Finite Group Databasebeta

← Group #13165408

Character table — Group #13165408

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111222244444444666666888888889999121212121212121212121212121212121212181818181818181824242424242424242424242436363636363636363636363654547272108108
order12223666336666664444443366666622224412121212121212121212121212121212444466661212121212121212121212124444121212121212121244121244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-11111-1-1-1-1111111111111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1
χ311111111111111111111-1-111111111111111111111111111-1-1-1-1-1-1-1-11111-1-11111111111-1-111-1-1-1-11111-1-1-1-1-1-1
χ411111111111111111111-1-1111111111111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111-1-1-1-11111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1
χ61111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-111
χ71111111111111111-1-1-1-1-1-111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111
χ81111111111111111-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-1
χ91-11-111-1-111-111-1-1-1ii−i−i1-11111-1-1-1-11-1-11i−iii−i−iii−i−iii−i−i11-1-1ii−i−i1-1-111-1i−iii−i−iii−i−ii−i1-1ii−i−i11-1-11-1i−i1-1
χ101-11-111-1-111-111-1-1-1ii−i−i1-11111-1-1-1-11-1-11−iiii−i−i−i−iiiii−i−i11-1-1ii−i−i1-1-111-1−iiii−i−i−i−iii−ii-11ii−i−i-1-1111-1−ii-11
χ111-11-111-1-111-111-1-1-1ii−i−i-111111-1-1-1-11-1-11i−iii−i−iii−i−iii−i−i-1-111−i−iii1-1-11-11i−iii−i−iii−i−i−ii1-1−i−iii11-1-1-11−ii-11
χ121-11-111-1-111-111-1-1-1ii−i−i-111111-1-1-1-11-1-11−iiii−i−i−i−iiiii−i−i-1-111−i−iii1-1-11-11−iiii−i−i−i−iiii−i-11−i−iii-1-111-11i−i1-1
χ131-11-111-1-111-111-1-1-1−i−iii1-11111-1-1-1-11-1-11i−i−i−iiiii−i−i−i−iii11-1-1−i−iii1-1-111-1i−i−i−iiiii−i−ii−i-11−i−iii-1-1111-1i−i-11
χ141-11-111-1-111-111-1-1-1−i−iii1-11111-1-1-1-11-1-11−ii−i−iii−i−iii−i−iii11-1-1−i−iii1-1-111-1−ii−i−iii−i−iii−ii1-1−i−iii11-1-11-1−ii1-1
χ151-11-111-1-111-111-1-1-1−i−iii-111111-1-1-1-11-1-11i−i−i−iiiii−i−i−i−iii-1-111ii−i−i1-1-11-11i−i−i−iiiii−i−i−ii-11ii−i−i-1-111-11−ii1-1
χ161-11-111-1-111-111-1-1-1−i−iii-111111-1-1-1-11-1-11−ii−i−iii−i−iii−i−iii-1-111ii−i−i1-1-11-11−ii−i−iii−i−iiii−i1-1ii−i−i11-1-1-11i−i-11
χ17222222222222222200002222222222-2-2-2-20000000000000022220000-2-2-2-2220000000000000000000000-2-20000
χ1822222222222222220000-2-222222222-2-2-2-200000000000000-2-2-2-20000-2-2-2-2-2-20000000000000000000000220000
χ192222-1-1-1-122222222222200-1-1-1-1-1-1-1-1222222-1-1-1-1-1-1-1-1222200000000-1-1-1-10022-1-1-1-1-1-1-1-100220000-1-1-1-1000000
χ202222-1-1-1-122222222222200-1-1-1-1-1-1-1-12222-2-2-1-1-1-11111222200000000-1-1-1-100-2-2-1-1-1-1111100-2-200001111000000
χ212222-1-1-1-122222222-2-2-2-200-1-1-1-1-1-1-1-12222221111-1-1-1-1-2-2-2-200000000-1-1-1-100221111-1-1-1-100-2-200001111000000
χ222222-1-1-1-122222222-2-2-2-200-1-1-1-1-1-1-1-12222-2-211111111-2-2-2-200000000-1-1-1-100-2-21111111100220000-1-1-1-1000000
