Finite Group Databasebeta

← Group #13168223

Character table — Group #13168223

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size1111222222222222444444444444466888888888888888881212121212121212121212121212121212181824242424242424242424242424242424242436363636363636363636365454727272108
order12223336666666663334666666666223666121212121212121212121212122444466666612121212121244666661212121212121212121212121244444121212121212441212122
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111-1-1111111-1-1-1-111-1-111111111-1-11111-1-1-1-1-111-1-1-1-1-1-111-1-1-1-11-1
χ3111111111111111111111111111111111111111111111111-11-11111-1-1111111-1-1-1-1-111-1-111-11111-1-111111-1-1-1111-1-1-1-1-1-11-1-1-1
χ4111111111111111111111111111111111111111111111111-11-1-1-111-1-111-1-1-1-1-1-111-111-1-111-1-1-111-1-1-1-1-1-1-1-1-11-1-1-111-1-111-11-11
χ511111111111111111111111111111-1-1111111111111111111-1111-1-111-1-1111111111-1-111-1-1111-1-1111111-1-1-11-1-1-111-1-1-1-1-11-1-1
χ611111111111111111111111111111-1-1111111111111111111-11-1-1-1-111-1-1-1-1-1-111-1-11-1-111-1-11-1-1-1-111-1-1-1-11-1-1-1111-1-1-1-1111-1-11
χ711111111111111111111111111111-1-111111111111111111-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-111-1-1-1-1-1-11111-1-111
χ811111111111111111111111111111-1-111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1111-1
χ91111111111111111111-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-111111111-1-1-1-11111111-1-1-11-1-1-1-1-111-1-111-1-1-1-1-111-1-1111-11-1
χ101111111111111111111-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11111111-1-111-1-1-1-111111-1-1-1-11-1-1-1-1-1-111-11-11111-1-1-1-1-1-1-1111
χ111111111111111111111-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-11111-1-111-1-1-111-1-1-1-111-1-1-11111-1-11-111-1-1-1-1-111-1-111-11
χ121111111111111111111-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1111-1-111-1-1111111-111-1-1-1-11-11-1-111-1-111-1-11-1111111111-1-1-1-1
χ131111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-11-1-1-111-1-111-1-1-1-1111-1-11111-11-111-1-111-1-1-1-11-11111111-1-1-1-1-11
χ141111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11-1-111-1-1-1-111-1-1-1-11-1-11111-1-1111-1-1-1-1111-111-1-1-1-1-1111111-1-1
χ151111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-11111-1111111-1-1-11-11111-1-1-1-111-111-1
χ161111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11-1-1-1-1-1-1-1-1111111-1-1-1-1-1111-111111-1-11111-1-1-1-1-111-1-1-1-11-111
χ17222222-122-1-12222-12-1-1222-1-1-1-1-1-1222-1-1-1-1-122-1-1-1-122-1-1-1-1222002222-1-10000-1-100-1-1-1-1-1-12200-1-1-1-10000022000000-1-10000-10
χ18222222-122-1-12222-12-1-1222-1-1-1-1-1-1222-1-1-1-1-122-1-1-1-122-1-1-1-1-22-20022-2-2-1-1000011001-1-111-12-200-1-11100000-2-200000011000010
