Finite Group Databasebeta

← Group #13150719

Character table — Group #13150719

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95
size11112222222244444446666666666666666121212121212121212121212121212121212121212121212181818181818181836363636363636363636363636363636363636363636363672727272
order12222234466646612121212336666666666121212123666666666121212121212121212121212121222444444224444446666661212121212121212121212121212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111-1-1-1-11-11-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111-1-1-1-11111-11-11-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1
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
χ51111111-1-1111-111-1-1-1-1111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111-1-1-11-11-1-1-1111111-1-111-1-1-1-11-11-1
χ61111111-1-1111-111-1-1-1-1111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-11-11-11111111-1-111-1-1-1-1-1-1-11-11
χ71111111-1-1111-111-1-1-1-1111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11-1-11-11-1-1-1-1-1-111-1-1111111-11-11
χ81111111-1-1111-111-1-1-1-1111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-11111-11-111-1-1-1-1-1-111-1-111111-11-1
χ91111-1-1111111-1-1-111-1-1111-1-1-1-11111111111-1-111-1-1-1-1111-1-1-1-11111-1-1-1-1111111-1-1-1-1-111-1-11-1-111-1-11111-1-111-1-11-1-11
χ101111-1-1111111-1-1-111-1-1111-1-1-1-11111111111-1-111-1-1-1-1111-1-1-1-11111-1-1-1-11111-1-111-11-1-1-111-11111-1-1-1-1-1-11111-1-1-111-1
χ111111-1-1111111-1-1-111-1-1111-1-1-1-11111111111-1-111-1-1-1-1111-1-1-1-11111-1-1-1-1-1-1-1-111-1-11-111-111-1-1-1-1-1111111-1-1-1-111-111-1
χ121111-1-1111111-1-1-111-1-1111-1-1-1-11111111111-1-111-1-1-1-1111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111-11-1-1111-1-111-1-1-1-111-1-1111-1-11
χ131111-1-11-1-11111-1-1-1-111111-1-1-1-111111-1-1-1-11-1-111-1-1-1-11-1-11111-1-1-1-1111111-1-111-1-1-111-111-1-11111-1-111-1-1-1-1-1-11111-1-1
χ141111-1-11-1-11111-1-1-1-111111-1-1-1-111111-1-1-1-11-1-111-1-1-1-11-1-11111-1-1-1-1111111-1-1-1-111-1-111-1-111-1-111-1-1-1-11111-1-111-1-111
χ151111-1-11-1-11111-1-1-1-111111-1-1-1-111111-1-1-1-11-1-111-1-1-1-11-1-11111-1-1-1-11111-1-11111-1-111-1-1-1-11111-1-11111-1-1-1-111-1-1-1-111
χ161111-1-11-1-11111-1-1-1-111111-1-1-1-111111-1-1-1-11-1-111-1-1-1-11-1-11111-1-1-1-11111-1-111-1-1111-1-1111-1-1-1-1-1-111-1-1111111-1-111-1-1
χ1722222222222222222222-1-1-1-1-1-1-1222-12222-122-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1222200002020000000-1-1-1-1000000-1-1-1-10000
χ1822222222222222222222-1-1-1-1-1-1-1222-12222-122-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-20000-20-20000000111100000011110000
χ192222222222222222222-12222222-1-1-12-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-10000222202020000-1-10000-1-1-1-1-1-100000000
χ202222222222222222222-12222222-1-1-12-1-1-1-1-1-1-1-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-10000-2-2-2-20-20-2000011000011111100000000
χ212222222-2-2222-222-2-2-2-22-1-1-1-1-1-1-1222-1-2-2-2-2-122-1-1-1-1-1-1-11111-2-21111111122-2-2000020-20000000-1-1-1-100000011110000
