Finite Group Databasebeta

← Group #13170767

Character table — Group #13170767

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size111122222222222244444444444446666668888888888888888812121212121212121212121212121218181818181824242424242424242424242424242424242427272727363636363636363636727272108
order12223336666666663334666666666224444366612121212121212121212121212444666612121212121212122244446612121212121212121212121212121212222244466121212121212124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-11111111111111111111-1111111-1-1-1-111-1-111-1-11111-111-1111111-1-1-1-1-1-1-1-1-1-11-1-1-1-111-1-11-1
χ31111111111111111111111111111111-1-111111111111111111111-111111-1-11111-1-1-1-1-1-111111-111-1111-1-1-1-11111-1-1-1-11-1-1-1-111-1-11-1-1-1
χ41111111111111111111111111111111-1-1-1-1111111111111111111-1-11111-1-1-1-1-1-1-1-111-1-1-1-1111-1-11-1-111-1-1-1-1-1-1-1-11111-11-111-1-1-1-1-11-11
χ511111111111111111111111111111-1-1111111111111111111111-111-1-1-1-11111111111-1-1-1-1-1-1-111-111-1-111111111-1-1-1-1-11-111-1-1-1-1-11-1-1
χ611111111111111111111111111111-1-111-1-111111111111111111-11-1-1-1-1-111-1-1-1-111-1-1-1-111-1-1-11-1-11-1-1-11111-1-1-1-111111-1-1-1-111-1-11-1-11
χ711111111111111111111111111111-1-1-1-11111111111111111111-1-11-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-11-1-11-1-1-1-1-1-111111111-1-11-1-1-1-111-1-111
χ811111111111111111111111111111-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1
χ91111111111111111111-11111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1111111-1-1-1-1
χ101111111111111111111-11111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-1-111-1-111-1-111-1-11-1-11-1-1-1-111-1-111-1-1-1-111-1-1-1-1-11111-11
χ111111111111111111111-111111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11111-1-11111-1-1-1-1-1-11111-11-1-11-1-1-111-1-111-1-1-1-1-1-1-111-1-111-1-1-1111
χ121111111111111111111-111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-111-111-111-1-111-1-1-1-11111111-1111-1-1-1-11-11-1
χ131111111111111111111-1111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-11111111111-1-1-1-1-1-11-1-11-1-111-1-11111-1-1-1-1-1-11-1111-1-1-1-11-111
χ141111111111111111111-1111111111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-111-1-1-1-111-1-1-1-111-1-11-111-1111-1-111-1-1111111-111-1-111-1-1-111-1
χ151111111111111111111-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111-111-11111-1-111-1-1111111-1-1-1-1-11111-1-1
χ161111111111111111111-1111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-11111111111-1-1-1-111-1-1-1-1-1-1-1111111-1-1-11
χ17222222-122-12-12-122-1-122-1-1-122-12-1-1002222-1-1-1-1-12222-1-1-1-1-1-1-1-10220000-1-1-1-122222200000002-10-1200-1-1-1-1-1-1-1-10000020-1-100000-100
χ18222222-122-12-12-122-1-122-1-1-122-12-1-10022-2-2-1-1-1-1-12222-1-1-1-1-1-1-1-102-20000-1-111-2-222-2-20000000210-1-200-1-1-1-1111100000-201100000100
χ19222222-122-12-12-122-1-122-1-1-122-12-1-100-2-222-1-1-1-1-12222-1-1-1-1-1-1-1-10-22000011-1-122-2-2-2-20000000-2-1012001111-1-1-1-100000-201100000100
χ20222222-122-12-12-122-1-122-1-1-122-12-1-100-2-2-2-2-1-1-1-1-12222-1-1-1-1-1-1-1-10-2-200001111-2-2-2-2220000000-2101-200111111110000020-1-100000-100
