Finite Group Databasebeta

← Group #13137963

Character table — Group #13137963

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74
size11112222224466666666888121212121212121218181818181818181818181824242424242424242424363636363636363636363636727272727272727272
order1222344666121233666666412123666121212122244888888881212121212121212121266121224242424242424242446612121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-11-1-111-1-1
χ31111111111111111111111111111111-1-1-1-11111-1-1-1-11111111111-1-1-1-11111-1-1-1-11-1-111-1-1-1-1
χ41111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-11111-11-1-1-1-1-111
χ511111111111111111111-1-1-111111111111111111111-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1
χ611111111111111111111-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111-111-1-111
χ711111111111111111111-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-111-1-11111
χ811111111111111111111-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111111-111111-1-1
χ92222222222222-1-12-12-12222-1-1-1-12-12-100002222000022-1-1-1-1-1-1-1-10000-1-1-1-10000200-1-10000
χ102222222222222-1-12-12-12222-1-1-1-12-12-10000-2-2-2-2000022-1-1-1-1-1-1-1-1000011110000-200110000
χ112222222222222-1-12-12-12-2-2-2-1-1-1-12-12-1000022220000-2-211-1-111110000-1-1-1-10000-200110000
χ122222222222222-1-12-12-12-2-2-2-1-1-1-12-12-10000-2-2-2-20000-2-211-1-11111000011110000200-1-10000
χ13222222222222-122-12-12-1222-1-1-1-1-12-12000000002222-1-122-1-1-1-1-1-100000000-1-1-1-10200000-1-1
χ14222222222222-122-12-12-1222-1-1-1-1-12-1200000000-2-2-2-2-1-122-1-1-1-1-1-10000000011110-20000011
χ15222222222222-122-12-12-1-2-2-2-1-1-1-1-12-1200000000222211-2-2-1-1111100000000-1-1-1-10-20000011
χ16222222222222-122-12-12-1-2-2-2-1-1-1-1-12-1200000000-2-2-2-211-2-2-1-111110000000011110200000-1-1
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
χ1922-2-2200-22-20022-2-2-222-20002-2-220000002i−2i22−2−2−i2−i2i2i20000000000002i−2i22−2−2−i2−i2i2i2000000000
χ2022-2-2200-22-20022-2-2-222-20002-2-220000002i−2i−2−222i2i2−i2−i20000000000002i−2i−2−222i2i2−i2−i2000000000
χ2122-2-2200-22-20022-2-2-222-20002-2-22000000−2i2i22−2−2i2i2−i2−i2000000000000−2i2i22−2−2i2i2−i2−i2000000000
χ2222-2-2200-22-20022-2-2-222-20002-2-22000000−2i2i−2−222−i2−i2i2i2000000000000−2i2i−2−222−i2−i2i2i2000000000
χ232-22-22002-2-200222-2-2-2-2200022-2-200002-200−i2i2−i2i2−i2i2−i2i200000000002-200−i2i2−i2i2−i2i2−i2i2000000000
χ242-22-22002-2-200222-2-2-2-2200022-2-200002-200i2−i2i2−i2i2−i2i2−i200000000002-200i2−i2i2−i2i2−i2i2−i2000000000
χ252-22-22002-2-200222-2-2-2-2200022-2-20000-2200−i2i2−i2i2i2−i2i2−i20000000000-2200−i2i2−i2i2i2−i2i2−i2000000000
χ262-22-22002-2-200222-2-2-2-2200022-2-20000-2200i2−i2i2−i2−i2i2−i2i20000000000-2200i2−i2i2−i2−i2i2−i2i2000000000
χ272-2-2222-2-2-222-222-222-2-2-20002-22-222-2-200002i−2i−2i2i000000002-2000000002i−2i−2i2i0000000000000
χ282-2-2222-2-2-222-222-222-2-2-20002-22-222-2-20000−2i2i2i−2i000000002-200000000−2i2i2i−2i0000000000000
χ292-2-2222-2-2-222-22-112-1-21-2000-11-112-1-2100002i−2i−2i2i0000003−3-1133−3−30000−iii−i0000000−i3i30000
χ302-2-2222-2-2-222-22-112-1-21-2000-11-112-1-2100002i−2i−2i2i000000−33-11−3−3330000−iii−i0000000i3−i30000
χ312-2-2222-2-2-222-22-112-1-21-2000-11-112-1-210000−2i2i2i−2i0000003−3-1133−3−30000i−i−ii0000000i3−i30000
χ322-2-2222-2-2-222-22-112-1-21-2000-11-112-1-210000−2i2i2i−2i000000−33-11−3−3330000i−i−ii0000000−i3i30000
