Finite Group Databasebeta

← Group #13150681

Character table — Group #13150681

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95
size11112222222244444446666666666666666121212121212121212121212121212121212121212121212181818181818181836363636363636363636363636363636363636363636363672727272
order1222223446664661212121233666666666612121212366666666612121212121212121212121212122222444422244444666666666612121212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111-1-1111-111-1-1-1-1111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111-1-1-11-11-1-1-11111-1-1-1-111-1-1111-11-1
χ61111111-1-1111-111-1-1-1-1111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11-111-11-11111111-1-1-1-1-1-111-1-1-11-11
χ71111111-1-1111-111-1-1-1-1111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-11-1-1-11-11-1-1-1-1-1-1111111-1-111-11-11
χ81111111-1-1111-111-1-1-1-1111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-11111-11-111-1-1-1-11111-1-111-1-11-11-1
χ91111-1-1111111-1-1-111-1-11111-1-1-1-1111111111-1-111-1-1-1-1111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1111-1-1-1-111-1-111-1-11111-1-111-1-1
χ101111-1-1111111-1-1-111-1-11111-1-1-1-1111111111-1-111-1-1-1-1111-1-1-1-11111-1-1-1-11111-1-111-1-11-1-1-1111111-1-111-1-1-1-1-1-111-1-111
χ111111-1-1111111-1-1-111-1-11111-1-1-1-1111111111-1-111-1-1-1-1111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-11-1-111-1-1-1-111-1-1111111-1-1-1-111
χ121111-1-1111111-1-1-111-1-11111-1-1-1-1111111111-1-111-1-1-1-1111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111-111-1-111-1-111-1-111-1-1-1-11111-1-1
χ131111-1-11-1-11111-1-1-1-1111111-1-1-1-11111-1-1-1-11-1-111-1-1-1-11-1-11111-1-1-1-1111111-1-111-1-1-111-11-1-111111-1-1-1-11111-1-1-1-11-1-11
χ141111-1-11-1-11111-1-1-1-1111111-1-1-1-11111-1-1-1-11-1-111-1-1-1-11-1-11111-1-1-1-1111111-1-1-1-111-11-11-111-1-1-111-1-1-1-111-1-11111-111-1
χ151111-1-11-1-11111-1-1-1-1111111-1-1-1-11111-1-1-1-11-1-111-1-1-1-11-1-11111-1-1-1-11111-1-11111-1-11-11-1-111-111-1-11111-1-111-1-1-1-1-111-1
χ161111-1-11-1-11111-1-1-1-1111111-1-1-1-11111-1-1-1-11-1-111-1-1-1-11-1-11111-1-1-1-11111-1-111-1-1111-1-111-1-11-1-1-1-11111-1-1-1-111111-1-11
χ1722222222222222222222-1-1-1-1-1-1-1-12222222-122-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1222200002200000000-1-1-1-1-1-1-1-10000000000
χ1822222222222222222222-1-1-1-1-1-1-1-12222222-122-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-20000-2-200000000111111110000000000
χ192222222222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-10000222200220000-1-100000000-1-1-1-1-1-10000
χ202222222222222222222-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-10000-2-2-2-200-2-2000011000000001111110000
χ212222222-2-2222-222-2-2-2-22-1-1-1-1-1-1-1-1222-2-2-2-2-122-1-1-1-1-1-1-11111-2-21111111122-2-200002-200000000-1-1-1-111110000000000
χ222222222-2-2222-222-2-2-2-22-1-1-1-1-1-1-1-1222-2-2-2-2-122-1-1-1-1-1-1-11111-2-211111111-2-2220000-22000000001111-1-1-1-10000000000
χ232222222-2-2222-222-2-2-2-2-122222222-1-1-11111-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111110000222200-2-200001100000000-1-111-1-10000