χ21222222-122-12-12-122-1-12-2-1-1-122-12-1-1002222-1-1-1-11-2-2-2-2111111110-2-20000-1-1-1-12222220000000-2101-20011-1-1-1-11100000-20-1-100000100
χ22222222-122-12-12-122-1-12-2-1-1-122-12-1-10022-2-2-1-1-1-11-2-2-2-2111111110-220000-1-111-2-222-2-20000000-2-10120011-1-111-1-100000201100000-100
χ23222222-122-12-12-122-1-12-2-1-1-122-12-1-100-2-222-1-1-1-11-2-2-2-21111111102-2000011-1-122-2-2-2-20000000210-1-200-1-111-1-11100000201100000-100
χ24222222-122-12-12-122-1-12-2-1-1-122-12-1-100-2-2-2-2-1-1-1-11-2-2-2-21111111102200001111-2-2-2-22200000002-10-1200-1-11111-1-100000-20-1-100000100
χ2522222-122-1222-12-122-1-122-1-1-1-12-12-1220022-1-1-1-12-12-1-122-1-1-1-1-1-120222-1-10022-1-100000022-1-1202-10-1-1-10000-1-1-1-1000020000-1-100-1000
χ2622222-122-1222-12-122-1-122-1-1-1-12-12-12200-2-2-1-1-1-12-12-1-122-1-1-1-1-1-120-222-1-100-2-211000000-2-2-1-120-2-101-1-1000011110000-2000011001000
χ2722222-122-1222-12-122-1-122-1-1-1-12-12-1-2-20022-1-1-1-12-12-1-122-1-1-1-1-1-1-202-2-2110022-1-1000000-2-211-20210-1110000-1-1-1-10000-2000011001000
χ2822222-122-1222-12-122-1-122-1-1-1-12-12-1-2-200-2-2-1-1-1-12-12-1-122-1-1-1-1-1-1-20-2-2-21100-2-2110000002211-20-21011100001111000020000-1-100-1000
χ2922222-122-1222-12-122-1-1-22-1-1-1-12-12-1220022-1-1-1-1-21-211-2-2111111-20-222-1-10022-1-100000022-1-1-20-2101110000-1-1110000-20000-1-1001000
χ3022222-122-1222-12-122-1-1-22-1-1-1-12-12-12200-2-2-1-1-1-1-21-211-2-2111111-20222-1-100-2-211000000-2-2-1-1-20210-111000011-1-10000200001100-1000
χ3122222-122-1222-12-122-1-1-22-1-1-1-12-12-1-2-20022-1-1-1-1-21-211-2-211111120-2-2-2110022-1-1000000-2-21120-2-101-1-10000-1-1110000200001100-1000
χ3222222-122-1222-12-122-1-1-22-1-1-1-12-12-1-2-200-2-2-1-1-1-1-21-211-2-2111111202-2-21100-2-2110000002211202-10-1-1-1000011-1-10000-20000-1-1001000
χ332222-122-122-12222-1-12-12-122-1-1-1-1-12222200-1-1-1-122-1-1-1-1-122-1-1-1-1220-1-122220000-1-1002200-1-1-1-10220-1-1-1-1-1-1000000000020000-1-100-10
χ342222-122-122-12222-1-12-12-122-1-1-1-1-1222-2-200-1-1-1-122-1-1-1-1-122-1-1-1-12-20-1-122-2-200001100-2-200-1-1-1102-20-1-111110000000000-20000110010
χ352222-122-122-12222-1-12-12-122-1-1-1-1-12-2-22200-1-1-1-122-1-1-1-1-122-1-1-1-1-22011-2-2220000-1-100-2-200111-10-22011-1-1-1-10000000000-20000110010
χ362222-122-122-12222-1-12-12-122-1-1-1-1-12-2-2-2-200-1-1-1-122-1-1-1-1-122-1-1-1-1-2-2011-2-2-2-200001100220011110-2-20111111000000000020000-1-100-10
χ372222-122-122-12222-1-12-1-2-122-1-1-1-1-12222200-1-1-1-1-2-211111-2-21111-2-20-1-122220000-1-1002200-1-1110-2-201111-1-10000000000-20000-1-10010
χ382222-122-122-12222-1-12-1-2-122-1-1-1-1-1222-2-200-1-1-1-1-2-211111-2-21111-220-1-122-2-200001100-2-200-1-11-10-22011-1-1110000000000200001100-10
χ392222-122-122-12222-1-12-1-2-122-1-1-1-1-12-2-22200-1-1-1-1-2-211111-2-211112-2011-2-2220000-1-100-2-20011-1102-20-1-111-1-10000000000200001100-10
χ402222-122-122-12222-1-12-1-2-122-1-1-1-1-12-2-2-2-200-1-1-1-1-2-211111-2-2111122011-2-2-2-200001100220011-1-10220-1-1-1-1110000000000-20000-1-10010
