Finite Group Databasebeta

← Group #13165381

Character table — Group #13165381

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size1111222244444444666666888888889999121212121212121212121212121212121212181818181818181824242424242424242424242436363636363636363636363654547272108108
order12223666336666662222443366666622224466666666121212121212121244446666666612121212121212124444121212121212121244121244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-111111111-1-1-1-11111111111111111-1-111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1
χ311111111111111111111-1-111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-11111-1-111-1-1-1-11111-1-1-1-1-1-1
χ411111111111111111111-1-1111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111
χ51111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-1
χ61111111111111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1111111-1-111
χ71111111111111111-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111
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
χ91-11-11-1-1111-11-11-1-111-1-1i−i11-1-11-1-111-11-11-111-1-111-1-111-1-1ii−i−iii−i−i1-1-1111-1-11-1i−i11-1-1i−i1-1ii−i−i11-1-1i−ii−ii−i
χ101-11-11-1-1111-11-11-1-111-1-1i−i11-1-11-1-111-11-1-1111-1-111-1-1-1-111ii−i−iii−i−i1-1-1111-1-1-11i−i-1-111−ii-11ii−i−i-1-111i−i−ii−ii
χ111-11-11-1-1111-11-11-1-111-1-1−ii11-1-11-1-111-11-11-111-1-111-1-111-1-1−i−iii−i−iii1-1-1111-1-11-1−ii11-1-1−ii1-1−i−iii11-1-1−ii−ii−ii
χ121-11-11-1-1111-11-11-1-111-1-1−ii11-1-11-1-111-11-1-1111-1-111-1-1-1-111−i−iii−i−iii1-1-1111-1-1-11−ii-1-111i−i-11−i−iii-1-111−iii−ii−i
χ131-11-11-1-1111-11-11-1-1-1-111i−i11-1-11-1-111-11-11-1-1-111-1-11111-1-1ii−i−i−i−iii1-1-11-1-1111-1i−i11-1-1i−i-11−i−iii-1-111i−ii−i−ii
χ141-11-11-1-1111-11-11-1-1-1-111i−i11-1-11-1-111-11-1-11-1-111-1-111-1-111ii−i−i−i−iii1-1-11-1-111-11i−i-1-111−ii1-1−i−iii11-1-1i−i−iii−i
χ151-11-11-1-1111-11-11-1-1-1-111−ii11-1-11-1-111-11-11-1-1-111-1-11111-1-1−i−iiiii−i−i1-1-11-1-1111-1−ii11-1-1−ii-11ii−i−i-1-111−ii−iii−i
χ161-11-11-1-1111-11-11-1-1-1-111−ii11-1-11-1-111-11-1-11-1-111-1-111-1-111−i−iiiii−i−i1-1-11-1-111-11−ii-1-111i−i1-1ii−i−i11-1-1−iii−i−ii
χ17222222222222222200002222222222-2-2-2-20000000000000022220000-2-2-2-2000000220000000000000000-2-20000
χ1822222222222222220000-2-222222222-2-2-2-200000000000000-2-2-2-20000-2-2-2-2000000-2-20000000000000000220000
χ192222-1-1-1-122222222222200-1-1-1-1-1-1-1-1222222-1-1-1-12222-1-1-1-100000000-1-1-1-1-1-1-1-12200-1-1-1-100220000-1-1-1-1000000
χ202222-1-1-1-122222222222200-1-1-1-1-1-1-1-12222-2-2-1-1-1-12222111100000000-1-1-1-1-1-1-1-1-2-200111100-2-200001111000000
χ212222-1-1-1-122222222-2-2-2-200-1-1-1-1-1-1-1-12222221111-2-2-2-2-1-1-1-100000000-1-1-1-111112200-1-1-1-100-2-200001111000000