χ222222222-2-2222-222-2-2-2-22-1-1-1-1-1-1-1222-1-2-2-2-2-122-1-1-1-1-1-1-11111-2-211111111-2-2220000-20200000001111000000-1-1-1-10000
χ232222222-2-2222-222-2-2-2-2-12222222-1-1-121111-1-1-1-1-1-1-1-1-1-1-2-2-2-21111111111000022220-20-20000110000-1-111-1-100000000
χ242222222-2-2222-222-2-2-2-2-12222222-1-1-121111-1-1-1-1-1-1-1-1-1-1-2-2-2-211111111110000-2-2-2-202020000-1-1000011-1-11100000000
χ252222-2-2222222-2-2-222-2-22-1-11111-1222-12222-1-2-2-1-11111-1-1-111-2-2-1-1-1-1111122220000-20-20000000-1-111000000-1-1110000
χ262222-2-2222222-2-2-222-2-22-1-11111-1222-12222-1-2-2-1-11111-1-1-111-2-2-1-1-1-11111-2-2-2-20000202000000011-1-100000011-1-10000
χ272222-2-2222222-2-2-222-2-2-122-2-2-2-22-1-1-12-1-1-1-1-111-1-11111-122-2-211-1-1-1-11111000022-2-20-2020000110000-1-1-1-11100000000
χ282222-2-2222222-2-2-222-2-2-122-2-2-2-22-1-1-12-1-1-1-1-111-1-11111-122-2-211-1-1-1-111110000-2-222020-20000-1-100001111-1-100000000
χ292222-2-22-2-22222-2-2-2-2222-1-11111-1222-1-2-2-2-2-1-2-2-1-11111-111-1-1221111-1-1-1-122-2-20000-2020000000-1-11100000011-1-10000
χ302222-2-22-2-22222-2-2-2-2222-1-11111-1222-1-2-2-2-2-1-2-2-1-11111-111-1-1221111-1-1-1-1-2-222000020-2000000011-1-1000000-1-1110000
χ312222-2-22-2-22222-2-2-2-222-122-2-2-2-22-1-1-121111-111-1-11111-1-2-222-1-11111-1-1-1-1000022-2-2020-20000-1-10000-1-1111100000000
χ322222-2-22-2-22222-2-2-2-222-122-2-2-2-22-1-1-121111-111-1-11111-1-2-222-1-11111-1-1-1-10000-2-2220-202000011000011-1-1-1-100000000
χ3322-2-20022i−2i-22-20002i−2i002220000-22-2-2-22i2i−2i−2i2002-20000-22i−2i00002i2i−2i−2i00002-22i−2i000000000000002-2000000002i−2i000000
χ3422-2-20022i−2i-22-20002i−2i002220000-22-2-2-22i2i−2i−2i2002-20000-22i−2i00002i2i−2i−2i0000-22−2i2i00000000000000-2200000000−2i2i000000
χ3522-2-20022i−2i-22-20002i−2i002-1-1−i3−i3i3i312-2-212i2i−2i−2i-100-11−i3−i3i3i31−ii3−300−i−iii33−3−32-22i−2i00000000000000-11−i3i3000000−ii3−30000
χ3622-2-20022i−2i-22-20002i−2i002-1-1−i3−i3i3i312-2-212i2i−2i−2i-100-11−i3−i3i3i31−ii3−300−i−iii33−3−3-22−2i2i000000000000001-1i3−i3000000i−i−330000
χ3722-2-20022i−2i-22-20002i−2i002-1-1i3i3−i3−i312-2-212i2i−2i−2i-100-11i3i3−i3−i31−ii−3300−i−iii−3−3332-22i−2i00000000000000-11i3−i3000000−ii−330000
χ3822-2-20022i−2i-22-20002i−2i002-1-1i3i3−i3−i312-2-212i2i−2i−2i-100-11i3i3−i3−i31−ii−3300−i−iii−3−333-22−2i2i000000000000001-1−i3i3000000i−i3−30000
χ3922-2-2002−2i2i-22-2000−2i2i002220000-22-2-2-2−2i−2i2i2i2002-20000-2−2i2i0000−2i−2i2i2i00002-2−2i2i000000000000002-200000000−2i2i000000
χ4022-2-2002−2i2i-22-2000−2i2i002220000-22-2-2-2−2i−2i2i2i2002-20000-2−2i2i0000−2i−2i2i2i0000-222i−2i00000000000000-22000000002i−2i000000
χ4122-2-2002−2i2i-22-2000−2i2i002-1-1−i3−i3i3i312-2-21−2i−2i2i2i-100-11−i3−i3i3i31i−i−3300ii−i−i−3−3332-2−2i2i00000000000000-11−i3i3000000i−i−330000
χ4222-2-2002−2i2i-22-2000−2i2i002-1-1−i3−i3i3i312-2-21−2i−2i2i2i-100-11−i3−i3i3i31i−i−3300ii−i−i−3−333-222i−2i000000000000001-1i3−i3000000−ii3−30000
χ4322-2-2002−2i2i-22-2000−2i2i002-1-1i3i3−i3−i312-2-21−2i−2i2i2i-100-11i3i3−i3−i31i−i3−300ii−i−i33−3−32-2−2i2i00000000000000-11i3−i3000000i−i3−30000