χ4122-2-2222222-2-2-2-2-2-2222022-22-2-2-2-2-22-2000022-2-200000000000000002-22-2000000002-200002-2000000000000000022-2-20002-200000000
χ4222-2-2222222-2-2-2-2-2-2222022-22-2-2-2-2-22-2000022-2-200000000000000002-22-200000000-2200002-20000000000000000-2-222000-2200000000
χ4322-2-2222222-2-2-2-2-2-2222022-22-2-2-2-2-2-22000022-2-20000000000000000-22-22000000002-20000-220000000000000000-2-2220002-200000000
χ4422-2-2222222-2-2-2-2-2-2222022-22-2-2-2-2-2-22000022-2-20000000000000000-22-2200000000-220000-22000000000000000022-2-2000-2200000000
χ452-22-2222-2-2-22-222-2-22220-2-22-2-222-2-2002i−2i002-22-2000000000000000000002i−2i00002i−2i00002i−2i0000000000002i−2i00002-22-2000002i−2i000000
χ462-22-2222-2-2-22-222-2-22220-2-22-2-222-2-2002i−2i002-22-2000000000000000000002i−2i00002i−2i0000−2i2i0000000000002i−2i0000-22-2200000−2i2i000000
χ472-22-2222-2-2-22-222-2-22220-2-22-2-222-2-200−2i2i002-22-200000000000000000000−2i2i0000−2i2i00002i−2i000000000000−2i2i0000-22-22000002i−2i000000
χ482-22-2222-2-2-22-222-2-22220-2-22-2-222-2-200−2i2i002-22-200000000000000000000−2i2i0000−2i2i0000−2i2i000000000000−2i2i00002-22-200000−2i2i000000
χ492-2-22222-2-2-2-22-2-2222220-2-2-2-22-2-22200002-22-2-2200000000000000000000002-22-200002-200000000000000002-2002-2-2200000002-20000
χ502-2-22222-2-2-2-22-2-2222220-2-2-2-22-2-22200002-22-2-2200000000000000000000002-22-20000-2200000000000000002-200-222-20000000-220000
χ512-2-22222-2-2-2-22-2-2222220-2-2-2-22-2-2220000-222-2-220000000000000000000000-22-2200002-20000000000000000-2200-222-200000002-20000
χ522-2-22222-2-2-2-22-2-2222220-2-2-2-22-2-2220000-222-2-220000000000000000000000-22-220000-220000000000000000-22002-2-220000000-220000
χ5344444-2-24-2-24-2-2-2-24-21-24-211-2-2-2-2-210000441111-2-24-2-2-2-2111111004000000-2-2-2-2000000000000-200-2000000111100000000000000000
χ5444444-2-24-2-24-2-2-2-24-21-24-211-2-2-2-2-210000-4-41111-2-24-2-2-2-211111100-400000022220000000000002002000000-1-1-1-100000000000000000
χ5544444-2-24-2-24-2-2-2-24-21-2-4-211-2-2-2-2-21000044111122-42222-1-1-1-1-1-100-4000000-2-2-2-2000000000000200200000011-1-100000000000000000
χ5644444-2-24-2-24-2-2-2-24-21-2-4-211-2-2-2-2-210000-4-4111122-42222-1-1-1-1-1-10040000002222000000000000-200-2000000-1-11100000000000000000
χ574444-24-2-24-2-2-24-24-21-2-241-2-2-2-21-21-20044001111-24-2-2-211-2-211110400000-2-20000-2-2000000000-200-20001111000000000000000000000
χ584444-24-2-24-2-2-24-24-21-2-241-2-2-2-21-21-200-4-4001111-24-2-2-211-2-211110-400000220000220000000002002000-1-1-1-1000000000000000000000
χ594444-24-2-24-2-2-24-24-21-2-2-41-2-2-2-21-21-200440011112-4222-1-122-1-1-1-10-400000-2-20000-2-20000000002002000-1-111000000000000000000000
χ604444-24-2-24-2-2-24-24-21-2-2-41-2-2-2-21-21-200-4-40011112-4222-1-122-1-1-1-1040000022000022000000000-200-200011-1-1000000000000000000000
χ614444-2-24-2-24-24-24-2-2-2-214-2-2-211-21-2-244000011114-2-211-2-2-2-21111400-2-2-2-20000000000000011-200-200110000000000000000000000000
χ624444-2-24-2-24-24-24-2-2-2-214-2-2-211-21-2-2-4-4000011114-2-211-2-2-2-21111-400222200000000000000-1-1200200-1-10000000000000000000000000
χ634444-2-24-2-24-24-24-2-2-2-21-4-2-2-211-21-2-24400001111-422-1-12222-1-1-1-1-400-2-2-2-20000000000000011200200-1-10000000000000000000000000
