Finite Group Databasebeta

← Group #13167478

Character table — Group #13167478

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11112222224444444444444488888888888888888899991818181818181818181818181818363636363636363636363636363636363636363636363636363672727272
order12223446663366666612121212121233666666121212121212121212122222444444444466664444444412121212121212121212121212121212121212121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ41111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ511111-1-111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111
χ611111-1-111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-111-1-111-1-11111-1-1-1-1-1-1-1-1111111-1-1
χ711111-1-111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-1-111
χ811111-1-111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1
χ91-1-111i−i1-1-111-1-111-1-1i−iii−i−i1111-1-1-1-1i−iiiii−i−i−i−i1-11-1ii−i−ii−i11-1-11-11-1i−i1-11-1i−ii−iii−i−i11-1-111-1-1ii−i−i1-1i−i
χ101-1-111i−i1-1-111-1-111-1-1i−iii−i−i1111-1-1-1-1i−iiiii−i−i−i−i1-11-1ii−i−ii−i11-1-11-11-1−ii-11-11−iii−iii−i−i11-1-1-1-111−i−iii-11−ii
χ111-1-111i−i1-1-111-1-111-1-1i−iii−i−i1111-1-1-1-1i−iiiii−i−i−i−i1-11-1−i−iiii−i-1-1111-11-1i−i1-1-11−iii−i−i−iii-1-111-1-111−i−iii1-1i−i
χ121-1-111i−i1-1-111-1-111-1-1i−iii−i−i1111-1-1-1-1i−iiiii−i−i−i−i1-11-1−i−iiii−i-1-1111-11-1−ii-111-1i−ii−i−i−iii-1-11111-1-1ii−i−i-11−ii
χ131-1-111−ii1-1-111-1-111-1-1−ii−i−iii1111-1-1-1-1−ii−i−i−i−iiiii1-11-1ii−i−i−ii-1-1111-11-1i−i-111-1−ii−iiii−i−i-1-11111-1-1−i−iii-11i−i
χ141-1-111−ii1-1-111-1-111-1-1−ii−i−iii1111-1-1-1-1−ii−i−i−i−iiiii1-11-1ii−i−i−ii-1-1111-11-1−ii1-1-11i−i−iiii−i−i-1-111-1-111ii−i−i1-1−ii
χ151-1-111−ii1-1-111-1-111-1-1−ii−i−iii1111-1-1-1-1−ii−i−i−i−iiiii1-11-1−i−iii−ii11-1-11-11-1i−i-11-11i−i−ii−i−iii11-1-1-1-111ii−i−i-11i−i
χ161-1-111−ii1-1-111-1-111-1-1−ii−i−iii1111-1-1-1-1−ii−i−i−i−iiiii1-11-1−i−iii−ii11-1-11-11-1−ii1-11-1−ii−ii−i−iii11-1-111-1-1−i−iii1-1−ii
χ17222222222222222222222222222222222222222222-2-2-2-20000-2-20000-2-2-2-200000000-2-200000000000000000000
χ1822222-2-222222222222-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-20000220000-2-2-2-2000000002200000000000000000000
χ192222-122-1-1-122222222-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122220000220000-1-1-1-100002222-1-100000000-1-1-1-1-1-1-1-10000
χ202222-122-1-1-122222222-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122220000220000-1-1-1-10000-2-2-2-2-1-100000000111111110000
χ212222-122-1-1-122222222-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-20000-2-2000011110000000011000000003−33−33−33−30000
χ222222-122-1-1-122222222-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-20000-2-200001111000000001100000000−33−33−33−330000
χ232222-1-2-2-1-1-12222222211-2-2-2-2-1-1-1-1-1-1-1-1-2-21111111122220000-2-20000-1-1-1-1000022-2-21100000000-1-1-1-111110000