χ222222-1-1-1-122222222-2-2-2-200-1-1-1-1-1-1-1-12222-2-21111-2-2-2-2111100000000-1-1-1-11111-2-200111100220000-1-1-1-1000000
χ2322-2-222-2-2222-22-2-2-2000000222-2-22-2-2-2-2220000000000000000002i−2i2i−2i-22-2200000000000000002i−2i2i−2i0000000000
χ2422-2-222-2-2222-22-2-2-2000000222-2-22-2-2-2-222000000000000000000−2i2i−2i2i-22-220000000000000000−2i2i−2i2i0000000000
χ2522-2-222-2-2222-22-2-2-22-22-200222-2-22-2-222-2-2002-22-22-22-20000000000002-22-22-22-200000000000000000000000000
χ2622-2-222-2-2222-22-2-2-2-22-2200222-2-22-2-222-2-200-22-22-22-220000000000002-22-2-22-2200000000000000000000000000
χ2722-2-2-1-111222-22-2-2-22-22-200-1-1-111-11122-2-200-11-112-22-23−33−300000000-11-11-11-1100003−33−3000000003−33−3000000
χ2822-2-2-1-111222-22-2-2-22-22-200-1-1-111-11122-2-200-11-112-22-2−33−3300000000-11-11-11-110000−33−3300000000−33−33000000
χ2922-2-2-1-111222-22-2-2-2-22-2200-1-1-111-11122-2-2001-11-1-22-223−33−300000000-11-111-11-100003−33−300000000−33−33000000
χ3022-2-2-1-111222-22-2-2-2-22-2200-1-1-111-11122-2-2001-11-1-22-22−33−3300000000-11-111-11-10000−33−33000000003−33−3000000
χ312-22-22-2-2222-22-22-2-200002i−2i22-2-22-2-22-22-22000000000000002i2i−2i−2i0000-222-20000002i−2i0000000000000000−2i2i0000
χ322-22-22-2-2222-22-22-2-20000−2i2i22-2-22-2-22-22-2200000000000000−2i−2i2i2i0000-222-2000000−2i2i00000000000000002i−2i0000
χ332-22-2-111-122-22-22-2-222-2-200-1-111-111-12-22-22-2-1-11122-2-2-1-11100000000-111-1-1-1112-200-1-111002-20000-1-111000000
χ342-22-2-111-122-22-22-2-222-2-200-1-111-111-12-22-2-22-1-11122-2-211-1-100000000-111-1-1-111-220011-1-100-22000011-1-1000000
χ352-22-2-111-122-22-22-2-2-2-22200-1-111-111-12-22-22-211-1-1-2-222-1-11100000000-111-111-1-12-200-1-11100-22000011-1-1000000
χ362-22-2-111-122-22-22-2-2-2-22200-1-111-111-12-22-2-2211-1-1-2-22211-1-100000000-111-111-1-1-220011-1-1002-20000-1-111000000
χ372-2-222-22-222-2-2-2-22200000022-22-2-22-2-222-20000000000000000002-2-22-2-22200000000000000002-2-220000000000
χ382-2-222-22-222-2-2-2-22200000022-22-2-22-2-222-2000000000000000000-222-2-2-2220000000000000000-222-20000000000
χ392-2-222-22-222-2-2-2-2222-2-220022-22-2-22-22-2-22002-2-222-2-2200000000000022-2-22-2-2200000000000000000000000000
χ402-2-222-22-222-2-2-2-222-222-20022-22-2-22-22-2-2200-222-2-222-200000000000022-2-2-222-200000000000000000000000000
χ412-2-22-11-1122-2-2-2-2222-2-2200-1-11-111-112-2-2200-111-12-2-223−3−3300000000-1-111-111-100003−3−33000000003−3−33000000
χ422-2-22-11-1122-2-2-2-2222-2-2200-1-11-111-112-2-2200-111-12-2-22−333−300000000-1-111-111-10000−333−300000000−333−3000000
χ432-2-22-11-1122-2-2-2-222-222-200-1-11-111-112-2-22001-1-11-222-23−3−3300000000-1-1111-1-1100003−3−3300000000−333−3000000
χ442-2-22-11-1122-2-2-2-222-222-200-1-11-111-112-2-22001-1-11-222-2−333−300000000-1-1111-1-110000−333−3000000003−3−33000000