χ332-2-222-22-2-22-2222-222-2-2-20002-22-2-2-222000000002-2-220000-220000000000002-2-22000000000
χ342-2-222-22-2-22-2222-222-2-2-20002-22-2-2-22200000000-222-20000-22000000000000-222-2000000000
χ352-2-222-22-2-22-22-12-2-121-21000-11-111-2-12000000002-2-223−3001-13−33−300000000-111-100000003−3
χ362-2-222-22-2-22-22-12-2-121-21000-11-111-2-12000000002-2-22−33001-1−33−3300000000-111-10000000−33
χ372-2-222-22-2-22-22-12-2-121-21000-11-111-2-1200000000-222-23−3001-13−33−3000000001-1-110000000−33
χ382-2-222-22-2-22-22-12-2-121-21000-11-111-2-1200000000-222-2−33001-1−33−33000000001-1-1100000003−3
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
χ4144444-4-4444-4-44-2-24-24-24000-2-2-2-2-42-420000000000000000220000000000000000000000000
χ4244444-4-4444-4-4-244-24-24-2000-2-2-2-22-42-40000000000000000220000000000000000000000000
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
χ4544-4-4400-44-4004-22-424-2-4000-222-2000000002222−22−22000000000000000000−2−2220000000000000
χ4644-4-4400-44-4004-22-424-2-4000-222-200000000−22−22222200000000000000000022−2−20000000000000
χ4744-4-4400-44-400-24-42-4-242000-222-2000000000000−2i2−2i22i22i2000000000000000000i2i2−i2−i2000000000
χ4844-4-4400-44-400-24-42-4-242000-222-20000000000002i22i2−2i2−2i2000000000000000000−i2−i2i2i2000000000
χ494-44-44004-4-4004-2-2-42-424000-2-22200000000−2i22i2−2i22i2000000000000000000i2−i2i2−i20000000000000
χ504-44-44004-4-4004-2-2-42-424000-2-222000000002i2−2i22i2−2i2000000000000000000−i2i2−i2i20000000000000
χ514-44-44004-4-400-2442-42-4-2000-2-222000000000000−2i22i2−2i22i2000000000000000000i2−i2i2−i2000000000
χ524-44-44004-4-400-2442-42-4-2000-2-2220000000000002i2−2i22i2−2i2000000000000000000−i2i2−i2i2000000000
χ534-4-4444-4-4-444-4-24-4-242-42000-22-22-242-40000000000000000-220000000000000000000000000
χ544-4-4444-4-4-444-4-2-22-2-22220001-11-1-2-2220000000000000023−231-1−3−333000000000000000000000
χ554-4-4444-4-4-444-4-2-22-2-22220001-11-1-2-22200000000000000−23231-133−3−3000000000000000000000
χ564-4-444-44-4-44-444-224-2-42-4000-22-22-424-200000000000000002-20000000000000000000000000
χ574-4-444-44-4-44-44-2-22-2-22220001-11-122-2-200000000000023−2300-11−33−33000000000000000000000
χ584-4-444-44-4-44-44-2-22-2-22220001-11-122-2-2000000000000−232300-113−33−3000000000000000000000
χ596666-366-3-3-3-3-3000000006-3-3000000002222000000000000000000-1-1-1-10000000000200-1-100
χ606666-366-3-3-3-3-3000000006-3-300000000-2-2-2-200000000000000000011110000000000-2001100
χ616666-366-3-3-3-3-300000000-633000000002222000000000000000000-1-1-1-10000000000-2001100
χ626666-366-3-3-3-3-300000000-63300000000-2-2-2-200000000000000000011110000000000200-1-100
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
χ6788-8-8800-88-800-4-4444-4-440002-2-2200000000000000000000000000000000000000000000000
χ688-88-88008-8-800-4-4-44444-400022-2-200000000000000000000000000000000000000000000000
χ691212-12-12-6006-66000000000000000000000004i−4i00000000000000000000−2i2i00000000000000000
χ701212-12-12-6006-6600000000000000000000000−4i4i000000000000000000002i−2i00000000000000000
χ7112-1212-12-600-6660000000000000000000004-400000000000000000000-220000000000000000000
χ7212-1212-12-600-666000000000000000000000-44000000000000000000002-20000000000000000000
χ7312-12-1212-612-1266-6-6600000000000000000000000000000000000000000000000000000000000000
χ7412-12-1212-6-121266-66-600000000000000000000000000000000000000000000000000000000000000

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