Finite Group Databasebeta

← Group #13172340

Character table — Group #13172340

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99
size111122222222222244444444444444488888888888888881212121212121212121212121212242424242424242424242424242424242424242436363636363636363636363636367272108108
order12223336666666662333666666666663666666666666666224444661212121212126666666121212121212121212121212122244446612121212121261224
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111-1-11111-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1
χ3111111111111111111111111111111111111111111111111-11-11111-1-111111-1-111-1-111-11111-1-111111-11-1-1-1-1-111-1-1-1-11-1-1-1
χ4111111111111111111111111111111111111111111111111-11-1-1-111-1-1-1-1-1-11-1-111-1-111-1-1-111-1-1-1-1-1-1-11-11-1-111-1-1-1-1-1-1-1111
χ511111111111111111111111111111111111111111111111-11-1111-1-1111111-111-1-111-1-1111-1-1111111-11-11-1-111-1-1-1-1-1-1-11-1-1
χ611111111111111111111111111111111111111111111111-11-11-1-1-1-111-1-1-1-1-111-1-111-1-11-1-1-1-111-1-1-1-11-11-1-1-1-1-111-1-1-1-11-111
χ711111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-11111-1-111
χ811111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1
χ91111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-111-1-11-111-1-111-1-11111111-1-1-11-1-1-1-1-111-1-11-1-111-1-1-1-1-111-1-1111-1
χ101111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-111-1-1-1111-1-1-1-1111111111-1-1-1-11-1-1-1-1-1-111-111-11-1111111-1-1-1-1-11
χ111111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-11-1-111-1111111-1-11-1-111-1-1-1-111-1-1-11111-1-111-1-1-1111-1-1-1-1111-1-11
χ121111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-11-1-11-111111-1-1111-1-111-1-1-1-11-11-1-111-1-111-1-111-11-1-111-1-111-111-1
χ131111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-1-111-11-1-1-1-1-111-1-1-111-1-11111-11-111-1-111-1-1-1-111-11-1-111-1-111-11-11
χ141111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-1-111-1-11-1-1-1-1-1-111-111-1-11111-1-1111-1-1-1-11111-1-1-1111-1-1-1-1111-11-1
χ151111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1111-1-1-11111-1-1-1-1-1-1-1-1-11111-1111111-1-1-111-11-1111111-1-1-1-11-1
χ161111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-111-11-1-111-1-111-1-1-1-1-1-1-1111-111111-1-1111-1-111-1-1-1-1-111-1-111-11
χ17222222-122-122-12-122-12-122-122-1-1-1-12-1-12-1-1-122-1-1-1-1-1-1-1-1-102022200-1-1-1-12202-100-1-10022-100-1-1-1-1-1-1020200-1-10000000-100
χ18222222-122-122-12-122-12-122-122-1-1-1-12-1-12-1-1-122-1-1-1-1-1-1-1-1-10202-2-200-1-111-2-202-100-1-1002-2100-1-111110-20-200110000000100
χ19222222-122-122-12-122-12-122-122-1-1-1-12-1-12-1-1-122-1-1-1-1-1-1-1-1-10-20-2220011-1-1220-21001100-22-10011-1-1-1-10-20-200110000000100
χ20222222-122-122-12-122-12-122-122-1-1-1-12-1-12-1-1-122-1-1-1-1-1-1-1-1-10-20-2-2-2001111-2-20-21001100-2-2100111111020200-1-10000000-100