χ4422-2-2002−2i2i-22-2000−2i2i002-1-1i3i3−i3−i312-2-21−2i−2i2i2i-100-11i3i3−i3−i31i−i3−300ii−i−i33−3−3-222i−2i000000000000001-1−i3i3000000−ii−330000
χ452-22-22-22002-2-202-2000022-22-22-2-2-22-22000022-2-222-22-2-20000000000000000002i−2i2i−2i000000000000002i−2i002i−2i00000000
χ462-22-22-22002-2-202-2000022-22-22-2-2-22-22000022-2-222-22-2-2000000000000000000−2i2i−2i2i00000000000000−2i2i00−2i2i00000000
χ472-22-22-22002-2-202-20000-12-22-22-2-21-1123−33−3-1-111-1-11-11100003−33−33−33−33−300002i−2i2i−2i00000000−i3i30000−ii−i3i3−ii00000000
χ482-22-22-22002-2-202-20000-12-22-22-2-21-1123−33−3-1-111-1-11-11100003−33−33−33−33−30000−2i2i−2i2i00000000i3−i30000i−ii3−i3i−i00000000
χ492-22-22-22002-2-202-20000-12-22-22-2-21-112−33−33-1-111-1-11-1110000−33−33−33−33−3300002i−2i2i−2i00000000i3−i30000−iii3−i3−ii00000000
χ502-22-22-22002-2-202-20000-12-22-22-2-21-112−33−33-1-111-1-11-1110000−33−33−33−33−330000−2i2i−2i2i00000000−i3i30000i−i−i3i3i−i00000000
χ512-22-2-222002-2-20-22000022-2-22-22-2-22-2200002-22-22-22-22-20000000000000000002i−2i−2i2i000000000000002i−2i00−2i2i00000000
χ522-22-2-222002-2-20-22000022-2-22-22-2-22-2200002-22-22-22-22-2000000000000000000−2i2i2i−2i00000000000000−2i2i002i−2i00000000
χ532-22-2-222002-2-20-220000-12-2-22-22-21-1123−33−3-11-11-11-11-110000−333−33−3−33−3300002i−2i−2i2i00000000i3−i30000−ii−i3i3i−i00000000
χ542-22-2-222002-2-20-220000-12-2-22-22-21-1123−33−3-11-11-11-11-110000−333−33−3−33−330000−2i2i2i−2i00000000−i3i30000i−ii3−i3−ii00000000
χ552-22-2-222002-2-20-220000-12-2-22-22-21-112−33−33-11-11-11-11-1100003−3−33−333−33−300002i−2i−2i2i00000000−i3i30000−iii3−i3i−i00000000
χ562-22-2-222002-2-20-220000-12-2-22-22-21-112−33−33-11-11-11-11-1100003−3−33−333−33−30000−2i2i2i−2i00000000i3−i30000i−i−i3i3−ii00000000
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
χ594444-4-4444444-4-4-444-4-4-2-2-22222-2-2-2-2-2-2-2-2-212211-1-1-1-11-2-222221111-1-1-1-1000000000000000000000000000000000000
χ604444-4-44-4-44444-4-4-4-444-2-2-22222-2-2-2-2-2222212211-1-1-1-1122-2-2-2-2-1-1-1-11111000000000000000000000000000000000000
χ6144-4-40044i−4i-44-40004i−4i00-2440000-4-222-4−2i−2i2i2i-200-22000024i−4i0000−2i−2i2i2i0000000000000000000000000000000000000000
χ6244-4-40044i−4i-44-40004i−4i00-2-2-2−2i3−2i32i32i32-2222−2i−2i2i2i1001-1i3i3−i3−i3-1−2i2i23−2300ii−i−i−3−333000000000000000000000000000000000000
χ6344-4-40044i−4i-44-40004i−4i00-2-2-22i32i3−2i3−2i32-2222−2i−2i2i2i1001-1−i3−i3i3i3-1−2i2i−232300ii−i−i33−3−3000000000000000000000000000000000000
χ6444-4-4004−4i4i-44-4000−4i4i00-2440000-4-222-42i2i−2i−2i-200-2200002−4i4i00002i2i−2i−2i0000000000000000000000000000000000000000
χ6544-4-4004−4i4i-44-4000−4i4i00-2-2-2−2i3−2i32i32i32-22222i2i−2i−2i1001-1i3i3−i3−i3-12i−2i−232300−i−iii33−3−3000000000000000000000000000000000000
χ6644-4-4004−4i4i-44-4000−4i4i00-2-2-22i32i3−2i3−2i32-22222i2i−2i−2i1001-1−i3−i3i3i3-12i−2i23−2300−i−iii−3−333000000000000000000000000000000000000
χ674-44-44-44004-4-404-400004-22-22-222-44-4-20000-24-42-2-22-22200000000000000000000000000000000000000000000000000
