Finite Group Databasebeta

← Group #13167382

Character table — Group #13167382

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
χ31111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ41111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ511111-1-111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1
χ611111-1-111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11111-1-111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-111
χ711111-1-111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-1
χ811111-1-111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111
χ91-1-1111-1-1-1111-1-11-1-111-111-1-111-1-1-1-1111-11111-1-1-1-111-1-1ii−i−iii−i−i1-111-1-11-11-1i−ii−i1-1ii−i−iii−i−iii−i−iii−i−i1-11-1
χ101-1-1111-1-1-1111-1-11-1-111-111-1-111-1-1-1-1111-11111-1-1-1-111-1-1ii−i−iii−i−i1-111-1-1-11-11−ii−ii1-1ii−i−iii−i−i−i−iii−i−iii-11-11
χ111-1-1111-1-1-1111-1-11-1-111-111-1-111-1-1-1-1111-11111-1-1-1-111-1-1−i−iii−i−iii1-111-1-11-11-1−ii−ii1-1−i−iii−i−iii−i−iii−i−iii1-11-1
χ121-1-1111-1-1-1111-1-11-1-111-111-1-111-1-1-1-1111-11111-1-1-1-111-1-1−i−iii−i−iii1-111-1-1-11-11i−ii−i1-1−i−iii−i−iiiii−i−iii−i−i-11-11
χ131-1-111-11-1-1111-1-11-1-11-11-1-11111-1-1-1-111-11-1-1-1-1111111-1-1ii−i−i−i−iii-1111-1-11-1-11i−i−ii-11ii−i−i−i−iiiii−i−i−i−iii1-1-11
χ141-1-111-11-1-1111-1-11-1-11-11-1-11111-1-1-1-111-11-1-1-1-1111111-1-1ii−i−i−i−iii-1111-1-1-111-1−iii−i-11ii−i−i−i−iii−i−iiiii−i−i-111-1
χ151-1-111-11-1-1111-1-11-1-11-11-1-11111-1-1-1-111-11-1-1-1-1111111-1-1−i−iiiii−i−i-1111-1-11-1-11−iii−i-11−i−iiiii−i−i−i−iiiii−i−i1-1-11
χ161-1-111-11-1-1111-1-11-1-11-11-1-11111-1-1-1-111-11-1-1-1-1111111-1-1−i−iiiii−i−i-1111-1-1-111-1i−i−ii-11−i−iiiii−i−iii−i−i−i−iii-111-1
χ17222222222222222222222222222222222222222222-2-2-2-200000000-2-2-2-2-2-200000000-2-200000000000000000000
χ1822222-2-222222222222-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-20000000022-2-2-2-2000000002200000000000000000000
χ192222-122-1-1-122222222-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122220000000022-1-1-1-100002222-1-100000000-1-1-1-1-1-1-1-10000
χ202222-122-1-1-122222222-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-122220000000022-1-1-1-10000-2-2-2-2-1-100000000111111110000
χ212222-122-1-1-122222222-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-200000000-2-211110000000011000000003−33−33−33−30000
χ222222-122-1-1-122222222-1-12222-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-1-2-2-2-200000000-2-21111000000001100000000−33−33−33−330000
χ232222-1-2-2-1-1-12222222211-2-2-2-2-1-1-1-1-1-1-1-1-2-211111111222200000000-2-2-1-1-1-1000022-2-21100000000-1-1-1-111110000
χ242222-1-2-2-1-1-12222222211-2-2-2-2-1-1-1-1-1-1-1-1-2-211111111222200000000-2-2-1-1-1-10000-2-22211000000001111-1-1-1-10000