χ242222-1-2-2-1-1-12222222211-2-2-2-2-1-1-1-1-1-1-1-1-2-21111111122220000-2-20000-1-1-1-10000-2-22211000000001111-1-1-1-10000
χ252222-1-2-2-1-1-12222222211-2-2-2-2-1-1-1-1-1-1-1-1-2-211111111-2-2-2-20000220000111100000000-1-1000000003−33−3−33−330000
χ262222-1-2-2-1-1-12222222211-2-2-2-2-1-1-1-1-1-1-1-1-2-211111111-2-2-2-20000220000111100000000-1-100000000−33−333−33−30000
χ2722-2-2200-22-2222-2-2-22-200000022-2-222-2-2000000000022-2-22-22-200000022-2-200000000002-22-20000000000000000
χ2822-2-2200-22-2222-2-2-22-200000022-2-222-2-2000000000022-2-2-22-2200000022-2-20000000000-22-220000000000000000
χ2922-2-2200-22-2222-2-2-22-200000022-2-222-2-20000000000-2-2220000002i−2i2i−2i-2-222000000000000002i−2i2i−2i000000000000
χ3022-2-2200-22-2222-2-2-22-200000022-2-222-2-20000000000-2-222000000−2i2i−2i2i-2-22200000000000000−2i2i−2i2i000000000000
χ312-22-2200-2-2222-22-2-2-2200000022-2-2-2-22200000000002-2-222i−2i−2i2i0000002-2-2200000000002i−2i−2i2i0000000000000000
χ322-22-2200-2-2222-22-2-2-2200000022-2-2-2-22200000000002-2-22−2i2i2i−2i0000002-2-220000000000−2i2i2i−2i0000000000000000
χ332-22-2200-2-2222-22-2-2-2200000022-2-2-2-2220000000000-222-20000002i−2i−2i2i-222-2000000000000002i−2i−2i2i000000000000
χ342-22-2200-2-2222-22-2-2-2200000022-2-2-2-2220000000000-222-2000000−2i2i2i−2i-222-200000000000000−2i2i2i−2i000000000000
χ352-2-2222i−2i2-2-222-2-222-2-22i−2i2i2i−2i−2i2222-2-2-2-22i−2i2i2i2i2i−2i−2i−2i−2i-22-220000−2i2i0000-22-2200000000−2i2i00000000000000000000
χ362-2-222−2i2i2-2-222-2-222-2-2−2i2i−2i−2i2i2i2222-2-2-2-2−2i2i−2i−2i−2i−2i2i2i2i2i-22-2200002i−2i0000-22-22000000002i−2i00000000000000000000
χ372-2-22-12i−2i-11122-2-222-2-2−ii2i2i−2i−2i-1-1-1-111112i−2i−i−i−i−iiiii2-22-200002i−2i0000-11-1100002-22i−2i−ii00000000-1-111−i−iii0000
χ382-2-22-12i−2i-11122-2-222-2-2−ii2i2i−2i−2i-1-1-1-111112i−2i−i−i−i−iiiii2-22-200002i−2i0000-11-110000-22−2i2i−ii0000000011-1-1ii−i−i0000
χ392-2-22-12i−2i-11122-2-222-2-2−ii2i2i−2i−2i-1-1-1-111112i−2i−i−i−i−iiiii-22-220000−2i2i00001-11-100000000i−i000000003−3−33i3−i3−i3i30000
χ402-2-22-12i−2i-11122-2-222-2-2−ii2i2i−2i−2i-1-1-1-111112i−2i−i−i−i−iiiii-22-220000−2i2i00001-11-100000000i−i00000000−333−3−i3i3i3−i30000
χ412-2-22-1−2i2i-11122-2-222-2-2i−i−2i−2i2i2i-1-1-1-11111−2i2iiiii−i−i−i−i2-22-20000−2i2i0000-11-1100002-2−2i2ii−i00000000-1-111ii−i−i0000
χ422-2-22-1−2i2i-11122-2-222-2-2i−i−2i−2i2i2i-1-1-1-11111−2i2iiiii−i−i−i−i2-22-20000−2i2i0000-11-110000-222i−2ii−i0000000011-1-1−i−iii0000
χ432-2-22-1−2i2i-11122-2-222-2-2i−i−2i−2i2i2i-1-1-1-11111−2i2iiiii−i−i−i−i-22-2200002i−2i00001-11-100000000−ii000000003−3−33−i3i3i3−i30000
χ442-2-22-1−2i2i-11122-2-222-2-2i−i−2i−2i2i2i-1-1-1-11111−2i2iiiii−i−i−i−i-22-2200002i−2i00001-11-100000000−ii00000000−333−3i3−i3−i3i30000