χ644444-2-24-2-24-24-24-2-2-2-21-4-2-2-211-21-2-2-4-400001111-422-1-12222-1-1-1-1400222200000000000000-1-1-200-200110000000000000000000000000
χ6544-4-444-244-2-42-42-4-4-2-240-2-224-42-422000000-2-22200000000000000000000000000004-400000000000000000000000000000-2200000000
χ6644-4-444-244-2-42-42-4-4-2-240-2-224-42-422000000-2-2220000000000000000000000000000-44000000000000000000000000000002-200000000
χ6744-4-44-244-24-4-42-42-44-2-204-22-22-42-424-40000-2-22200000000000000004-4-2200000000000000-22000000000000000000000000000000000
χ6844-4-44-244-24-4-42-42-44-2-204-22-22-42-42-440000-2-2220000000000000000-442-2000000000000002-2000000000000000000000000000000000
χ6944-4-4-244-2442-4-4-4-42-24-20-24-4-22222-44-40000-2-2220000000000000000-224-400000000000000-22000000000000000000000000000000000
χ7044-4-4-244-2442-4-4-4-42-24-20-24-4-22222-4-440000-2-22200000000000000002-2-44000000000000002-2000000000000000000000000000000000
χ7144-4-4-2-24-2-242-42-422-2-210-2-221-12-1224-4000011-1-10003i−3i00003i3i−3i−3i000-22-22000000000000001-10000003i−3i0000000000000000000000000
χ7244-4-4-2-24-2-242-42-422-2-210-2-221-12-1224-4000011-1-1000−3i3i0000−3i−3i3i3i000-22-22000000000000001-1000000−3i3i0000000000000000000000000
χ7344-4-4-2-24-2-242-42-422-2-210-2-221-12-122-44000011-1-10003i−3i00003i3i−3i−3i0002-22-200000000000000-11000000−3i3i0000000000000000000000000
χ7444-4-4-2-24-2-242-42-422-2-210-2-221-12-122-44000011-1-1000−3i3i0000−3i−3i3i3i0002-22-200000000000000-110000003i−3i0000000000000000000000000
χ754-44-444-2-4-42424-2-4-4-2-24022-2-4-4-2422004i−4i00-22-2200000000000000000000−2i2i00004i−4i000000000000000000−2i2i000000000000000000000
χ764-44-444-2-4-42424-2-4-4-2-24022-2-4-4-242200−4i4i00-22-22000000000000000000002i−2i0000−4i4i0000000000000000002i−2i000000000000000000000
χ774-44-44-24-42-44-4-242-44-2-20-42-2224-2-42000000-22-22000000000000000000000000000000004i−4i000000000000000000000000000−2i2i000000
χ784-44-44-24-42-44-4-242-44-2-20-42-2224-2-42000000-22-2200000000000000000000000000000000−4i4i0000000000000000000000000002i−2i000000
χ794-44-4-2442-4-4-2-444-42-24-202-4422-2-22-4004i−4i00-22-22000000000000000000004i−4i0000−2i2i000000000000000000−2i2i000000000000000000000
χ804-44-4-2442-4-4-2-444-42-24-202-4422-2-22-400−4i4i00-22-2200000000000000000000−4i4i00002i−2i0000000000000000002i−2i000000000000000000000
χ814-44-4-24-22-42-224-2-421-2-20-12-2221-2-12004i−4i001-11-1000003i−3i003i−3i3i−3i0000000−2i2i0000−2i2i00000000000000003-3i−i000000000000000000000
χ824-44-4-24-22-42-224-2-421-2-20-12-2221-2-12004i−4i001-11-100000−3i3i00−3i3i−3i3i0000000−2i2i0000−2i2i0000000000000000-33i−i000000000000000000000
χ834-44-4-24-22-42-224-2-421-2-20-12-2221-2-1200−4i4i001-11-1000003i−3i003i−3i3i−3i00000002i−2i00002i−2i0000000000000000-33−ii000000000000000000000
χ844-44-4-24-22-42-224-2-421-2-20-12-2221-2-1200−4i4i001-11-100000−3i3i00−3i3i−3i3i00000002i−2i00002i−2i00000000000000003-3−ii000000000000000000000
χ854-4-4444-2-4-42-4-2-4244-2-240222-442-4-2-200004-4-222-20000000000000000000000-224-40000000000000000000000-220000000000000000000