χ19222222-122-1-12222-12-1-1222-1-1-1-1-1-12-2-2-1-1-1-1-122-1-1-1-122-1-1-1-12-2200-2-222110000-1-100-111-1-11-220011-1-100000-2-200000011000010
χ20222222-122-1-12222-12-1-1222-1-1-1-1-1-12-2-2-1-1-1-1-122-1-1-1-122-1-1-1-1-2-2-200-2-2-2-21100001100111111-2-20011110000022000000-1-10000-10
χ21222222-122-1-12222-12-1-1-222-1-1-1-1-1-1222-1-1-1-11-2-21111-2-211112-2-2002222-1-100001100-1-1-1-1-11-2-2001111000002-2000000110000-10
χ22222222-122-1-12222-12-1-1-222-1-1-1-1-1-1222-1-1-1-11-2-21111-2-21111-2-220022-2-2-1-10000-1-1001-1-1111-220011-1-100000-22000000-1-1000010
χ23222222-122-1-12222-12-1-1-222-1-1-1-1-1-12-2-2-1-1-1-11-2-21111-2-2111122-200-2-2221100001100-111-1-1-12-200-1-11100000-22000000-1-1000010
χ24222222-122-1-12222-12-1-1-222-1-1-1-1-1-12-2-2-1-1-1-11-2-21111-2-21111-22200-2-2-2-2110000-1-10011111-12200-1-1-1-1000002-2000000110000-10
χ2522222-122-1222-12-12-12-12-1-12-12-12-1-100-1-1-1-122-122-1-1-1-1-1-1-1-12022200-1-100-1-1222222200-1-100-12-100-1-1-1-1-1-10002000-1-100000-100
χ2622222-122-1222-12-12-12-12-1-12-12-12-1-100-1-1-1-122-122-1-1-1-1-1-1-1-1202-2-200-1-10011-2-222-2-2200-1-100-1-2100-1-11111000-20001100000100
χ2722222-122-1222-12-12-12-12-1-12-12-12-1-100-1-1-1-122-122-1-1-1-1-1-1-1-1-20-222001100-1-122-2-2-2-2-200110012-10011-1-1-1-1000-20001100000100
χ2822222-122-1222-12-12-12-12-1-12-12-12-1-100-1-1-1-122-122-1-1-1-1-1-1-1-1-20-2-2-200110011-2-2-2-222-20011001-21001111110002000-1-100000-100
χ2922222-122-1222-12-12-12-1-2-1-12-12-12-1-100-1-1-1-1-2-21-2-21111111120-22-200-1-100-1-1-2-2-2-222200-1-1001210011-1-111000-2000-1-100000100
χ3022222-122-1222-12-12-12-1-2-1-12-12-12-1-100-1-1-1-1-2-21-2-21111111120-2-2200-1-1001122-2-2-2-2200-1-1001-2-1001111-1-100020001100000-100
χ3122222-122-1222-12-12-12-1-2-1-12-12-12-1-100-1-1-1-1-2-21-2-211111111-2022-2001100-1-1-2-222-2-2-2001100-12100-1-1-1-11100020001100000-100
χ3222222-122-1222-12-12-12-1-2-1-12-12-12-1-100-1-1-1-1-2-21-2-211111111-202-2200110011222222-2001100-1-2-100-1-111-1-1000-2000-1-100000100
χ332222-122-1222-12-122-1-122-1-1-12-12-12-122-1-1-1-12-12-1-122-1-1-1-1-1-102022-1-1002222-1-100000-1-1002-10-12-1-100-1-1-1-120002-1-1000000-1000
χ342222-122-1222-12-122-1-122-1-1-12-12-12-122-1-1-1-12-12-1-122-1-1-1-1-1-1020-2-2-1-10022-2-21100000-1-1002-101-2-1-1001111-2000-2110000001000
χ352222-122-1222-12-122-1-122-1-1-12-12-12-1-2-2-1-1-1-12-12-1-122-1-1-1-1-1-10-20221100-2-222-1-1000001100-210-121100-1-1-1-1-2000-2110000001000
χ362222-122-1222-12-122-1-122-1-1-12-12-12-1-2-2-1-1-1-12-12-1-122-1-1-1-1-1-10-20-2-21100-2-2-2-211000001100-2101-21100111120002-1-1000000-1000
χ372222-122-1222-12-122-1-12-2-1-1-12-12-12-122-1-1-1-1-21-211-2-21111110-202-2-1-10022221100000-1-100-210-1-21100-1-1112000-211000000-1000
χ382222-122-1222-12-122-1-12-2-1-1-12-12-12-122-1-1-1-1-21-211-2-21111110-20-22-1-10022-2-2-1-100000-1-100-21012110011-1-1-20002-1-10000001000
