Finite Group Databasebeta

← Group #13150703

Character table — Group #13150703

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95
size1111222222222222444446666666666661212121212121212121212121212121212121212121212121212181818181818181836363636363636363636363636363636363636363636363672727272
order1222223446666666412121212336666661212121236666666666612121212121212121212121212124444444422244444661212121212121212121212121212661212
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111-1-1-1-11-1-11-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-111-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111-1-11111111-1-1-1-1-111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-11-1-11-11-1-1-11111-1-1-1-111-1-1111-11-1
χ61111111-1-11111111-1-1-1-1-111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-11-1-11-11-1-1-1-1-1-1111111-1-111-11-11
χ71111111-1-11111111-1-1-1-1-111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11-111-111-1111111-1-1-1-1-1-111-1-1-11-11
χ81111111-1-11111111-1-1-1-1-111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-1111-1-1-1-11111-1-111-1-11-11-1
χ91111-1-111111-1-1-1-11-111-1-11111111111111-1-1-1-111-1-1-1-1111-1-1-1-11111-1-1-1-111-1-11111-1-1-1111-1-1-1-111-1-111-1-11111-1-1-1-111
χ101111-1-111111-1-1-1-11-111-1-11111111111111-1-1-1-111-1-1-1-1111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1111-1-111-1-1-1-111-1-1111111-1-111-1-1
χ111111-1-111111-1-1-1-11-111-1-11111111111111-1-1-1-111-1-1-1-1111-1-1-1-11111-1-1-1-1-1-1111111111-1-1-1-1-11111-1-111-1-1-1-1-1-11111-1-1
χ121111-1-111111-1-1-1-11-111-1-11111111111111-1-1-1-111-1-1-1-1111-1-1-1-11111-1-1-1-1-1-111-1-1-1-11-1-1-1111111-1-111-1-111-1-1-1-111-1-111
χ131111-1-11-1-111-1-1-1-111-1-11111111111-1-1-1-11-1-1-1-111-1-1-1-11-1-11111-1-1-1-1111111-1-111-1-11-11-11-1-111111-1-1-1-11111-1-1-1-1-111-1
χ141111-1-11-1-111-1-1-1-111-1-11111111111-1-1-1-11-1-1-1-111-1-1-1-11-1-11111-1-1-1-1111111-1-1-1-11111-1-1-111-111-1-11111-1-111-1-1-1-11-1-11
χ151111-1-11-1-111-1-1-1-111-1-11111111111-1-1-1-11-1-1-1-111-1-1-1-11-1-11111-1-1-1-11111-1-11111-1-1-11-11-11-11-1-111-1-1-1-111-1-111111-1-11
χ161111-1-11-1-111-1-1-1-111-1-11111111111-1-1-1-11-1-1-1-111-1-1-1-11-1-11111-1-1-1-11111-1-111-1-111-1-1111-11-1-1-1-1-11111-1-1-1-11111-111-1
χ172222222222222222222222-1-1-1222-12222-122-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-100000000022022000000000000000000-1-1-1-1
χ182222222222222222222222-1-1-1222-12222-122-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1000000000-2-20-2-20000000000000000001111
χ19222222222222222222222-1222-1-1-12-1-1-1-1-1-1-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-12222000020020000-1-100000000-1-1-1-1-1-10000
χ20222222222222222222222-1222-1-1-12-1-1-1-1-1-1-122-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-2-2-2-20000-200-2000011000000001111110000
χ212222222-2-22222222-2-2-2-2-22-1-1-1222-1-2-2-2-2-122-1-1-1-1-1-1-1-1-11111-2-2111111110000000002-202-2000000000000000000-11-11
χ222222222-2-22222222-2-2-2-2-22-1-1-1222-1-2-2-2-2-122-1-1-1-1-1-1-1-1-11111-2-211111111000000000-220-220000000000000000001-11-1
