Finite Group Databasebeta

← Group #13140571

Character table — Group #13140571

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11112222224466666666888121212121212121218181818181818181818181824242424242424242424363636363636363636363636727272727272727272
order122234466612123366666626636661212121222448888888866666666121266121224242424242424242446612121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-11-1-1-111-1-1
χ31111111111111111111111111111111-1-1-1-11111-1-1-1-11111111111-1-1-1-11111-1-1-1-11-1-111-1-1-1-1
χ41111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-11111-1-11-1-1-1-111
χ511111111111111111111-1-1-111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1
χ611111111111111111111-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11-1111-1-111
χ711111111111111111111-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-111-1-11111
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
χ92222222222222-12-1-12-12222-1-1-1-12-12-100002222000022-1-1-1-1-1-1-1-10000-1-1-1-10000200-1-10000
χ102222222222222-12-1-12-12222-1-1-1-12-12-10000-2-2-2-2000022-1-1-1-1-1-1-1-1000011110000-200110000
χ112222222222222-12-1-12-12-2-2-2-1-1-1-12-12-1000022220000-2-2111111-1-10000-1-1-1-10000-200110000
χ122222222222222-12-1-12-12-2-2-2-1-1-1-12-12-10000-2-2-2-20000-2-2111111-1-1000011110000200-1-10000
χ13222222222222-12-122-12-1222-1-1-1-1-12-12000000002222-1-122-1-1-1-1-1-100000000-1-1-1-10020000-1-1
χ14222222222222-12-122-12-1222-1-1-1-1-12-1200000000-2-2-2-2-1-122-1-1-1-1-1-100000000111100-2000011
χ15222222222222-12-122-12-1-2-2-2-1-1-1-1-12-1200000000222211-2-21111-1-100000000-1-1-1-100-2000011
χ16222222222222-12-122-12-1-2-2-2-1-1-1-1-12-1200000000-2-2-2-211-2-21111-1-10000000011110020000-1-1
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
χ1922-2-22002-2-2002222-2-2-2-200022-2-20000002i−2i22−2−2−i2−i2i2i20000000000002i−2i22−2−2−i2−i2i2i2000000000
χ2022-2-22002-2-2002222-2-2-2-200022-2-20000002i−2i−2−222i2i2−i2−i20000000000002i−2i−2−222i2i2−i2−i2000000000
χ2122-2-22002-2-2002222-2-2-2-200022-2-2000000−2i2i22−2−2i2i2−i2−i2000000000000−2i2i22−2−2i2i2−i2−i2000000000
χ2222-2-22002-2-2002222-2-2-2-200022-2-2000000−2i2i−2−222−i2−i2i2i2000000000000−2i2i−2−222−i2−i2i2i2000000000
χ232-22-222-2-22-22-222-2-2-222-20002-2-2222-2-2000000002i−2i2i−2i000000002-2000000002i−2i2i−2i000000000
χ242-22-222-2-22-22-222-2-2-222-20002-2-2222-2-200000000−2i2i−2i2i000000002-200000000−2i2i−2i2i000000000
χ252-22-222-2-22-22-2-121-2-2-121000-111-1-121-2000000002i−2i2i−2i−i3i300−i3−i3i3i3-1100000000−ii−ii00000003−3
χ262-22-222-2-22-22-2-121-2-2-121000-111-1-121-2000000002i−2i2i−2ii3−i300i3i3−i3−i3-1100000000−ii−ii0000000−33
χ272-22-222-2-22-22-2-121-2-2-121000-111-1-121-200000000−2i2i−2i2i−i3i300−i3−i3i3i3-1100000000i−ii−i0000000−33
χ282-22-222-2-22-22-2-121-2-2-121000-111-1-121-200000000−2i2i−2i2ii3−i300i3i3−i3−i3-1100000000i−ii−i00000003−3
χ292-22-22-22-22-2-2222-2-2-222-20002-2-22-2-22200002-22-2000000000000-2200002-22-20000000000000
χ302-22-22-22-22-2-2222-2-2-222-20002-2-22-2-2220000-22-22000000000000-220000-22-220000000000000
χ312-22-22-22-22-2-222-1-2112-1-2000-111-1-212-100002-22-2000000−i3i3−i3i3−i3i31-10000-11-110000000−i3i30000
χ322-22-22-22-22-2-222-1-2112-1-2000-111-1-212-100002-22-2000000i3−i3i3−i3i3−i31-10000-11-110000000i3−i30000
χ332-22-22-22-22-2-222-1-2112-1-2000-111-1-212-10000-22-22000000−i3i3−i3i3−i3i31-100001-11-10000000i3−i30000
χ342-22-22-22-22-2-222-1-2112-1-2000-111-1-212-10000-22-22000000i3−i3i3−i3i3−i31-100001-11-10000000−i3i30000