χ2322-2-22-22-2222-2-2-22-200000022-2-222-2-222-2-20000000000000000002-22-222-2-200000000000000002-22-20000000000
χ2422-2-22-22-2222-2-2-22-200000022-2-222-2-222-2-2000000000000000000-22-2222-2-20000000000000000-22-220000000000
χ2522-2-22-22-2222-2-2-22-22i−2i2i−2i0022-2-222-2-2-2-222002i−2i2i−2i00002i−2i2i−2i00000000-2-22200002i−2i2i−2i0000000000000000000000
χ2622-2-22-22-2222-2-2-22-2−2i2i−2i2i0022-2-222-2-2-2-22200−2i2i−2i2i0000−2i2i−2i2i00000000-2-2220000−2i2i−2i2i0000000000000000000000
χ2722-2-2-11-11222-2-2-22-22i−2i2i−2i00-1-111-1-111-2-22200−ii−ii3−33−32i−2i2i−2i0000000011-1-10000−ii−ii3−33−300000000−i3i3−i3i3000000
χ2822-2-2-11-11222-2-2-22-22i−2i2i−2i00-1-111-1-111-2-22200−ii−ii−33−332i−2i2i−2i0000000011-1-10000−ii−ii−33−3300000000i3−i3i3−i3000000
χ2922-2-2-11-11222-2-2-22-2−2i2i−2i2i00-1-111-1-111-2-22200i−ii−i3−33−3−2i2i−2i2i0000000011-1-10000i−ii−i3−33−300000000i3−i3i3−i3000000
χ3022-2-2-11-11222-2-2-22-2−2i2i−2i2i00-1-111-1-111-2-22200i−ii−i−33−33−2i2i−2i2i0000000011-1-10000i−ii−i−33−3300000000−i3i3−i3i3000000
χ312-22-222-2-222-222-2-2-200002-22222-2-2-2-2-222-20000000000000022-2-20000-222-22-20000000000000000000000-220000
χ322-22-222-2-222-222-2-2-20000-222222-2-2-2-2-222-200000000000000-2-2220000-222-2-2200000000000000000000002-20000
χ332-22-2-1-11122-222-2-2-22i2i−2i−2i00-1-1-1-111112-2-222i−2i−i−iii−i−iii2i2i−2i−2i00000000-111-1002i−2i−i−iii−i−iii002-20000-1-111000000
χ342-22-2-1-11122-222-2-2-22i2i−2i−2i00-1-1-1-111112-2-22−2i2i−i−iiiii−i−i2i2i−2i−2i00000000-111-100−2i2i−i−iiiii−i−i00-22000011-1-1000000
χ352-22-2-1-11122-222-2-2-2−2i−2i2i2i00-1-1-1-111112-2-222i−2iii−i−i−i−iii−2i−2i2i2i00000000-111-1002i−2iii−i−i−i−iii00-22000011-1-1000000
χ362-22-2-1-11122-222-2-2-2−2i−2i2i2i00-1-1-1-111112-2-22−2i2iii−i−iii−i−i−2i−2i2i2i00000000-111-100−2i2iii−i−iii−i−i002-20000-1-111000000
χ372-2-222-2-2222-2-2-22-2200000022-2-2-2-2222-22-20000000000000000002i−2i−2i2i2-22-200000000000000002i−2i−2i2i0000000000
χ382-2-222-2-2222-2-2-22-2200000022-2-2-2-2222-22-2000000000000000000−2i2i2i−2i2-22-20000000000000000−2i2i2i−2i0000000000
χ392-2-222-2-2222-2-2-22-222-2-220022-2-2-2-222-22-22002-2-2200002-2-2200000000-22-2200002-2-220000000000000000000000
χ402-2-222-2-2222-2-2-22-22-222-20022-2-2-2-222-22-2200-222-20000-222-200000000-22-220000-222-20000000000000000000000
χ412-2-22-111-122-2-2-22-222-2-2200-1-11111-1-1-22-2200-111-1−i3i3i3−i32-2-22000000001-11-10000-111-1−i3i3i3−i300000000−i3i3i3−i3000000
χ422-2-22-111-122-2-2-22-222-2-2200-1-11111-1-1-22-2200-111-1i3−i3−i3i32-2-22000000001-11-10000-111-1i3−i3−i3i300000000i3−i3−i3i3000000
χ432-2-22-111-122-2-2-22-22-222-200-1-11111-1-1-22-22001-1-11−i3i3i3−i3-222-2000000001-11-100001-1-11−i3i3i3−i300000000i3−i3−i3i3000000
χ442-2-22-111-122-2-2-22-22-222-200-1-11111-1-1-22-22001-1-11i3−i3−i3i3-222-2000000001-11-100001-1-11i3−i3−i3i300000000−i3i3i3−i3000000