χ4544444444441-21-21-2-2144-2-2-2-21-21-21-21-21111-2-211-2-200000000000000000022220000000000000000000000-1-1-1-1
χ4644444444441-21-21-2-2144-2-2-2-21-21-21-21-21111-2-211-2-2000000000000000000-2-2-2-200000000000000000000001111
χ474444444444-21-21-211-2441111-21-21-21-21-2-2-2-211-2-2110000222200222200000000000000-1-1-1-1-1-1-1-1000000000000
χ484444444444-21-21-211-2441111-21-21-21-21-2-2-2-211-2-2110000-2-2-2-200-2-2-2-20000000000000011111111000000000000
χ4944444-4-44441-21-21-2-21-4-422221-21-21-21-2-1-1-1-122-1-12200000000000000000022-2-2000000000000000000000011-1-1
χ5044444-4-44441-21-21-2-21-4-422221-21-21-21-2-1-1-1-122-1-122000000000000000000-2-2220000000000000000000000-1-111
χ5144444-4-4444-21-21-211-2-4-4-1-1-1-1-21-21-21-212222-1-122-1-10000222200-2-2-2-200000000000000-1-1-1-11111000000000000
χ5244444-4-4444-21-21-211-2-4-4-1-1-1-1-21-21-21-212222-1-122-1-10000-2-2-2-2002222000000000000001111-1-1-1-1000000000000
χ5344-4-4400-44-4-21-2-12-112003i−3i3i−3i-212-1-212-100003i−3i003i−3i00002-22-2002i−2i2i−2i00000000000000-11-11−ii−ii000000000000
χ5444-4-4400-44-4-21-2-12-112003i−3i3i−3i-212-1-212-100003i−3i003i−3i0000-22-2200−2i2i−2i2i000000000000001-11-1i−ii−i000000000000
χ5544-4-4400-44-4-21-2-12-11200−3i3i−3i3i-212-1-212-10000−3i3i00−3i3i00002-22-200−2i2i−2i2i00000000000000-11-11i−ii−i000000000000
χ5644-4-4400-44-4-21-2-12-11200−3i3i−3i3i-212-1-212-10000−3i3i00−3i3i0000-22-22002i−2i2i−2i000000000000001-11-1−ii−ii000000000000
χ5744-4-4-2002-22444-4-4-44-4000000-2-222-2-222000000000044-4-40000000000-2-222000000000000000000000000000000
χ5844-4-4-2002-22444-4-4-44-4000000-2-222-2-2220000000000-4-444000000000022-2-2000000000000000000000000000000
χ594-44-4400-4-44-21212-1-1-2003-3-33-212-12-1-2100003-300-3300002i−2i−2i2i00−2i2i2i−2i00000000000000−iii−ii−i−ii000000000000
χ604-44-4400-4-44-21212-1-1-2003-3-33-212-12-1-2100003-300-330000−2i2i2i−2i002i−2i−2i2i00000000000000i−i−ii−iii−i000000000000
χ614-44-4400-4-44-21212-1-1-200-333-3-212-12-1-210000-33003-300002i−2i−2i2i002i−2i−2i2i00000000000000−iii−i−iii−i000000000000
χ624-44-4400-4-44-21212-1-1-200-333-3-212-12-1-210000-33003-30000−2i2i2i−2i00−2i2i2i−2i00000000000000i−i−iii−i−ii000000000000
χ634-44-4-20022-244-44-4-4-44000000-2-22222-2-200000000004-4-440000000000-222-2000000000000000000000000000000
χ644-44-4-20022-244-44-4-4-44000000-2-22222-2-20000000000-444-400000000002-2-22000000000000000000000000000000
χ654-4-4444i−4i4-4-41-2-121-22-14i−4i−2i−2i2i2i1-21-2-12-12i−iii−2i−2i−i−i2i2i0000000000000000002i−2i2-20000000000000000000000-11−ii
χ664-4-4444i−4i4-4-41-2-121-22-14i−4i−2i−2i2i2i1-21-2-12-12i−iii−2i−2i−i−i2i2i000000000000000000−2i2i-2200000000000000000000001-1i−i
χ674-4-4444i−4i4-4-4-212-1-21-124i−4iii−i−i-21-212-12-1−2i2i−2i−2iii2i2i−i−i00002i2i−2i−2i0022-2-200000000000000−i−iii-1-111000000000000