χ45444444441-21-2-211-20000441-211-2-2-21000022000000002222-2-2-2-2000000000000-1-111-1-1-1-122000000000000-1-100
χ46444444441-21-2-211-20000441-211-2-2-210000-2-200000000-2-2-2-2-2-2-2-200000000000011111111-2-20000000000001100
χ47444444441-21-2-211-20000-4-41-211-2-2-210000220000000022222222000000000000-1-1-1-1-1-1-1-1-2-20000000000001100
χ48444444441-21-2-211-20000-4-41-211-2-2-210000-2-200000000-2-2-2-2222200000000000011-1-1111122000000000000-1-100
χ4944444444-21-211-2-21222244-21-2-2111-20000002222-1-1-1-10000111122220000-1-1-1-100-2-200000000-1-1-1-10000000000
χ5044444444-21-211-2-212222-4-4-21-2-2111-20000002222-1-1-1-10000-1-1-1-1-2-2-2-20000-1-1-1-100220000000011110000000000
χ5144444444-21-211-2-21-2-2-2-244-21-2-2111-2000000-2-2-2-2111100001111-2-2-2-20000111100-2-20000000011110000000000
χ5244444444-21-211-2-21-2-2-2-2-4-4-21-2-2111-2000000-2-2-2-211110000-1-1-1-1222200001111002200000000-1-1-1-10000000000
χ534444-2-2-2-244444444000000-2-2-2-2-2-2-2-2-4-4-4-400000000000000000000002222000000000000000000000000000000
χ5444-4-444-4-4-21-2-1122-12-22-200-21-22-11-120000002-22-2-11-1100003i−3i3i−3i2i−2i2i−2i0000-11-11000000000000−ii−ii0000000000
χ5544-4-444-4-4-21-2-1122-12-22-200-21-22-11-120000002-22-2-11-110000−3i3i−3i3i−2i2i−2i2i0000-11-11000000000000i−ii−i0000000000
χ5644-4-444-4-4-21-2-1122-1-22-2200-21-22-11-12000000-22-221-11-100003i−3i3i−3i−2i2i−2i2i00001-11-1000000000000i−ii−i0000000000
χ5744-4-444-4-4-21-2-1122-1-22-2200-21-22-11-12000000-22-221-11-10000−3i3i−3i3i2i−2i2i−2i00001-11-1000000000000−ii−ii0000000000
χ5844-4-4-2-222444-44-4-4-4000000-2-2-222-222-4-44400000000000000000000002-22-2000000000000000000000000000000
χ594-44-44-4-441-2-1-221-1200004i−4i1-2-1-1-222100002-20000000022-2-2−2i−2i2i2i000000000000-11i−i-1-1112i−2i000000000000−ii00
χ604-44-44-4-441-2-1-221-1200004i−4i1-2-1-1-22210000-2200000000-2-222−2i−2i2i2i0000000000001-1i−i11-1-1−2i2i000000000000i−i00
χ614-44-44-4-441-2-1-221-120000−4i4i1-2-1-1-222100002-20000000022-2-22i2i−2i−2i000000000000-11−ii-1-111−2i2i000000000000i−i00
χ624-44-44-4-441-2-1-221-120000−4i4i1-2-1-1-22210000-2200000000-2-2222i2i−2i−2i0000000000001-1−ii11-1-12i−2i000000000000−ii00
χ634-44-44-4-44-2121-1-22-122-2-24i−4i-21221-1-1-200000022-2-2-1-1110000ii−i−i2i2i−2i−2i0000-1-11100−2i2i00000000−i−iii0000000000
χ644-44-44-4-44-2121-1-22-122-2-2−4i4i-21221-1-1-200000022-2-2-1-1110000−i−iii−2i−2i2i2i0000-1-111002i−2i00000000ii−i−i0000000000
χ654-44-44-4-44-2121-1-22-1-2-2224i−4i-21221-1-1-2000000-2-22211-1-10000ii−i−i−2i−2i2i2i000011-1-100−2i2i00000000ii−i−i0000000000
χ664-44-44-4-44-2121-1-22-1-2-222−4i4i-21221-1-1-2000000-2-22211-1-10000−i−iii2i2i−2i−2i000011-1-1002i−2i00000000−i−iii0000000000