χ392222-122-1222-12-122-1-12-2-1-1-12-12-12-1-2-2-1-1-1-1-21-211-2-21111110202-21100-2-222110000011002-10-1-2-1-100-1-111-20002-1-10000001000
χ402222-122-1222-12-122-1-12-2-1-1-12-12-12-1-2-2-1-1-1-1-21-211-2-2111111020-221100-2-2-2-2-1-10000011002-1012-1-10011-1-12000-211000000-1000
χ412-22-22222-2-2-2-22-2-2222202-22-2-2-2-22-22-222-2-20000000000000000002-2002-20000002i−2i02-200000000000000000000002i−2i002i−2i0000
χ422-22-22222-2-2-2-22-2-2222202-22-2-2-2-22-22-222-2-20000000000000000002-2002-2000000−2i2i02-20000000000000000000000−2i2i00−2i2i0000
χ432-22-22222-2-2-2-22-2-2222202-22-2-2-2-22-2-2222-2-2000000000000000000-2200-220000002i−2i0-2200000000000000000000002i−2i00−2i2i0000
χ442-22-22222-2-2-2-22-2-2222202-22-2-2-2-22-2-2222-2-2000000000000000000-2200-22000000−2i2i0-220000000000000000000000−2i2i002i−2i0000
χ4544444-2-24-2-2-24-24-2-2-2-214-2-2-21-21-21-2001111-24-2-2-211-2-211114040000-2-2000000-2-200-2001100-2000011000000000000000000000
χ4644444-2-24-2-2-24-24-2-2-2-214-2-2-21-21-21-2001111-24-2-2-211-2-21111-40-40000220000002200200-1-10020000-1-1000000000000000000000
χ4744444-2-24-2-2-24-24-2-2-2-21-4-2-2-21-21-21-20011112-4222-1-122-1-1-1-140-40000-2-20000002200-200110020000-1-1000000000000000000000
χ4844444-2-24-2-2-24-24-2-2-2-21-4-2-2-21-21-21-20011112-4222-1-122-1-1-1-1-404000022000000-2-200200-1-100-2000011000000000000000000000
χ494444-24-2-24-2-2-24-24-2-21-24-2-21-21-21-2-2441111-2-2411-2-2-2-2111104000-2-200-2-20000000001100-2-20001100000000000000000000000
χ504444-24-2-24-2-2-24-24-2-21-24-2-21-21-21-2-2-4-41111-2-2411-2-2-2-211110-4000220022000000000-1-10022000-1-100000000000000000000000
χ514444-24-2-24-2-2-24-24-2-21-2-4-2-21-21-21-2-244111122-4-1-12222-1-1-1-10-4000-2-200-2-2000000000110022000-1-100000000000000000000000
χ524444-24-2-24-2-2-24-24-2-21-2-4-2-21-21-21-2-2-4-4111122-4-1-12222-1-1-1-104000220022000000000-1-100-2-20001100000000000000000000000
χ534444-2-24-2-244-2-2-2-241-2-2411-2-2-2-2-2-210011114-2-2-2-2-2-211111100044000000-2-2-2-2000000000000-2-20000111100000000000000000
χ544444-2-24-2-244-2-2-2-241-2-2411-2-2-2-2-2-210011114-2-2-2-2-2-2111111000-4-40000002222000000000000220000-1-1-1-100000000000000000
χ554444-2-24-2-244-2-2-2-241-2-2-411-2-2-2-2-2-21001111-4222222-1-1-1-1-1-10004-4000000-2-222000000000000-22000011-1-100000000000000000
χ564444-2-24-2-244-2-2-2-241-2-2-411-2-2-2-2-2-21001111-4222222-1-1-1-1-1-1000-4400000022-2-20000000000002-20000-1-11100000000000000000
χ5744-4-4444-44-444-4-4-4-44440-44-44-4-44-4-4004-44-40000000000000000000000000000000000000000000000000000000000000000000
χ5844-4-444-2-442-24-4-4-424-2-20-442-222-22-400-22-22000000000000000000000000000023−230000000000000023−23000000000000000000000
χ5944-4-444-2-442-24-4-4-424-2-20-442-222-22-400-22-220000000000000000000000000000−232300000000000000−2323000000000000000000000