χ232222222-2-22222222-2-2-2-2-2-1222-1-1-121111-1-1-122-1-1-1-1-1-1-1-2-2-2-2111111111122220000-200-200001100000000-1-111-1-10000
χ242222222-2-22222222-2-2-2-2-2-1222-1-1-121111-1-1-122-1-1-1-1-1-1-1-2-2-2-21111111111-2-2-2-2000020020000-1-10000000011-1-1110000
χ252222-2-222222-2-2-2-22-222-2-22-1-1-1222-12222-1-2-211-1-11111-1-1-111-2-2-1-1-1-11111000000000220-2-2000000000000000000-1-111
χ262222-2-222222-2-2-2-22-222-2-22-1-1-1222-12222-1-2-211-1-11111-1-1-111-2-2-1-1-1-11111000000000-2-202200000000000000000011-1-1
χ272222-2-222222-2-2-2-22-222-2-2-1222-1-1-12-1-1-1-1-111-2-2-1-11111-122-2-211-1-1-1-1111122-2-20000-200200001100000000-1-1-1-1110000
χ282222-2-222222-2-2-2-22-222-2-2-1222-1-1-12-1-1-1-1-111-2-2-1-11111-122-2-211-1-1-1-11111-2-2220000200-20000-1-1000000001111-1-10000
χ292222-2-22-2-222-2-2-2-222-2-2222-1-1-1222-1-2-2-2-2-1-2-211-1-11111-111-1-1221111-1-1-1-10000000002-20-22000000000000000000-111-1
χ302222-2-22-2-222-2-2-2-222-2-2222-1-1-1222-1-2-2-2-2-1-2-211-1-11111-111-1-1221111-1-1-1-1000000000-2202-20000000000000000001-1-11
χ312222-2-22-2-222-2-2-2-222-2-222-1222-1-1-121111-111-2-2-1-11111-1-2-222-1-11111-1-1-1-122-2-20000200-20000-1-100000000-1-111110000
χ322222-2-22-2-222-2-2-2-222-2-222-1222-1-1-121111-111-2-2-1-11111-1-2-222-1-11111-1-1-1-1-2-2220000-20020000110000000011-1-1-1-10000
χ332-22-22-22002-222-2-2-20000022-2-22-2-22000022-22-22-222-2-2-2000000000000002i−2i2i−2i00000000000000000000002i−2i002i−2i0000
χ342-22-22-22002-222-2-2-20000022-2-22-2-22000022-22-22-222-2-2-200000000000000−2i2i−2i2i0000000000000000000000−2i2i00−2i2i0000
χ352-22-22-22002-222-2-2-200000-12-2-2-111233−3−3-1-112-2-11-1-111100003−333−3−333−3−32i−2i2i−2i000000000000−i3i300000000−ii−i3i3−ii0000
χ362-22-22-22002-222-2-2-200000-12-2-2-111233−3−3-1-112-2-11-1-111100003−333−3−333−3−3−2i2i−2i2i000000000000i3−i300000000i−ii3−i3i−i0000
χ372-22-22-22002-222-2-2-200000-12-2-2-1112−3−333-1-112-2-11-1-11110000−33−3−333−3−3332i−2i2i−2i000000000000i3−i300000000−iii3−i3−ii0000
χ382-22-22-22002-222-2-2-200000-12-2-2-1112−3−333-1-112-2-11-1-11110000−33−3−333−3−333−2i2i−2i2i000000000000−i3i300000000i−i−i3i3i−i0000
χ392-22-2-222002-2-2-222-20000022-2-22-2-2200002-22-222-2-2-222-2000000000000002i−2i−2i2i00000000000000000000002i−2i00−2i2i0000
χ402-22-2-222002-2-2-222-20000022-2-22-2-2200002-22-222-2-2-222-200000000000000−2i2i2i−2i0000000000000000000000−2i2i002i−2i0000
χ412-22-2-222002-2-2-222-200000-12-2-2-111233−3−3-11-1-22-1111-1-110000−3333−3−3−3−3332i−2i−2i2i000000000000i3−i300000000−ii−i3i3i−i0000
χ422-22-2-222002-2-2-222-200000-12-2-2-111233−3−3-11-1-22-1111-1-110000−3333−3−3−3−333−2i2i2i−2i000000000000−i3i300000000i−ii3−i3−ii0000
χ432-22-2-222002-2-2-222-200000-12-2-2-1112−3−333-11-1-22-1111-1-1100003−3−3−33333−3−32i−2i−2i2i000000000000−i3i300000000−iii3−i3i−i0000
χ442-22-2-222002-2-2-222-200000-12-2-2-1112−3−333-11-1-22-1111-1-1100003−3−3−33333−3−3−2i2i2i−2i000000000000i3−i300000000i−i−i3i3−ii0000
χ452-2-220022-2-2-20000202-20022-22-2-22-22-22-220000-2-2000022-200002-22-2000000002-22-200000000002-2002-2000000000000