χ45444444441-211-2-2-210000441-21-21-21-2000022000022220000-2-2-2-20000000011-1-10000-1-1-1-122000000000000-1-100
χ46444444441-211-2-2-210000441-21-21-21-20000-2-20000-2-2-2-20000-2-2-2-200000000111100001111-2-20000000000001100
χ47444444441-211-2-2-210000-4-41-21-21-21-2000022000022220000222200000000-1-1-1-10000-1-1-1-1-2-20000000000001100
χ48444444441-211-2-2-210000-4-41-21-21-21-20000-2-20000-2-2-2-20000222200000000-1-1110000111122000000000000-1-100
χ4944444444-21-2-2111-2222244-21-21-21-2100000022220000-1-1-1-1111122220000-2-200-1-1-1-100000000-1-1-1-10000000000
χ5044444444-21-2-2111-22222-4-4-21-21-21-2100000022220000-1-1-1-1-1-1-1-1-2-2-2-200002200-1-1-1-10000000011110000000000
χ5144444444-21-2-2111-2-2-2-2-244-21-21-21-21000000-2-2-2-2000011111111-2-2-2-20000-2-20011110000000011110000000000
χ5244444444-21-2-2111-2-2-2-2-2-4-4-21-21-21-21000000-2-2-2-200001111-1-1-1-1222200002200111100000000-1-1-1-10000000000
χ534444-2-2-2-244444444000000-2-2-2-2-2-2-2-2-4-4-4-400000000000000000000002222000000000000000000000000000000
χ5444-4-44-44-4-21-22-1-1122i−2i2i−2i00-212-1-212-10000002i−2i2i−2i0000−ii−ii3i−3i3i−3i2-22-200000000−ii−ii00000000-11-110000000000
χ5544-4-44-44-4-21-22-1-1122i−2i2i−2i00-212-1-212-10000002i−2i2i−2i0000−ii−ii−3i3i−3i3i-22-2200000000−ii−ii000000001-11-10000000000
χ5644-4-44-44-4-21-22-1-112−2i2i−2i2i00-212-1-212-1000000−2i2i−2i2i0000i−ii−i3i−3i3i−3i-22-2200000000i−ii−i000000001-11-10000000000
χ5744-4-44-44-4-21-22-1-112−2i2i−2i2i00-212-1-212-1000000−2i2i−2i2i0000i−ii−i−3i3i−3i3i2-22-200000000i−ii−i00000000-11-110000000000
χ5844-4-4-22-22444-4-4-44-4000000-2-222-2-22244-4-40000000000000000000000-2-222000000000000000000000000000000
χ594-44-444-4-41-2-11-222-100004-41-21-2-12-1200002i−2i00002i2i−2i−2i0000-2-222000000001-1−ii0000−i−iii2i−2i000000000000−ii00
χ604-44-444-4-41-2-11-222-100004-41-21-2-12-120000−2i2i0000−2i−2i2i2i0000-2-222000000001-1i−i0000ii−i−i−2i2i000000000000i−i00
χ614-44-444-4-41-2-11-222-10000-441-21-2-12-1200002i−2i00002i2i−2i−2i000022-2-200000000-11−ii0000−i−iii−2i2i000000000000i−i00
χ624-44-444-4-41-2-11-222-10000-441-21-2-12-120000−2i2i0000−2i−2i2i2i000022-2-200000000-11i−i0000ii−i−i2i−2i000000000000−ii00
χ634-44-444-4-4-212-21-1-122i2i−2i−2i4-4-21-212-12-10000002i2i−2i−2i0000−i−iii11-1-12i2i−2i−2i0000-2200−i−iii00000000−i−iii0000000000
χ644-44-444-4-4-212-21-1-122i2i−2i−2i-44-21-212-12-10000002i2i−2i−2i0000−i−iii-1-111−2i−2i2i2i00002-200−i−iii00000000ii−i−i0000000000
χ654-44-444-4-4-212-21-1-12−2i−2i2i2i4-4-21-212-12-1000000−2i−2i2i2i0000ii−i−i11-1-1−2i−2i2i2i0000-2200ii−i−i00000000ii−i−i0000000000
χ664-44-444-4-4-212-21-1-12−2i−2i2i2i-44-21-212-12-1000000−2i−2i2i2i0000ii−i−i-1-1112i2i−2i−2i00002-200ii−i−i00000000−i−iii0000000000
χ674-44-4-2-22244-444-4-4-4000000-2-2-2-22222-444-400000000000000000000002-2-22000000000000000000000000000000
