Finite Group Databasebeta

← Group #13140590

Character table — Group #13140590

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11112222224466666666888121212121212121218181818181818181818181824242424242424242424363636363636363636363636727272727272727272
order1222344666121233666666266366612121212444488888888666666661212121212122424242424242424222666666
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
χ92222222222222-122-1-12-1222-1-1-1-12-12-100000000222222-1-1-1-1-1-1-1-100000000-1-1-1-10020000-1-1
χ102222222222222-122-1-12-1222-1-1-1-12-12-100000000-2-2-2-222-1-1-1-1-1-1-1-100000000111100-2000011
χ112222222222222-122-1-12-1-2-2-2-1-1-1-12-12-1000000002222-2-2111111-1-100000000-1-1-1-100-2000011
χ122222222222222-122-1-12-1-2-2-2-1-1-1-12-12-100000000-2-2-2-2-2-2111111-1-10000000011110020000-1-1
χ13222222222222-12-1-122-12222-1-1-1-1-12-12000022220000-1-122-1-1-1-1-1-10000-1-1-1-1000002000-1-100
χ14222222222222-12-1-122-12222-1-1-1-1-12-120000-2-2-2-20000-1-122-1-1-1-1-1-10000111100000-20001100
χ15222222222222-12-1-122-12-2-2-2-1-1-1-1-12-1200002222000011-2-21111-1-10000-1-1-1-100000-20001100
χ16222222222222-12-1-122-12-2-2-2-1-1-1-1-12-120000-2-2-2-2000011-2-21111-1-100001111000002000-1-100
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
χ1922-2-222-22-2-22-222-2-2-2-2220002-2-222-2-220000000022-2-2000000002-20000000022-2-2000000000
χ2022-2-222-22-2-22-222-2-2-2-2220002-2-222-2-2200000000-2-222000000002-200000000-2-222000000000
χ2122-2-222-22-2-22-22-1-2-2112-1000-111-121-2-10000000022-2-200−i3i3−i3−i3i3i3-1100000000-1-1110000000−i3i3
χ2222-2-222-22-2-22-22-1-2-2112-1000-111-121-2-10000000022-2-200i3−i3i3i3−i3−i3-1100000000-1-1110000000i3−i3
χ2322-2-222-22-2-22-22-1-2-2112-1000-111-121-2-100000000-2-22200−i3i3−i3−i3i3i3-110000000011-1-10000000i3−i3
χ2422-2-222-22-2-22-22-1-2-2112-1000-111-121-2-100000000-2-22200i3−i3i3i3−i3−i3-110000000011-1-10000000−i3i3
χ2522-2-22-222-2-2-2222-2-2-2-2220002-2-22-222-2000022-2-2000000000000-22000022-2-20000000000000
χ2622-2-22-222-2-2-2222-2-2-2-2220002-2-22-222-20000-2-222000000000000-220000-2-2220000000000000
χ2722-2-22-222-2-2-22-1211-2-2-12000-111-112-1-2000022-2-20000−i3i300−i3i3−i3i31-10000-1-111000000000−i3i300
χ2822-2-22-222-2-2-22-1211-2-2-12000-111-112-1-2000022-2-20000i3−i300i3−i3i3−i31-10000-1-111000000000i3−i300
χ2922-2-22-222-2-2-22-1211-2-2-12000-111-112-1-20000-2-2220000−i3i300−i3i3−i3i31-1000011-1-1000000000i3−i300
χ3022-2-22-222-2-2-22-1211-2-2-12000-111-112-1-20000-2-2220000i3−i300i3−i3i3−i31-1000011-1-1000000000−i3i300
χ312-22-2200-22-200222-22-2-2-200022-2-20000002-22−22−22−22−20000000000002-22−22−22−22−2000000000
χ322-22-2200-22-200222-22-2-2-200022-2-20000002-2−22−22−22−220000000000002-2−22−22−22−22000000000
χ332-22-2200-22-200222-22-2-2-200022-2-2000000-222−22−2−22−22000000000000-222−22−2−22−22000000000
χ342-22-2200-22-200222-22-2-2-200022-2-2000000-22−22−222−22−2000000000000-22−22−222−22−2000000000
χ352-2-22200-2-220022-22-22-2-20002-22-200002-2002−2−222−2−2200000000002-2002−2−222−2−22000000000