χ6044-4-44-24-4-2-4442-42-4-24-202-2-4-2-4242200-22-2200000000000000000000−2i32i30000000000000−2i32i3000000000000000000000000000000
χ6144-4-44-24-4-2-4442-42-4-24-202-2-4-2-4242200-22-22000000000000000000002i3−2i300000000000002i3−2i3000000000000000000000000000000
χ6244-4-44-2-2-4-22-242-422-2-2102-2212-1-2-12001-11-1000003i−3i003i3i−3i−3i0000000−2i32i300000023−2300000i3−i30000000−33000000000000000000000
χ6344-4-44-2-2-4-22-242-422-2-2102-2212-1-2-12001-11-1000003i−3i003i3i−3i−3i00000002i3−2i3000000−232300000−i3i300000003−3000000000000000000000
χ6444-4-44-2-2-4-22-242-422-2-2102-2212-1-2-12001-11-100000−3i3i00−3i−3i3i3i0000000−2i32i3000000−232300000i3−i300000003−3000000000000000000000
χ6544-4-44-2-2-4-22-242-422-2-2102-2212-1-2-12001-11-100000−3i3i00−3i−3i3i3i00000002i3−2i300000023−2300000−i3i30000000−33000000000000000000000
χ6644-4-4-24424-44-2-42-4-4-2-2402-2242-4-2-4200-22-22000000000000000000000000000000000000000000000000000000023−230000000000
χ6744-4-4-24424-44-2-42-4-4-2-2402-2242-4-2-4200-22-220000000000000000000000000000000000000000000000000000000−23230000000000
χ684-44-444-24-422-44-4-4-24-2-204-4-22222-2-44-4-2-2220000000000000000004-400-22000000000-2200000000000000000000000000000000
χ694-44-444-24-422-44-4-4-24-2-204-4-22222-2-4-44-2-222000000000000000000-44002-20000000002-200000000000000000000000000000000
χ704-44-44-2442-4-4-4-2-424-24-20-2242-42-4-2200-2-2220000000000000000000000000000004i−4i0000000000000000000000000−2i2i00000000
χ714-44-44-2442-4-4-4-2-424-24-20-2242-42-4-2200-2-222000000000000000000000000000000−4i4i00000000000000000000000002i−2i00000000
χ724-44-4-244-2-4-4-4242-44-2-240-22-2-42-42424-4-2-222000000000000000000-22004-4000000000-2200000000000000000000000000000000
χ734-44-4-244-2-4-4-4242-44-2-240-22-2-42-4242-44-2-2220000000000000000002-200-440000000002-200000000000000000000000000000000
χ744-44-4-24-2-2-422242-4-2-21-20-2212-12-1-224-411-1-10003i−3i00003i−3i3i−3i00000-2200-220000000001-100000003i−3i00000000000000000000000
χ754-44-4-24-2-2-422242-4-2-21-20-2212-12-1-224-411-1-1000−3i3i0000−3i3i−3i3i00000-2200-220000000001-10000000−3i3i00000000000000000000000
χ764-44-4-24-2-2-422242-4-2-21-20-2212-12-1-22-4411-1-10003i−3i00003i−3i3i−3i000002-2002-2000000000-110000000−3i3i00000000000000000000000
χ774-44-4-24-2-2-422242-4-2-21-20-2212-12-1-22-4411-1-1000−3i3i0000−3i3i−3i3i000002-2002-2000000000-1100000003i−3i00000000000000000000000
χ784-4-44444-4-44-4-4-444-44440-4-4-4-444-4-44004-4-440000000000000000000000000000000000000000000000000000000000000000000
χ794-4-4444-2-4-4-22-4-44424-2-20-4-422-2-222400-222-20000000000000000000000000000000000000000000000000000000000023−23000000
χ804-4-4444-2-4-4-22-4-44424-2-20-4-422-2-222400-222-200000000000000000000000000000000000000000000000000000000000−2323000000
χ814-4-444-24-424-4-424-2-4-24-2022-424-2-42-200-222-2000000000000000000000000−2i32i300000000000000000000−2i32i30000000000000000000