χ252222-1-2-2-1-1-12222222211-2-2-2-2-1-1-1-1-1-1-1-1-2-211111111-2-2-2-20000000022111100000000-1-1000000003−33−3−33−330000
χ262222-1-2-2-1-1-12222222211-2-2-2-2-1-1-1-1-1-1-1-1-2-211111111-2-2-2-20000000022111100000000-1-100000000−33−333−33−30000
χ2722-2-22002-2-2222-2-22-2-20000002222-2-2-2-200000000002-22-200002-22-2002-22-2000000000000002-22-2000000000000
χ2822-2-22002-2-2222-2-22-2-20000002222-2-2-2-200000000002-22-20000-22-22002-22-200000000000000-22-22000000000000
χ2922-2-22002-2-2222-2-22-2-20000002222-2-2-2-20000000000-22-222i−2i2i−2i000000-22-2200000000002i−2i2i−2i0000000000000000
χ3022-2-22002-2-2222-2-22-2-20000002222-2-2-2-20000000000-22-22−2i2i−2i2i000000-22-220000000000−2i2i−2i2i0000000000000000
χ312-22-2200-22-222-22-2-22-200000022-2-222-2-200000000002-2-2200002i−2i−2i2i002-2-22000000000000002i−2i−2i2i000000000000
χ322-22-2200-22-222-22-2-22-200000022-2-222-2-200000000002-2-220000−2i2i2i−2i002-2-2200000000000000−2i2i2i−2i000000000000
χ332-22-2200-22-222-22-2-22-200000022-2-222-2-20000000000-222-22-2-22000000-222-200000000002-2-220000000000000000
χ342-22-2200-22-222-22-2-22-200000022-2-222-2-20000000000-222-2-222-2000000-222-20000000000-222-20000000000000000
χ352-2-2222-2-2-2222-2-22-2-222-222-2-222-2-2-2-2222-22222-2-2-2-2-2-22200000000-22-2-22200000000-2200000000000000000000
χ362-2-222-22-2-2222-2-22-2-22-22-2-22222-2-2-2-222-22-2-2-2-22222-2-222000000002-2-2-222000000002-200000000000000000000
χ372-2-22-12-211-122-2-22-2-22-1122-2-2-1-11111-1-12-2-1-1-1-1111122-2-2000000002-2-1-11100002i−2i2i−2i-1100000000−i−iii−i−iii0000
χ382-2-22-12-211-122-2-22-2-22-1122-2-2-1-11111-1-12-2-1-1-1-1111122-2-2000000002-2-1-1110000−2i2i−2i2i-1100000000ii−i−iii−i−i0000
χ392-2-22-12-211-122-2-22-2-22-1122-2-2-1-11111-1-12-2-1-1-1-11111-2-22200000000-2211-1-1000000001-100000000−i3i3i3−i3−i3i3i3−i30000
χ402-2-22-12-211-122-2-22-2-22-1122-2-2-1-11111-1-12-2-1-1-1-11111-2-22200000000-2211-1-1000000001-100000000i3−i3−i3i3i3−i3−i3i30000
χ412-2-22-1-2211-122-2-22-2-221-1-2-222-1-11111-1-1-221111-1-1-1-122-2-200000000-22-1-11100002i−2i−2i2i1-100000000−i−iiiii−i−i0000
χ422-2-22-1-2211-122-2-22-2-221-1-2-222-1-11111-1-1-221111-1-1-1-122-2-200000000-22-1-1110000−2i2i2i−2i1-100000000ii−i−i−i−iii0000
χ432-2-22-1-2211-122-2-22-2-221-1-2-222-1-11111-1-1-221111-1-1-1-1-2-222000000002-211-1-100000000-1100000000−i3i3i3−i3i3−i3−i3i30000
χ442-2-22-1-2211-122-2-22-2-221-1-2-222-1-11111-1-1-221111-1-1-1-1-2-222000000002-211-1-100000000-1100000000i3−i3−i3i3−i3i3i3−i30000
χ4544444444441-211-2-2-2144-2-2-2-21-21-21-21-21111-2-211-2-200000000000000000022220000000000000000000000-1-1-1-1