χ242222222-2-2222-222-2-2-2-2-122222222-1-1-11111-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111110000-2-2-2-200220000-1-10000000011-1-1110000
χ252222-2-2222222-2-2-222-2-22-1-1-11111-12222222-1-2-2-1-11111-1-1-111-2-2-1-1-1-1111122220000-2-200000000-1-111-1-1110000000000
χ262222-2-2222222-2-2-222-2-22-1-1-11111-12222222-1-2-2-1-11111-1-1-111-2-2-1-1-1-11111-2-2-2-20000220000000011-1-111-1-10000000000
χ272222-2-2222222-2-2-222-2-2-1222-2-2-2-22-1-1-1-1-1-1-1-111-1-11111-122-2-211-1-1-1-11111000022-2-200-2200001100000000-1-1-1-1110000
χ282222-2-2222222-2-2-222-2-2-1222-2-2-2-22-1-1-1-1-1-1-1-111-1-11111-122-2-211-1-1-1-111110000-2-222002-20000-1-1000000001111-1-10000
χ292222-2-22-2-22222-2-2-2-2222-1-1-11111-1222-2-2-2-2-1-2-2-1-11111-111-1-1221111-1-1-1-122-2-20000-2200000000-1-11111-1-10000000000
χ302222-2-22-2-22222-2-2-2-2222-1-1-11111-1222-2-2-2-2-1-2-2-1-11111-111-1-1221111-1-1-1-1-2-22200002-20000000011-1-1-1-1110000000000
χ312222-2-22-2-22222-2-2-2-222-1222-2-2-2-22-1-1-11111-111-1-11111-1-2-222-1-11111-1-1-1-1000022-2-2002-20000-1-100000000-1-111110000
χ322222-2-22-2-22222-2-2-2-222-1222-2-2-2-22-1-1-11111-111-1-11111-1-2-222-1-11111-1-1-1-10000-2-22200-220000110000000011-1-1-1-10000
χ3322-2-22-22002-2-202-20000222-222-2-2-22-2-2000022-22-222-2-2-20000000000000000002i−2i2i−2i0000000000000000002i−2i002i−2i0000
χ3422-2-22-22002-2-202-20000222-222-2-2-22-2-2000022-22-222-2-2-2000000000000000000−2i2i−2i2i000000000000000000−2i2i00−2i2i0000
χ3522-2-22-22002-2-202-20000-122-222-2-2-2-11133−3−3-1-11-11-1-111100003−333−3−333−3−300002i−2i2i−2i00000000−i3i300000000−ii−i3i3−ii0000
χ3622-2-22-22002-2-202-20000-122-222-2-2-2-11133−3−3-1-11-11-1-111100003−333−3−333−3−30000−2i2i−2i2i00000000i3−i300000000i−ii3−i3i−i0000
χ3722-2-22-22002-2-202-20000-122-222-2-2-2-111−3−333-1-11-11-1-11110000−33−3−333−3−33300002i−2i2i−2i00000000i3−i300000000−iii3−i3−ii0000
χ3822-2-22-22002-2-202-20000-122-222-2-2-2-111−3−333-1-11-11-1-11110000−33−3−333−3−3330000−2i2i−2i2i00000000−i3i300000000i−i−i3i3i−i0000
χ3922-2-2-222002-2-20-220000222-2-2-222-22-2-200002-222-2-2-222-20000000000000000002i−2i−2i2i0000000000000000002i−2i00−2i2i0000
χ4022-2-2-222002-2-20-220000222-2-2-222-22-2-200002-222-2-2-222-2000000000000000000−2i2i2i−2i000000000000000000−2i2i002i−2i0000
χ4122-2-2-222002-2-20-220000-122-2-2-222-2-11133−3−3-11-1-1111-1-110000−3333−3−3−3−33300002i−2i−2i2i00000000i3−i300000000−ii−i3i3i−i0000
χ4222-2-2-222002-2-20-220000-122-2-2-222-2-11133−3−3-11-1-1111-1-110000−3333−3−3−3−3330000−2i2i2i−2i00000000−i3i300000000i−ii3−i3−ii0000
χ4322-2-2-222002-2-20-220000-122-2-2-222-2-111−3−333-11-1-1111-1-1100003−3−3−33333−3−300002i−2i−2i2i00000000−i3i300000000−iii3−i3i−i0000
χ4422-2-2-222002-2-20-220000-122-2-2-222-2-111−3−333-11-1-1111-1-1100003−3−3−33333−3−30000−2i2i2i−2i00000000i3−i300000000i−i−i3i3−ii0000
χ452-2-220022-2-2-220002-20022-2-200002-2-222-22-2200-2-2000022-200002-22-200002-22-2000000000000002-2002-2000000000000
χ462-2-220022-2-2-220002-20022-2-200002-2-222-22-2200-2-2000022-200002-22-20000-22-2200000000000000-2200-22000000000000