χ684-44-44-44004-4-404-40000-2-22-22-2222-22-223−2323−231-22-111-11-1-1000023−23−33−33−33−33000000000000000000000000000000000000
χ694-44-44-44004-4-404-40000-2-22-22-2222-22-2−2323−23231-22-111-11-1-10000−23233−33−33−33−3000000000000000000000000000000000000
χ704-44-4-444004-4-40-4400004-222-22-22-44-4-20000-2-442-22-22-2200000000000000000000000000000000000000000000000000
χ714-44-4-444004-4-40-440000-2-222-22-222-22-223−2323−2312-2-11-11-11-10000−2323−33−333−33−3000000000000000000000000000000000000
χ724-44-4-444004-4-40-440000-2-222-22-222-22-2−2323−232312-2-11-11-11-1000023−233−33−3−33−33000000000000000000000000000000000000
χ734-4-4400400-4-44000000044-400004-4-44-40000400-4-40000400000000000000000000000000000000000000000000000000
χ744-4-4400400-4-4400000004-22−2i32i32i3−2i3-2-4-4420000-20022−2i32i32i3−2i3-200000000000000000000000000000000000000000000000000
χ754-4-4400400-4-4400000004-222i3−2i3−2i32i3-2-4-4420000-200222i3−2i3−2i32i3-200000000000000000000000000000000000000000000000000
χ764-4-4400400-4-440000000-24-40000422-2-4−2i32i32i3−2i3-200220000-2000000−2i32i32i3−2i30000000000000000000000000000000000000000
χ774-4-4400400-4-440000000-24-40000422-2-42i3−2i3−2i32i3-200220000-20000002i3−2i3−2i32i30000000000000000000000000000000000000000
χ784-4-4400400-4-440000000-2-22−2i32i32i3−2i3-222-22−2i32i32i3−2i3100-1-1i3−i3−i3i31000000i3−i3−i3i3-333-3000000000000000000000000000000000000
χ794-4-4400400-4-440000000-2-22−2i32i32i3−2i3-222-222i3−2i3−2i32i3100-1-1i3−i3−i3i31000000−i3i3i3−i33-3-33000000000000000000000000000000000000
χ804-4-4400400-4-440000000-2-222i3−2i3−2i32i3-222-22−2i32i32i3−2i3100-1-1−i3i3i3−i31000000i3−i3−i3i33-3-33000000000000000000000000000000000000
χ814-4-4400400-4-440000000-2-222i3−2i3−2i32i3-222-222i3−2i3−2i32i3100-1-1−i3i3i3−i31000000−i3i3i3−i3-333-3000000000000000000000000000000000000
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
χ866666-6-6-366-3-3-3-633-3-33300000000000000000000000000000000000000000000000000002-2-220000000000000000-111-1
χ876666-6-6-366-3-3-3-633-3-3330000000000000000000000000000000000000000000000000000-222-200000000000000001-1-11
χ886666-6-6-3-6-6-3-3-363333-3-3000000000000000000000000000000000000000000000000000022-2-20000000000000000-1-111
χ896666-6-6-3-6-6-3-3-363333-3-30000000000000000000000000000000000000000000000000000-2-222000000000000000011-1-1
χ901212-12-1200-612i−12i6-66000−6i6i000000000000000000000000000000000000000000000000000000000000000000000000000000
χ911212-12-1200-6−12i12i6-660006i−6i000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9212-1212-1212-12-600-6660-6600000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9312-1212-12-1212-600-66606-600000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9412-12-121200-60066-600000−6i36i30000000000000000000000000000000000000000000000000000000000000000000000000000
χ9512-12-121200-60066-6000006i3−6i30000000000000000000000000000000000000000000000000000000000000000000000000000

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