χ684-4-4444i−4i4-4-4-212-1-21-124i−4iii−i−i-21-212-12-1−2i2i−2i−2iii2i2i−i−i0000−2i−2i2i2i00-2-22200000000000000ii−i−i11-1-1000000000000
χ694-4-444−4i4i4-4-41-2-121-22-1−4i4i2i2i−2i−2i1-21-2-12-12−ii−i−i2i2iii−2i−2i0000000000000000002i−2i-2200000000000000000000001-1−ii
χ704-4-444−4i4i4-4-41-2-121-22-1−4i4i2i2i−2i−2i1-21-2-12-12−ii−i−i2i2iii−2i−2i000000000000000000−2i2i2-20000000000000000000000-11i−i
χ714-4-444−4i4i4-4-4-212-1-21-12−4i4i−i−iii-21-212-12-12i−2i2i2i−i−i−2i−2iii00002i2i−2i−2i00-2-22200000000000000−i−iii11-1-1000000000000
χ724-4-444−4i4i4-4-4-212-1-21-12−4i4i−i−iii-21-212-12-12i−2i2i2i−i−i−2i−2iii0000−2i−2i2i2i0022-2-200000000000000ii−i−i-1-111000000000000
χ738888-488-4-4-42-42-42-4-42-4-4-4-4-4-4-12-12-12-1222-1-122-1-122000000000000000000000000000000000000000000000000
χ748888-488-4-4-4-42-42-422-4-4-422222-12-12-12-1-4-422-1-122-1-1000000000000000000000000000000000000000000000000
χ758888-4-8-8-4-4-42-42-42-4-42444444-12-12-12-12-2-211-2-211-2-2000000000000000000000000000000000000000000000000
χ768888-4-8-8-4-4-4-42-42-422-444-2-2-2-22-12-12-12-144-2-211-2-211000000000000000000000000000000000000000000000000
χ7788-8-8800-88-82-424-24-4-20000002-4-242-4-240000000000000000000000000000000000000000000000000000000000
χ7888-8-8-4004-442-424-24-4-2000000-121-2-121-20033−330033−3300000000000000000000000000000000000000000000000000
χ7988-8-8-4004-442-424-24-4-2000000-121-2-121-200−333300−333300000000000000000000000000000000000000000000000000
χ8088-8-8-4004-44-42-4-24-224006i−6i6i−6i2-1-212-1-210000−3i3i00−3i3i000000000000000000000000000000000000000000000000
χ8188-8-8-4004-44-42-4-24-22400−6i6i−6i6i2-1-212-1-2100003i−3i003i−3i000000000000000000000000000000000000000000000000
χ828-88-8800-8-882-4-2-4-24420000002-4-24-242-40000000000000000000000000000000000000000000000000000000000
χ838-88-8-40044-42-4-2-4-2442000000-121-21-2-1200−3i33i3003i3−3i300000000000000000000000000000000000000000000000000
χ848-88-8-40044-42-4-2-4-2442000000-121-21-2-12003i3−3i300−3i33i300000000000000000000000000000000000000000000000000
χ858-88-8-40044-4-42424-2-2-4006-6-662-1-21-212-10000-33003-3000000000000000000000000000000000000000000000000
χ868-88-8-40044-4-42424-2-2-400-666-62-1-21-212-100003-300-33000000000000000000000000000000000000000000000000
χ878-8-88-48i−8i-4442-4-242-44-2−4i4i−4i−4i4i4i-12-121-21-22i−2i−i−i2i2iii−2i−2i000000000000000000000000000000000000000000000000
χ888-8-88-48i−8i-444-424-2-42-24−4i4i2i2i−2i−2i2-12-1-21-21−4i4i2i2i−i−i−2i−2iii000000000000000000000000000000000000000000000000
χ898-8-88-4−8i8i-4442-4-242-44-24i−4i4i4i−4i−4i-12-121-21-2−2i2iii−2i−2i−i−i2i2i000000000000000000000000000000000000000000000000
χ908-8-88-4−8i8i-444-424-2-42-244i−4i−2i−2i2i2i2-12-1-21-214i−4i−2i−2iii2i2i−i−i000000000000000000000000000000000000000000000000

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