χ462-2-220022-2-2-20000202-20022-22-2-22-22-22-220000-2-2000022-200002-22-200000000-22-220000000000-2200-22000000000000
χ472-2-22002-22-2-2000020-220022-22-2-22-2-22-2220000-2-200002-220000-22-22000000002-2-2200000000002-200-22000000000000
χ482-2-22002-22-2-2000020-220022-22-2-22-2-22-2220000-2-200002-220000-22-2200000000-222-20000000000-22002-2000000000000
χ49444444444444444444444-2-2-2-2-2-2-2-2-2-2-2-21-2-2-2-21111111-2-2-2-2-2-211111111000000000000000000000000000000000000
χ504444444-4-44444444-4-4-4-4-4-2-2-2-2-2-2-2-222221-2-2-2-21111111222222-1-1-1-1-1-1-1-1000000000000000000000000000000000000
χ514444-4-444444-4-4-4-44-444-4-4-2-2-2-2-2-2-2-2-2-2-2-21222211-1-1-1-11-2-222221111-1-1-1-1000000000000000000000000000000000000
χ524444-4-44-4-444-4-4-4-444-4-444-2-2-2-2-2-2-2-222221222211-1-1-1-1122-2-2-2-2-1-1-1-11111000000000000000000000000000000000000
χ5344-4-400400-440000-400000444-4-44-4-4000040000-440000-400000000000000000000000000000000000000000000000000
χ5444-4-400400-440000-4000004-2-22-44-420000-200002-2000020023−2300000023−2323−23000000000000000000000000000000000000
χ5544-4-400400-440000-4000004-2-22-44-420000-200002-20000200−2323000000−2323−2323000000000000000000000000000000000000
χ5644-4-400400-440000-400000-244-42-22-423−23−2323-200002-20000200000023−23−23230000000000000000000000000000000000000000
χ5744-4-400400-440000-400000-244-42-22-4−232323−23-200002-200002000000−232323−230000000000000000000000000000000000000000
χ5844-4-400400-440000-400000-2-2-222-22223−23−232310000-113-33-3-10023−2300−333−3−33−33000000000000000000000000000000000000
χ5944-4-400400-440000-400000-2-2-222-22223−23−232310000-11-33-33-100−232300−333−33−33−3000000000000000000000000000000000000
χ6044-4-400400-440000-400000-2-2-222-222−232323−2310000-113-33-3-100−2323003−3−333−33−3000000000000000000000000000000000000
χ6144-4-400400-440000-400000-2-2-222-222−232323−2310000-11-33-33-10023−23003−3−33−33−33000000000000000000000000000000000000
χ624-44-44-44004-444-4-4-4000004-2224-4-4-20000-24-4-22-22-2-222200000000000000000000000000000000000000000000000000
χ634-44-44-44004-444-4-4-400000-2-222-222-22323−23−231-22-221-111-1-1-1000023−23−3−333−3−333000000000000000000000000000000000000
χ644-44-44-44004-444-4-4-400000-2-222-222-2−23−2323231-22-221-111-1-1-10000−232333−3−333−3−3000000000000000000000000000000000000
χ654-44-4-444004-4-4-444-4000004-2224-4-4-20000-2-442-2-2222-2-2200000000000000000000000000000000000000000000000000
χ664-44-4-444004-4-4-444-400000-2-222-222-22323−23−2312-22-21-1-1-111-10000−2323−3−33333−3−3000000000000000000000000000000000000
χ674-44-4-444004-4-4-444-400000-2-222-222-2−23−23232312-22-21-1-1-111-1000023−2333−3−3−3−333000000000000000000000000000000000000
χ684-4-440044-4-4-40000404-4004-22-2-4-4424-44-4-20000220000-2-220000-22-220000000000000000000000000000000000000000
χ694-4-440044-4-4-40000404-400-24-4422-2-4-22-22-20000220000-24-40000-22-220000000000000000000000000000000000000000
χ704-4-440044-4-4-40000404-400-2-22-222-22-22-2210000-1-13-3-331-2200001-11-1-333-3000000000000000000000000000000000000