χ4644444444441-211-2-2-2144-2-2-2-21-21-21-21-21111-2-211-2-2000000000000000000-2-2-2-200000000000000000000001111
χ474444444444-21-2-2111-2441111-21-21-21-21-2-2-2-211-2-2110000222222220000000000000000-1-1-1-1-1-1-1-1000000000000
χ484444444444-21-2-2111-2441111-21-21-21-21-2-2-2-211-2-2110000-2-2-2-2-2-2-2-2000000000000000011111111000000000000
χ4944444-4-44441-211-2-2-21-4-422221-21-21-21-2-1-1-1-122-1-12200000000000000000022-2-20000000000000000000000-1-111
χ5044444-4-44441-211-2-2-21-4-422221-21-21-21-2-1-1-1-122-1-122000000000000000000-2-222000000000000000000000011-1-1
χ5144444-4-4444-21-2-2111-2-4-4-1-1-1-1-21-21-21-212222-1-122-1-100002222-2-2-2-20000000000000000-1-1-1-11111000000000000
χ5244444-4-4444-21-2-2111-2-4-4-1-1-1-1-21-21-21-212222-1-122-1-10000-2-2-2-2222200000000000000001111-1-1-1-1000000000000
χ5344-4-44004-4-4-21-22-11-12003i−3i3i−3i-21-212-12-100003i−3i003i−3i00002i−2i2i−2i2-22-20000000000000000−ii−ii-11-11000000000000
χ5444-4-44004-4-4-21-22-11-12003i−3i3i−3i-21-212-12-100003i−3i003i−3i0000−2i2i−2i2i-22-220000000000000000i−ii−i1-11-1000000000000
χ5544-4-44004-4-4-21-22-11-1200−3i3i−3i3i-21-212-12-10000−3i3i00−3i3i00002i−2i2i−2i-22-220000000000000000−ii−ii1-11-1000000000000
χ5644-4-44004-4-4-21-22-11-1200−3i3i−3i3i-21-212-12-10000−3i3i00−3i3i0000−2i2i−2i2i2-22-20000000000000000i−ii−i-11-11000000000000
χ5744-4-4-200-222444-4-44-4-4000000-2-2-2-2222200000000004-44-40000000000-22-22000000000000000000000000000000
χ5844-4-4-200-222444-4-44-4-4000000-2-2-2-222220000000000-44-4400000000002-22-2000000000000000000000000000000
χ594-44-4400-44-4-212-2-1-112003i−3i−3i3i-212-1-212-100003i−3i00−3i3i00002-2-22−2i2i2i−2i0000000000000000-111-1i−i−ii000000000000
χ604-44-4400-44-4-212-2-1-112003i−3i−3i3i-212-1-212-100003i−3i00−3i3i0000-222-22i−2i−2i2i00000000000000001-1-11−iii−i000000000000
χ614-44-4400-44-4-212-2-1-11200−3i3i3i−3i-212-1-212-10000−3i3i003i−3i00002-2-222i−2i−2i2i0000000000000000-111-1−iii−i000000000000
χ624-44-4400-44-4-212-2-1-11200−3i3i3i−3i-212-1-212-10000−3i3i003i−3i0000-222-2−2i2i2i−2i00000000000000001-1-11i−i−ii000000000000
χ634-44-4-2002-2244-44-4-44-4000000-2-222-2-22200000000004-4-440000000000-222-2000000000000000000000000000000
χ644-44-4-2002-2244-44-4-44-4000000-2-222-2-2220000000000-444-400000000002-2-22000000000000000000000000000000
χ654-4-4444-4-4-441-2-1-1-22214-4-2-2221-2-12-121-21-111-2-2-1-1220000000000000000002-22-20000000000000000000000-11-11
χ664-4-4444-4-4-441-2-1-1-22214-4-2-2221-2-12-121-21-111-2-2-1-122000000000000000000-22-2200000000000000000000001-11-1
χ674-4-4444-4-4-44-21221-1-1-24-411-1-1-212-12-1-21-22-2-21122-1-100002i2i−2i−2i2i2i−2i−2i0000000000000000−i−iii−i−iii000000000000