χ472-2-220022-2-2-220002-2002-111−i3i3−i3i3-1-2-222-22-2-10011−i3i3−i3i3-1-11−i3i300-11-11−i3i3−i3i32-22-200000000000000-11−i3i3-11−i3i30000000000
χ482-2-220022-2-2-220002-2002-111−i3i3−i3i3-1-2-222-22-2-10011−i3i3−i3i3-1-11−i3i300-11-11−i3i3−i3i3-22-22000000000000001-1i3−i31-1i3−i30000000000
χ492-2-220022-2-2-220002-2002-111i3−i3i3−i3-1-2-222-22-2-10011i3−i3i3−i3-1-11i3−i300-11-11i3−i3i3−i32-22-200000000000000-11i3−i3-11i3−i30000000000
χ502-2-220022-2-2-220002-2002-111i3−i3i3−i3-1-2-222-22-2-10011i3−i3i3−i3-1-11i3−i300-11-11i3−i3i3−i3-22-22000000000000001-1−i3i31-1−i3i30000000000
χ512-2-22002-22-2-22000-220022-2-200002-2-22-22-22200-2-200002-220000-22-2200002-2-22000000000000002-200-22000000000000
χ522-2-22002-22-2-22000-220022-2-200002-2-22-22-22200-2-200002-220000-22-220000-222-200000000000000-22002-2000000000000
χ532-2-22002-22-2-22000-22002-111−i3i3−i3i3-1-2-22-22-22-10011−i3i3−i3i3-11-1i3−i3001-11-1i3−i3i3−i32-2-2200000000000000-11−i3i31-1i3−i30000000000
χ542-2-22002-22-2-22000-22002-111−i3i3−i3i3-1-2-22-22-22-10011−i3i3−i3i3-11-1i3−i3001-11-1i3−i3i3−i3-222-2000000000000001-1i3−i3-11−i3i30000000000
χ552-2-22002-22-2-22000-22002-111i3−i3i3−i3-1-2-22-22-22-10011i3−i3i3−i3-11-1−i3i3001-11-1−i3i3−i3i32-2-2200000000000000-11i3−i31-1−i3i30000000000
χ562-2-22002-22-2-22000-22002-111i3−i3i3−i3-1-2-22-22-22-10011i3−i3i3−i3-11-1−i3i3001-11-1−i3i3−i3i3-222-2000000000000001-1−i3i3-11i3−i30000000000
χ574444444444444444444-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-21-2-21111111-2-2-2-2-2-211111111000000000000000000000000000000000000
χ584444444-4-4444-444-4-4-4-4-2-2-2-2-2-2-2-2-2-2-2-222221-2-21111111222222-1-1-1-1-1-1-1-1000000000000000000000000000000000000
χ594444-4-4444444-4-4-444-4-4-2-2-2-22222-2-2-2-2-2-2-2-212211-1-1-1-11-2-222221111-1-1-1-1000000000000000000000000000000000000
χ604444-4-44-4-44444-4-4-4-444-2-2-2-22222-2-2-2-2222212211-1-1-1-1122-2-2-2-2-1-1-1-11111000000000000000000000000000000000000
χ6144-4-44-44004-4-404-400004-2-22-2-22224-4-40000-24-4-22-2-222200000000000000000000000000000000000000000000000000
χ6244-4-44-44004-4-404-40000-2-2-22-2-2222-2222323−23−231-221-111-1-1-1000023−23−3−333−3−333000000000000000000000000000000000000
χ6344-4-44-44004-4-404-40000-2-2-22-2-2222-222−23−2323231-221-111-1-1-10000−232333−3−333−3−3000000000000000000000000000000000000
χ6444-4-4-444004-4-40-4400004-2-2222-2-224-4-40000-2-44-2222-2-2200000000000000000000000000000000000000000000000000
χ6544-4-4-444004-4-40-440000-2-2-2222-2-22-2222323−23−2312-21-1-1-111-10000−2323−3−33333−3−3000000000000000000000000000000000000
χ6644-4-4-444004-4-40-440000-2-2-2222-2-22-222−23−23232312-21-1-1-111-1000023−2333−3−3−3−333000000000000000000000000000000000000
χ674-44-400400-44-4000000044-440000-4-44-40000400-440000-400000000000000000000000000000000000000000000000000
χ684-44-400400-44-400000004-22-2−2i32i32i3−2i32-44-40000-2002-2−2i32i32i3−2i3200000000000000000000000000000000000000000000000000
χ694-44-400400-44-400000004-22-22i3−2i3−2i32i32-44-40000-2002-22i3−2i3−2i32i3200000000000000000000000000000000000000000000000000
χ704-44-400400-44-40000000-24-440000-42-2223−23−2323-2002-20000200000023−23−23230000000000000000000000000000000000000000