χ684-4-444-4-44-2122-11-1-22-2-2200-212-12-1-210000002-2-220000-111-13i−3i−3i3i−2i2i2i−2i00000000-111-100000000i−i−ii0000000000
χ694-4-444-4-44-2122-11-1-22-2-2200-212-12-1-210000002-2-220000-111-1−3i3i3i−3i2i−2i−2i2i00000000-111-100000000−iii−i0000000000
χ704-4-444-4-44-2122-11-1-2-222-200-212-12-1-21000000-222-200001-1-113i−3i−3i3i2i−2i−2i2i000000001-1-1100000000−iii−i0000000000
χ714-4-444-4-44-2122-11-1-2-222-200-212-12-1-21000000-222-200001-1-11−3i3i3i−3i−2i2i2i−2i000000001-1-1100000000i−i−ii0000000000
χ724-4-44-222-244-4-4-44-44000000-2-22222-2-24-44-40000000000000000000000-22-22000000000000000000000000000000
χ738888-4-4-4-42-422-4-4-42000000-12-12-12-120000440000-2-2-2-2000000000000000000-2-200001111000000000000000000
χ748888-4-4-4-42-422-4-4-42000000-12-12-12-120000-4-400002222000000000000000000220000-1-1-1-1000000000000000000
χ758888-4-4-4-4-42-4-4222-44444002-12-12-12-1000000-2-2-2-20000-2-2-2-2000000000000000011110000000000000000000000
χ768888-4-4-4-4-42-4-4222-4-4-4-4-4002-12-12-12-10000002222000022220000000000000000-1-1-1-10000000000000000000000
χ7788-8-88-88-82-42-244-4-20000002-4-242-4-24000000000000000000000000000000000000000000000000000000000000
χ7888-8-8-44-442-42-244-4-2000000-121-2-121-2000000000023−2323−23000000000000000000000000−33−33000000000000000000
χ7988-8-8-44-442-42-244-4-2000000-121-2-121-20000000000−2323−23230000000000000000000000003−33−3000000000000000000
χ8088-8-8-44-44-42-44-2-2244i−4i4i−4i002-1-212-1-21000000−2i2i−2i2i0000−2i2i−2i2i0000000000000000i−ii−i0000000000000000000000
χ8188-8-8-44-44-42-44-2-224−4i4i−4i4i002-1-212-1-210000002i−2i2i−2i00002i−2i2i−2i0000000000000000−ii−ii0000000000000000000000
χ828-88-8-4-4442-4-22-444-2000000-12-121-21-200004i−4i0000−2i−2i2i2i000000000000000000−2i2i0000ii−i−i000000000000000000
χ838-88-8-4-4442-4-22-444-2000000-12-121-21-20000−4i4i00002i2i−2i−2i0000000000000000002i−2i0000−i−iii000000000000000000
χ848-88-8-4-444-424-42-2-244i4i−4i−4i002-12-1-21-21000000−2i−2i2i2i0000−2i−2i2i2i0000000000000000ii−i−i0000000000000000000000
χ858-88-8-4-444-424-42-2-24−4i−4i4i4i002-12-1-21-210000002i2i−2i−2i00002i2i−2i−2i0000000000000000−i−iii0000000000000000000000
χ868-8-888-8-882-4-2-24-4420000002-4-24-242-4000000000000000000000000000000000000000000000000000000000000
χ878-8-88-444-42-4-2-24-442000000-121-21-2-120000000000−2i32i32i3−2i3000000000000000000000000i3−i3−i3i3000000000000000000
χ888-8-88-444-42-4-2-24-442000000-121-21-2-1200000000002i3−2i3−2i32i3000000000000000000000000−i3i3i3−i3000000000000000000
χ898-8-88-444-4-4244-22-2-44-4-44002-1-21-212-1000000-222-20000-222-200000000000000001-1-110000000000000000000000
χ908-8-88-444-4-4244-22-2-4-444-4002-1-21-212-10000002-2-2200002-2-220000000000000000-111-10000000000000000000000

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