χ674-44-4-222-244-44-44-4-4000000-2-222-222-2-44-4400000000000000000000002-2-22000000000000000000000000000000
χ684-4-444-44-4-212-1-12-212-2-2200-212-2-1-1120000002-2-22-111-100003-3-332-2-220000-111-1000000000000-111-10000000000
χ694-4-444-44-4-212-1-12-212-2-2200-212-2-1-1120000002-2-22-111-10000-333-3-222-20000-111-10000000000001-1-110000000000
χ704-4-444-44-4-212-1-12-21-222-200-212-2-1-112000000-222-21-1-1100003-3-33-222-200001-1-110000000000001-1-110000000000
χ714-4-444-44-4-212-1-12-21-222-200-212-2-1-112000000-222-21-1-110000-333-32-2-2200001-1-11000000000000-111-10000000000
χ724-4-44-22-2244-4-4-4-444000000-2-22-222-22-444-4000000000000000000000022-2-2000000000000000000000000000000
χ738888-4-4-4-42-42-4-422-4000000-12-1-1222-100004400000000-2-2-2-20000000000000000-2-2001111000000000000000000
χ748888-4-4-4-42-42-4-422-4000000-12-1-1222-10000-4-400000000222200000000000000002200-1-1-1-1000000000000000000
χ758888-4-4-4-4-42-422-4-424444002-122-1-1-12000000-2-2-2-2-2-2-2-20000000000000000111100000000000000000000000000
χ768888-4-4-4-4-42-422-4-42-4-4-4-4002-122-1-1-12000000222222220000000000000000-1-1-1-100000000000000000000000000
χ7788-8-888-8-82-424-4-2-240000002-42-24-44-2000000000000000000000000000000000000000000000000000000000000
χ7888-8-8-4-4442-424-4-2-24000000-12-11-22-210000000000000023−2323−2300000000000000000000−33−33000000000000000000
χ7988-8-8-4-4442-424-4-2-24000000-12-11-22-2100000000000000−2323−2323000000000000000000003−33−3000000000000000000
χ8088-8-8-4-444-42-4-2244-24-44-4002-12-21-11-2000000-22-22-22-2200000000000000001-11-100000000000000000000000000
χ8188-8-8-4-444-42-4-2244-2-44-44002-12-21-11-20000002-22-22-22-20000000000000000-11-1100000000000000000000000000
χ828-88-8-444-42-4-2-442-24000000-12112-2-2-100004-400000000-2-2220000000000000000-220011-1-1000000000000000000
χ838-88-8-444-42-4-2-442-24000000-12112-2-2-10000-440000000022-2-200000000000000002-200-1-111000000000000000000
χ848-88-8-444-4-4242-2-44-244-4-4002-1-2-2-1112000000-2-222-2-222000000000000000011-1-100000000000000000000000000
χ858-88-8-444-4-4242-2-44-2-4-444002-1-2-2-111200000022-2-222-2-20000000000000000-1-11100000000000000000000000000
χ868-8-888-88-82-4-244-22-40000002-4-2244-4-2000000000000000000000000000000000000000000000000000000000000
χ878-8-88-44-442-4-244-22-4000000-121-1-2-2210000000000000023−23−232300000000000000000000−333−3000000000000000000
χ888-8-88-44-442-4-244-22-4000000-121-1-2-22100000000000000−232323−23000000000000000000003−3−33000000000000000000
χ898-8-88-44-44-424-2-24-424-4-44002-1-2211-1-2000000-222-2-222-200000000000000001-1-1100000000000000000000000000
χ908-8-88-44-44-424-2-24-42-444-4002-1-2211-1-20000002-2-222-2-220000000000000000-111-100000000000000000000000000

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