χ714-44-400400-44-40000000-24-440000-42-22−232323−23-2002-200002000000−232323−230000000000000000000000000000000000000000
χ724-44-400400-44-40000000-2-22-2−2i32i32i3−2i322-2223−23−2323100-11i3−i3−i3i3-1000000−333−3−3i3i3i−3i000000000000000000000000000000000000
χ734-44-400400-44-40000000-2-22-2−2i32i32i3−2i322-22−232323−23100-11i3−i3−i3i3-10000003−3−333i−3i−3i3i000000000000000000000000000000000000
χ744-44-400400-44-40000000-2-22-22i3−2i3−2i32i322-2223−23−2323100-11−i3i3i3−i3-1000000−333−33i−3i−3i3i000000000000000000000000000000000000
χ754-44-400400-44-40000000-2-22-22i3−2i3−2i32i322-22−232323−23100-11−i3i3i3−i3-10000003−3−33−3i3i3i−3i000000000000000000000000000000000000
χ764-4-440044-4-4-440004-400-24-4-40000422-2-22-22-200220000-24-40000-22-220000000000000000000000000000000000000000
χ774-4-440044-4-4-440004-400-2-222−2i32i3−2i32i3-222-2-22-22100-1-1i3−i3i3−i31-22−2i32i3001-11-1i3−i3i3−i3000000000000000000000000000000000000
χ784-4-440044-4-4-440004-400-2-2222i3−2i32i3−2i3-222-2-22-22100-1-1−i3i3−i3i31-222i3−2i3001-11-1−i3i3−i3i3000000000000000000000000000000000000
χ794-4-44004-44-4-44000-4400-24-4-40000422-22-22-2-200220000-2-4400002-22-20000000000000000000000000000000000000000
χ804-4-44004-44-4-44000-4400-2-222−2i32i3−2i32i3-222-22-22-2100-1-1i3−i3i3−i312-22i3−2i300-11-11−i3i3−i3i3000000000000000000000000000000000000
χ814-4-44004-44-4-44000-4400-2-2222i3−2i32i3−2i3-222-22-22-2100-1-1−i3i3−i3i312-2−2i32i300-11-11i3−i3i3−i3000000000000000000000000000000000000
χ82666666-366-3-3-36-3-3-3-3-3-3000000000000000000000000000000000000000000000000000022220000000000000000-1-1-1-1
χ83666666-366-3-3-36-3-3-3-3-3-30000000000000000000000000000000000000000000000000000-2-2-2-200000000000000001111
χ84666666-3-6-6-3-3-3-6-3-3333300000000000000000000000000000000000000000000000000002-22-20000000000000000-11-11
χ85666666-3-6-6-3-3-3-6-3-333330000000000000000000000000000000000000000000000000000-22-2200000000000000001-11-1
χ866666-6-6-366-3-3-3-633-3-333000000000000000000000000000000000000000000000000000022-2-20000000000000000-1-111
χ876666-6-6-366-3-3-3-633-3-3330000000000000000000000000000000000000000000000000000-2-222000000000000000011-1-1
χ886666-6-6-3-6-6-3-3-363333-3-300000000000000000000000000000000000000000000000000002-2-220000000000000000-111-1
χ896666-6-6-3-6-6-3-3-363333-3-30000000000000000000000000000000000000000000000000000-222-200000000000000001-1-11
χ901212-12-1212-12-600-6660-6600000000000000000000000000000000000000000000000000000000000000000000000000000000
χ911212-12-12-1212-600-66606-600000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9212-1212-1200-6006-660000063−630000000000000000000000000000000000000000000000000000000000000000000000000000
χ9312-1212-1200-6006-6600000−63630000000000000000000000000000000000000000000000000000000000000000000000000000
χ9412-12-121200-612-1266-6000-66000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9512-12-121200-6-121266-60006-6000000000000000000000000000000000000000000000000000000000000000000000000000000

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