χ714-4-440044-4-4-40000404-400-2-22-222-22-22-2210000-1-1-333-31-2200001-11-13-3-33000000000000000000000000000000000000
χ724-4-44004-44-4-4000040-44004-22-2-4-442-44-44-20000220000-22-200002-22-20000000000000000000000000000000000000000
χ734-4-44004-44-4-4000040-4400-24-4422-2-42-22-2-20000220000-2-4400002-22-20000000000000000000000000000000000000000
χ744-4-44004-44-4-4000040-4400-2-22-222-222-22-210000-1-13-3-3312-20000-11-113-3-33000000000000000000000000000000000000
χ754-4-44004-44-4-4000040-4400-2-22-222-222-22-210000-1-1-333-312-20000-11-11-333-3000000000000000000000000000000000000
χ76666666-366-3-3-3-3-3-3-36-3-3-3-300000000000000000000000000000000000000000022220000002200-1-1-1-1-1-1-1-10000000000
χ77666666-366-3-3-3-3-3-3-36-3-3-3-3000000000000000000000000000000000000000000-2-2-2-2000000-2-200111111110000000000
χ78666666-3-6-6-3-3-3-3-3-3-3-6333300000000000000000000000000000000000000000022-2-20000002-200-1-1-1-111110000000000
χ79666666-3-6-6-3-3-3-3-3-3-3-63333000000000000000000000000000000000000000000-2-222000000-22001111-1-1-1-10000000000
χ806666-6-6-366-3-33333-3-6-3-3330000000000000000000000000000000000000000002222000000-2-200-1-111-1-1110000000000
χ816666-6-6-366-3-33333-3-6-3-333000000000000000000000000000000000000000000-2-2-2-2000000220011-1-111-1-10000000000
χ826666-6-6-3-6-6-3-33333-3633-3-300000000000000000000000000000000000000000022-2-2000000-2200-1-11111-1-10000000000
χ836666-6-6-3-6-6-3-33333-3633-3-3000000000000000000000000000000000000000000-2-2220000002-20011-1-1-1-1110000000000
χ846-6-6600-36-633−3i33i3−3i33i3-30-33−3i33i30000000000000000000000000000000000000000002-22-20000000000-11−i3i3-11−i3i30000000000
χ856-6-6600-36-633−3i33i3−3i33i3-30-33−3i33i3000000000000000000000000000000000000000000-22-2200000000001-1i3−i31-1i3−i30000000000
χ866-6-6600-36-6333i3−3i33i3−3i3-30-333i3−3i30000000000000000000000000000000000000000002-22-20000000000-11i3−i3-11i3−i30000000000
χ876-6-6600-36-6333i3−3i33i3−3i3-30-333i3−3i3000000000000000000000000000000000000000000-22-2200000000001-1−i3i31-1−i3i30000000000
χ886-6-6600-3-6633−3i33i3−3i33i3-303-33i3−3i30000000000000000000000000000000000000000002-2-220000000000-11−i3i31-1i3−i30000000000
χ896-6-6600-3-6633−3i33i3−3i33i3-303-33i3−3i3000000000000000000000000000000000000000000-222-200000000001-1i3−i3-11−i3i30000000000
χ906-6-6600-3-66333i3−3i33i3−3i3-303-3−3i33i30000000000000000000000000000000000000000002-2-220000000000-11i3−i31-1−i3i30000000000
χ916-6-6600-3-66333i3−3i33i3−3i3-303-3−3i33i3000000000000000000000000000000000000000000-222-200000000001-1−i3i3-11i3−i30000000000
χ921212-12-1200-6006-6−6i36i36i3−6i360000000000000000000000000000000000000000000000000000000000000000000000000000000
χ931212-12-1200-6006-66i3−6i3−6i36i360000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9412-1212-1212-12-600-66-6-66660000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9512-1212-12-1212-600-6666-6-660000000000000000000000000000000000000000000000000000000000000000000000000000000

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