χ362-2-22200-2-220022-22-22-2-20002-22-200002-200−222−2−222−200000000002-200−222−2−222−2000000000
χ372-2-22200-2-220022-22-22-2-20002-22-20000-22002−2−22−222−20000000000-22002−2−22−222−2000000000
χ382-2-22200-2-220022-22-22-2-20002-22-20000-2200−222−22−2−220000000000-2200−222−22−2−22000000000
χ39444444444444-2-2-2-2-2-2-2-24441111-2-2-2-2000000000000-2-2-2-2111111000000000000000000000
χ40444444444444-2-2-2-2-2-2-2-2-4-4-41111-2-2-2-20000000000002222-1-1-1-111000000000000000000000
χ4144444-4-4444-4-44-244-2-24-2000-2-2-2-2-42-420000000000000000000022000000000000000000000
χ4244444-4-4444-4-4-24-2-244-24000-2-2-2-22-42-40000000000000000000022000000000000000000000
χ4344444-4-4444-4-4-2-2-2-2-2-2-2-20001111222200000000000000003-3-33-1-1000000000000000000000
χ4444444-4-4444-4-4-2-2-2-2-2-2-2-2000111122220000000000000000-333-3-1-1000000000000000000000
χ4544-4-444-44-4-44-4-2422-4-4-24000-222-2-2-42400000000000000000000-22000000000000000000000
χ4644-4-444-44-4-44-4-2-22222-2-20001-1-11-222-200000000000000−2i32i3i3i3−i3−i31-1000000000000000000000
χ4744-4-444-44-4-44-4-2-22222-2-20001-1-11-222-2000000000000002i3−2i3−i3−i3i3i31-1000000000000000000000
χ4844-4-44-444-4-4-444-2-4-4224-2000-222-2-4-242000000000000000000002-2000000000000000000000
χ4944-4-44-444-4-4-44-2-22222-2-20001-1-112-2-22000000000000−2i32i300i3−i3i3−i3-11000000000000000000000
χ5044-4-44-444-4-4-44-2-22222-2-20001-1-112-2-220000000000002i3−2i300−i3i3−i3i3-11000000000000000000000
χ514-44-4400-44-4004-24-4-22-42000-2-22200000000000022−2222−22000000000000000000−22−22000000000
χ524-44-4400-44-4004-24-4-22-42000-2-222000000000000−2222−22220000000000000000002−22−2000000000
χ534-44-4400-44-400-24-224-42-4000-2-2220000000022−2222−22000000000000000000−22−220000000000000
χ544-44-4400-44-400-24-224-42-4000-2-22200000000−2222−22220000000000000000002−22−20000000000000
χ554-4-44400-4-44004-2-442-2-42000-22-2200000000000022−22−2222000000000000000000−222−2000000000
χ564-4-44400-4-44004-2-442-2-42000-22-22000000000000−222222−220000000000000000002−2−22000000000
χ574-4-44400-4-4400-242-2-442-4000-22-220000000022−22−2222000000000000000000−222−20000000000000
χ584-4-44400-4-4400-242-2-442-4000-22-2200000000−222222−220000000000000000002−2−220000000000000
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
χ678-88-8800-88-800-4-4-44-444400022-2-200000000000000000000000000000000000000000000000
χ688-8-88800-8-8800-4-44-44-4440002-22-200000000000000000000000000000000000000000000000
χ691212-12-12-612-12-666-6600000000000000000000000000000000000000000000000000000000000000
χ701212-12-12-6-1212-6666-600000000000000000000000000000000000000000000000000000000000000
χ7112-1212-12-6006-66000000000000000000000004-400000000000000000000-2200000000000000000
χ7212-1212-12-6006-6600000000000000000000000-44000000000000000000002-200000000000000000
χ7312-12-1212-60066-60000000000000000000004-400000000000000000000-220000000000000000000
χ7412-12-1212-60066-6000000000000000000000-44000000000000000000002-20000000000000000000

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