χ864-4-4444-2-4-42-4-2-4244-2-240222-442-4-2-20000-44-222-200000000000000000000002-2-4400000000000000000000002-20000000000000000000
χ874-4-444-24-42-4-442-4-244-2-20-4222-2-424-200004-4-222-200000000000000000000004-4-220000000000000000000000-220000000000000000000
χ884-4-444-24-42-4-442-4-244-2-20-4222-2-424-20000-44-222-20000000000000000000000-442-200000000000000000000002-20000000000000000000
χ894-4-444-2-2-422-4-222-24-21-202-1-12-222-2100004-41-1-1100000003-33-3-33000000000-22-2200000000000000000000001-13-300000000000000000
χ904-4-444-2-2-422-4-222-24-21-202-1-12-222-2100004-41-1-110000000-33-333-3000000000-22-2200000000000000000000001-1-3300000000000000000
χ914-4-444-2-2-422-4-222-24-21-202-1-12-222-210000-441-1-1100000003-33-3-330000000002-22-20000000000000000000000-11-3300000000000000000
χ924-4-444-2-2-422-4-222-24-21-202-1-12-222-210000-441-1-110000000-33-333-30000000002-22-20000000000000000000000-113-300000000000000000
χ934-4-44-2442-4-424-4-44-2-24-202-4-42-222-24000000-222-20000000000000000000000000000004-40000000000000000000000000000000-220000
χ944-4-44-2442-4-424-4-44-2-24-202-4-42-222-24000000-222-2000000000000000000000000000000-4400000000000000000000000000000002-20000
χ958888-4-4-4-4-4-4-4-4-4-4-4-42228222222222000000-1-1-1-1-4-4-4222222-1-1-1-100000000000000000000000000000000000000000000000000000000
χ968888-4-4-4-4-4-4-4-4-4-4-4-4222-8222222222000000-1-1-1-1444-2-2-2-2-2-2111100000000000000000000000000000000000000000000000000000000
χ9788-8-88-4-48-4-4-84444-8-42-40-42-2-44444-200000022-2-2000000000000000000000000000000000000000000000000000000000000000000000
χ9888-8-8-48-4-48-444-84-842-4-402-44-44-24-2400000022-2-2000000000000000000000000000000000000000000000000000000000000000000000
χ9988-8-8-4-4-4-4-4-4444444222022-22-2-2-2-2-2000000-1-1110006i−6i0000−3i−3i3i3i00000000000000000000000000000000000000000000000000000000
χ10088-8-8-4-4-4-4-4-4444444222022-22-2-2-2-2-2000000-1-111000−6i6i00003i3i−3i−3i00000000000000000000000000000000000000000000000000000000
χ1018-88-88-4-4-84484-4-44-8-42-404-2244-4-44-20000002-22-2000000000000000000000000000000000000000000000000000000000000000000000
χ1028-88-8-4-4844-8-4-8-4844-4-42044-4-2-2-42440000002-22-2000000000000000000000000000000000000000000000000000000000000000000000
χ1038-88-8-4-4-4444-44-4-4442220-2-22-2-222-2-2000000-11-11000006i−6i00−3i3i−3i3i00000000000000000000000000000000000000000000000000000000
χ1048-88-8-4-4-4444-44-4-4442220-2-22-2-222-2-2000000-11-1100000−6i6i003i−3i3i−3i00000000000000000000000000000000000000000000000000000000
χ1058-8-88-48-44-844-4-848-42-4-40-2444-4-242-40000002-2-22000000000000000000000000000000000000000000000000000000000000000000000
χ1068-8-88-4-4844-8484-8-4-4-4-420444-224-2-4-40000002-2-22000000000000000000000000000000000000000000000000000000000000000000000
χ1078-8-88-4-4-44444-444-4-42220-2-2-2-22-2-222000000-111-100000006-6-333-300000000000000000000000000000000000000000000000000000000
χ1088-8-88-4-4-44444-444-4-42220-2-2-2-22-2-222000000-111-10000000-663-3-3300000000000000000000000000000000000000000000000000000000

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