χ352-2-22200-2-220022-2-22-2-220002-22-200002-2002−2−222−2−2200000000002-2002−2−222−2−22000000000
χ362-2-22200-2-220022-2-22-2-220002-22-200002-200−222−2−222−200000000002-200−222−2−222−2000000000
χ372-2-22200-2-220022-2-22-2-220002-22-20000-22002−2−22−222−20000000000-22002−2−22−222−2000000000
χ382-2-22200-2-220022-2-22-2-220002-22-20000-2200−222−22−2−220000000000-2200−222−22−2−22000000000
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
χ4144444-4-4444-4-44-24-2-24-24000-2-2-2-2-42-420000000000000000000022000000000000000000000
χ4244444-4-4444-4-4-24-244-24-2000-2-2-2-22-42-40000000000000000000022000000000000000000000
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
χ4544-4-44004-4-4004-24-22-42-4000-2-222000000002222−22−22000000000000000000−2−2220000000000000
χ4644-4-44004-4-4004-24-22-42-4000-2-22200000000−22−22222200000000000000000022−2−20000000000000
χ4744-4-44004-4-400-24-24-42-42000-2-222000000000000−2i2−2i22i22i2000000000000000000i2i2−i2−i2000000000
χ4844-4-44004-4-400-24-24-42-42000-2-2220000000000002i22i2−2i2−2i2000000000000000000−i2−i2i2i2000000000
χ494-44-444-4-44-44-44-2-4224-2-4000-222-24-2-4200000000000000000000-22000000000000000000000
χ504-44-444-4-44-44-4-2-2222-2-220001-1-11-2-222000000000000−2i32i300i3i3−i3−i31-1000000000000000000000
χ514-44-444-4-44-44-4-2-2222-2-220001-1-11-2-2220000000000002i3−2i300−i3−i3i3i31-1000000000000000000000
χ524-44-44-44-44-4-44-242-4-4-242000-222-22-4-24000000000000000000002-2000000000000000000000
χ534-44-44-44-44-4-44-2-2222-2-220001-1-1122-2-200000000000000−2i32i3i3−i3i3−i3-11000000000000000000000
χ544-44-44-44-44-4-44-2-2222-2-220001-1-1122-2-2000000000000002i3−2i3−i3i3−i3i3-11000000000000000000000
χ554-4-44400-4-44004-2-42-2-424000-22-220000000022−22−2222000000000000000000−222−20000000000000
χ564-4-44400-4-44004-2-42-2-424000-22-2200000000−222222−220000000000000000002−2−220000000000000
χ574-4-44400-4-4400-242-442-4-2000-22-2200000000000022−22−2222000000000000000000−222−2000000000
χ584-4-44400-4-4400-242-442-4-2000-22-22000000000000−222222−220000000000000000002−2−22000000000
χ596666-366-3-3-3-3-3000000006-3-3000000002222000000000000000000-1-1-1-10000000002000-1-100
χ606666-366-3-3-3-3-3000000006-3-300000000-2-2-2-20000000000000000001111000000000-20001100
χ616666-366-3-3-3-3-300000000-633000000002222000000000000000000-1-1-1-1000000000-20001100
χ626666-366-3-3-3-3-300000000-63300000000-2-2-2-200000000000000000011110000000002000-1-100
χ636666-3-6-6-3-3-333000000000−3i33i30000000022-2-2000000000000000000-1-1110000000000000−i3i300
χ646666-3-6-6-3-3-333000000000−3i33i300000000-2-22200000000000000000011-1-10000000000000i3−i300
χ656666-3-6-6-3-3-3330000000003i3−3i30000000022-2-2000000000000000000-1-1110000000000000i3−i300
χ666666-3-6-6-3-3-3330000000003i3−3i300000000-2-22200000000000000000011-1-10000000000000−i3i300
χ6788-8-88008-8-800-4-4-4-4444400022-2-200000000000000000000000000000000000000000000000
χ688-8-88800-8-8800-4-444-444-40002-22-200000000000000000000000000000000000000000000000
χ691212-12-12-600-666000000000000000000000004i−4i00000000000000000000−2i2i00000000000000000
χ701212-12-12-600-66600000000000000000000000−4i4i000000000000000000002i−2i00000000000000000
χ7112-1212-12-612-126-66-6600000000000000000000000000000000000000000000000000000000000000
χ7212-1212-12-6-12126-666-600000000000000000000000000000000000000000000000000000000000000
χ7312-12-1212-60066-60000000000000000000004-400000000000000000000-220000000000000000000
χ7412-12-1212-60066-6000000000000000000000-44000000000000000000002-20000000000000000000

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