000000-2200i2−i2i2−i2−i2i2−i2i2000000000
χ312-2-2222-2-2-222-222-2-22-2-220002-2-222-2-22000000002-2-22000000002-2000000002-2-22000000000
χ322-2-2222-2-2-222-222-2-22-2-220002-2-222-2-2200000000-222-2000000002-200000000-222-2000000000
χ332-2-2222-2-2-222-2-12112-2-2-1000-111-12-21-1000000002-2-22−i3i300−i3i3−i3i3-1100000000-111-10000000−i3i3
χ342-2-2222-2-2-222-2-12112-2-2-1000-111-12-21-1000000002-2-22i3−i300i3−i3i3−i3-1100000000-111-10000000i3−i3
χ352-2-2222-2-2-222-2-12112-2-2-1000-111-12-21-100000000-222-2−i3i300−i3i3−i3i3-11000000001-1-110000000i3−i3
χ362-2-2222-2-2-222-2-12112-2-2-1000-111-12-21-100000000-222-2i3−i300i3−i3i3−i3-11000000001-1-110000000−i3i3
χ372-2-222-22-2-22-2222-2-22-2-220002-2-22-222-200002-2-22000000000000-2200002-2-220000000000000
χ382-2-222-22-2-22-2222-2-22-2-220002-2-22-222-20000-222-2000000000000-220000-222-20000000000000
χ39444444444444-2-2-2-2-2-2-2-24441111-2-2-2-2000000000000-2-2-2-2111111000000000000000000000
χ40444444444444-2-2-2-2-2-2-2-2-4-4-41111-2-2-2-20000000000002222-1-1-1-111000000000000000000000
χ4144444-4-4444-4-4-24-2-2444-2000-2-2-2-2-4-4220000000000000000000022000000000000000000000
χ4244444-4-4444-4-4-2-2-2-2-2-2-2-20001111222200000000000000−2i32i3i3i3−i3−i3-1-1000000000000000000000
χ4344444-4-4444-4-4-2-2-2-2-2-2-2-200011112222000000000000002i3−2i3−i3−i3i3i3-1-1000000000000000000000
χ4444-4-44004-4-4004-24-42-22-4000-2-2220000004-400000000000000000000-2200000000000000000
χ4544-4-44004-4-4004-24-42-22-4000-2-222000000-44000000000000000000002-200000000000000000
χ4644-4-44004-4-400-24-22-44-42000-2-222000000000000−2i2−2i22i22i2000000000000000000i2i2−i2−i2000000000
χ4744-4-44004-4-400-24-22-44-42000-2-2220000000000002i22i2−2i2−2i2000000000000000000−i2−i2i2i2000000000
χ484-44-4400-44-4004-2-4422-2-4000-22-2200004-400000000000000000000-220000000000000000000
χ494-44-4400-44-4004-2-4422-2-4000-22-220000-44000000000000000000002-20000000000000000000
χ504-44-4400-44-400-242-2-4-442000-22-22000000000000−2i22i2−2i22i2000000000000000000i2−i2i2−i2000000000
χ514-44-4400-44-400-242-2-4-442000-22-220000000000002i2−2i22i2−2i2000000000000000000−i2i2−i2i2000000000
χ524-4-4444-4-4-444-44-2-4-4-2224000-222-2-22-4400000000000000000000-22000000000000000000000
χ534-4-4444-4-4-444-4-2-222-222-20001-1-11-222-2000000000000−2i32i300i3−i3i3−i31-1000000000000000000000
χ544-4-4444-4-4-444-4-2-222-222-20001-1-11-222-20000000000002i3−2i300−i3i3−i3i31-1000000000000000000000
χ554-4-444-44-4-44-444-2-4-4-2224000-222-22-24-4000000000000000000002-2000000000000000000000
χ564-4-444-44-4-44-44-24224-4-4-2000-222-2-44-22000000000000000000002-2000000000000000000000
χ574-4-444-44-4-44-44-2-222-222-20001-1-112-2-2200000000000000003-3-33-11000000000000000000000
χ584-4-444-44-4-44-44-2-222-222-20001-1-112-2-220000000000000000-333-3-11000000000000000000000
χ596666-366-3-3-3-3-3000000006-3-30000000000002222000000000000000000-1-1-1-1000002000-1-100
χ606666-366-3-3-3-3-3000000006-3-3000000000000-2-2-2-2000000000000000000111100000-20001100
χ616666-366-3-3-3-3-300000000-6330000000000002222000000000000000000-1-1-1-100000-20001100
χ626666-366-3-3-3-3-300000000-633000000000000-2-2-2-20000000000000000001111000002000-1-100
χ636-6-66-3-6633-33-3000000000−3i33i30000000000002-2-22000000000000000000-111-1000000000−i3i300
χ646-6-66-3-6633-33-3000000000−3i33i3000000000000-222-20000000000000000001-1-11000000000i3−i300
χ656-6-66-3-6633-33-30000000003i3−3i30000000000002-2-22000000000000000000-111-1000000000i3−i300
χ666-6-66-3-6633-33-30000000003i3−3i3000000000000-222-20000000000000000001-1-11000000000−i3i300
χ6788-8-88008-8-800-4-4-444-44400022-2-200000000000000000000000000000000000000000000000
χ688-88-8800-88-800-4-44-444-440002-22-200000000000000000000000000000000000000000000000
χ6912121212-6-12-12-6-6-66600000000000000000000000000000000000000000000000000000000000000
χ701212-12-12-600-6660000000000000000000000000−2i2−2i22i22i2000000000000000000i2i2−i2−i20000000000000
χ711212-12-12-600-66600000000000000000000000002i22i2−2i2−2i2000000000000000000−i2−i2i2i20000000000000
χ7212-1212-12-6006-660000000000000000000000000−2i22i2−2i22i2000000000000000000i2−i2i2−i20000000000000
χ7312-1212-12-6006-6600000000000000000000000002i2−2i22i2−2i2000000000000000000−i2i2−i2i20000000000000
χ7412-12-1212-612-1266-6-6600000000000000000000000000000000000000000000000000000000000000

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