χ824-4-444-24-424-4-424-2-4-24-2022-424-2-42-200-222-20000000000000000000000002i3−2i3000000000000000000002i3−2i30000000000000000000
χ834-4-44-2442-44-42-4-24-4-2-240222-4-242-4-200-222-200000000000000000000000000−2i32i300000000000000000000−2i32i300000000000000000
χ844-4-44-2442-44-42-4-24-4-2-240222-4-242-4-200-222-2000000000000000000000000002i3−2i3000000000000000000002i3−2i300000000000000000
χ854-4-44-2-24224-422-2-2-41-2-20-1-122-2-2221001-1-1100000003-33-3-3300000000000−2i32i3−2i32i3000000000000000000i3−i3i3−i300000000000000000
χ864-4-44-2-24224-422-2-2-41-2-20-1-122-2-2221001-1-1100000003-33-3-33000000000002i3−2i32i3−2i3000000000000000000−i3i3−i3i300000000000000000
χ874-4-44-2-24224-422-2-2-41-2-20-1-122-2-2221001-1-110000000-33-333-300000000000−2i32i32i3−2i3000000000000000000i3−i3−i3i300000000000000000
χ884-4-44-2-24224-422-2-2-41-2-20-1-122-2-2221001-1-110000000-33-333-3000000000002i3−2i3−2i32i3000000000000000000−i3i3i3−i300000000000000000
χ898888-4-4-4-4-4-4-4-4-4-4-4-4222822222222200-1-1-1-1-4-4-4222222-1-1-1-1000000000000000000000000000000000000000000000000000000
χ908888-4-4-4-4-4-4-4-4-4-4-4-4222-822222222200-1-1-1-1444-2-2-2-2-2-21111000000000000000000000000000000000000000000000000000000
χ9188-8-8-48-4484-4-4-84-84-42-404-4-2-4-24244002-22-20000000000000000000000000000000000000000000000000000000000000000000
χ9288-8-8-4-484-4-88-4444-82-4-40-224-444-44-2002-22-20000000000000000000000000000000000000000000000000000000000000000000
χ9388-8-8-4-4-44-44-4-444442220-22-22-2-22-2-200-11-11000006i−6i00−3i−3i3i3i000000000000000000000000000000000000000000000000000000
χ9488-8-8-4-4-44-44-4-444442220-22-22-2-22-2-200-11-1100000−6i6i003i3i−3i−3i000000000000000000000000000000000000000000000000000000
χ958-88-88-4-48444-8-4-84-4-4-420-44-4-24-24240022-2-20000000000000000000000000000000000000000000000000000000000000000000
χ968-88-8-4-48-44-8-84-44482-4-402-2-44444-4-20022-2-20000000000000000000000000000000000000000000000000000000000000000000
χ978-88-8-4-4-4-44444-444-422202-22-2-2-2-22-200-1-1110006i−6i0000−3i3i−3i3i000000000000000000000000000000000000000000000000000000
χ988-88-8-4-4-4-44444-444-422202-22-2-2-2-22-200-1-111000−6i6i00003i−3i3i−3i000000000000000000000000000000000000000000000000000000
χ998-8-888-4-4-84-44-848-44-4-420444-2-424-2-4002-2-220000000000000000000000000000000000000000000000000000000000000000000
χ1008-8-88-48-44-8-444-8-484-42-4044-242-4-24-4002-2-220000000000000000000000000000000000000000000000000000000000000000000
χ1018-8-88-4-4-444-4444-4-442220-2-2-2-222-2-2200-111-100000006-6-333-3000000000000000000000000000000000000000000000000000000
χ1028-8-88-4-4-444-4444-4-442220-2-2-2-222-2-2200-111-10000000-663-3-33000000000000000000000000000000000000000000000000000000

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