χ684-4-4444-4-4-44-21221-1-1-24-411-1-1-212-12-1-21-22-2-21122-1-10000−2i−2i2i2i−2i−2i2i2i0000000000000000ii−i−iii−i−i000000000000
χ694-4-444-44-4-441-2-1-1-2221-4422-2-21-2-12-121-2-11-1-12211-2-20000000000000000002-2-220000000000000000000000-111-1
χ704-4-444-44-4-441-2-1-1-2221-4422-2-21-2-12-121-2-11-1-12211-2-2000000000000000000-222-200000000000000000000001-1-11
χ714-4-444-44-4-44-21221-1-1-2-44-1-111-212-12-1-212-222-1-1-2-21100002i2i−2i−2i−2i−2i2i2i0000000000000000−i−iiiii−i−i000000000000
χ724-4-444-44-4-44-21221-1-1-2-44-1-111-212-12-1-212-222-1-1-2-2110000−2i−2i2i2i2i2i−2i−2i0000000000000000ii−i−i−i−iii000000000000
χ738888-488-4-4-42-422-4-4-42-4-4-4-4-4-4-12-12-12-1222-1-122-1-122000000000000000000000000000000000000000000000000
χ748888-488-4-4-4-42-4-4222-4-4-422222-12-12-12-1-4-422-1-122-1-1000000000000000000000000000000000000000000000000
χ758888-4-8-8-4-4-42-422-4-4-42444444-12-12-12-12-2-211-2-211-2-2000000000000000000000000000000000000000000000000
χ768888-4-8-8-4-4-4-42-4-4222-444-2-2-2-22-12-12-12-144-2-211-2-211000000000000000000000000000000000000000000000000
χ7788-8-88008-8-82-42-24-44-20000002-42-4-24-240000000000000000000000000000000000000000000000000000000000
χ7888-8-8-400-4442-42-24-44-2000000-12-121-21-20033−330033−3300000000000000000000000000000000000000000000000000
χ7988-8-8-400-4442-42-24-44-2000000-12-121-21-200−333300−333300000000000000000000000000000000000000000000000000
χ8088-8-8-400-444-42-44-22-24006i−6i6i−6i2-12-1-21-210000−3i3i00−3i3i000000000000000000000000000000000000000000000000
χ8188-8-8-400-444-42-44-22-2400−6i6i−6i6i2-12-1-21-2100003i−3i003i−3i000000000000000000000000000000000000000000000000
χ828-88-8800-88-82-4-2244-4-20000002-4-242-4-240000000000000000000000000000000000000000000000000000000000
χ838-88-8-4004-442-4-2244-4-2000000-121-2-121-20033−3300−333300000000000000000000000000000000000000000000000000
χ848-88-8-4004-442-4-2244-4-2000000-121-2-121-200−33330033−3300000000000000000000000000000000000000000000000000
χ858-88-8-4004-44-424-4-2-224006i−6i−6i6i2-1-212-1-210000−3i3i003i−3i000000000000000000000000000000000000000000000000
χ868-88-8-4004-44-424-4-2-22400−6i6i6i−6i2-1-212-1-2100003i−3i00−3i3i000000000000000000000000000000000000000000000000
χ878-8-88-48-844-42-4-2-2-4442-44-4-444-121-21-2-122-2-1-12211-2-2000000000000000000000000000000000000000000000000
χ888-8-88-48-844-4-42442-2-2-4-4422-2-22-1-21-212-1-4422-1-1-2-211000000000000000000000000000000000000000000000000
χ898-8-88-4-8844-42-4-2-2-44424-444-4-4-121-21-2-12-2211-2-2-1-122000000000000000000000000000000000000000000000000
χ908-8-88-4-8844-4-42442-2-2-44-4-2-2222-1-21-212-14-4-2-21122-1-1000000000000000000000000000000000000000000000000

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