χ21222222-122-122-12-12-2-12-1-2-2-122-1-1-1-12-1-1-2111-2-211-1-1-11111020-22-20011-1-1-2-202-100-1-100-2210011-1-1110-20200110000000-100
χ22222222-122-122-12-12-2-12-1-2-2-122-1-1-1-12-1-1-2111-2-211-1-1-11111020-2-220011112202-100-1-100-2-2-1001111-1-1020-200-1-10000000100
χ23222222-122-122-12-12-2-12-1-2-2-122-1-1-1-12-1-1-2111-2-211-1-1-111110-2022-200-1-1-1-1-2-20-2100110022100-1-1-1-111020-200-1-10000000100
χ24222222-122-122-12-12-2-12-1-2-2-122-1-1-1-12-1-1-2111-2-211-1-1-111110-202-2200-1-111220-210011002-2-100-1-111-1-10-20200110000000-100
χ2522222-122-122-12-1222-1-1222-1-1-122-1-1-12-1-12-1-1-1-122-1-1-1-1-1-1-1202022-1-10022-1-1200-1-1002-10-12-1-100-1-1-1-120200000-1-10000-1000
χ2622222-122-122-12-1222-1-1222-1-1-122-1-1-12-1-12-1-1-1-122-1-1-1-1-1-1-12020-2-2-1-100-2-211200-1-1002-101-2-1-1001111-20-2000001100001000
χ2722222-122-122-12-1222-1-1222-1-1-122-1-1-12-1-12-1-1-1-122-1-1-1-1-1-1-1-20-2022110022-1-1-2001100-210-121100-1-1-1-1-20-2000001100001000
χ2822222-122-122-12-1222-1-1222-1-1-122-1-1-12-1-12-1-1-1-122-1-1-1-1-1-1-1-20-20-2-21100-2-211-2001100-2101-21100111120200000-1-10000-1000
χ2922222-122-122-12-122-2-1-12-2-2-1-1-122-1-1-12-11-21111-2-2-1-1-1111120-202-2-1-1002211200-1-100-210-1-21100-1-11120-200000110000-1000
χ3022222-122-122-12-122-2-1-12-2-2-1-1-122-1-1-12-11-21111-2-2-1-1-1111120-20-22-1-100-2-2-1-1200-1-100-21012110011-1-1-20200000-1-100001000
χ3122222-122-122-12-122-2-1-12-2-2-1-1-122-1-1-12-11-21111-2-2-1-1-11111-20202-211002211-20011002-10-1-2-1-100-1-111-20200000-1-100001000
χ3222222-122-122-12-122-2-1-12-2-2-1-1-122-1-1-12-11-21111-2-2-1-1-11111-2020-221100-2-2-1-1-20011002-1012-1-10011-1-120-200000110000-1000
χ332222-122-122-12222-122-1-1-1-12-1-1-1-122-1-1-12222-1-1-1-1-1-1-1-1-1-1-122220022220000-1-12-1-1-1-1-12-100-1-1-1-100000000220000-1-1-1-10000
χ342222-122-122-12222-122-1-1-1-12-1-1-1-122-1-1-12222-1-1-1-1-1-1-1-1-1-1-12-22-20022-2-20000-11-2-1-111-12100-1-11100000000-2-2000011110000
χ352222-122-122-12222-122-1-1-1-12-1-1-1-122-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-22-2200-2-22200001-1211-1-11-2-10011-1-100000000-2-2000011110000
χ362222-122-122-12222-122-1-1-1-12-1-1-1-122-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-2-2-2-200-2-2-2-2000011-211111-2100111100000000220000-1-1-1-10000
χ372222-122-122-12222-1-22-1-1112-1-1-1-122-1-1-1-2-2-2-21111-1-1-1111122-2-20022-2-20000-1-12-1-1-1-11-21001111000000002-20000-1-1110000
χ382222-122-122-12222-1-22-1-1112-1-1-1-122-1-1-1-2-2-2-21111-1-1-111112-2-220022220000-11-2-1-1111-2-10011-1-100000000-22000011-1-10000
χ392222-122-122-12222-1-22-1-1112-1-1-1-122-1-1-1-2-2-2-21111-1-1-11111-222-200-2-2-2-200001-1211-1-1-12100-1-11100000000-22000011-1-10000
χ402222-122-122-12222-1-22-1-1112-1-1-1-122-1-1-1-2-2-2-21111-1-1-11111-2-22200-2-222000011-21111-12-100-1-1-1-1000000002-20000-1-1110000
χ4144444-2-24-2-24-2-2-2-2441-2-2441-2-2-2-211-2-21-2-211-2-2-2-211111110000440000-2-2-2-20000000000-2-200001111000000000000000000
χ4244444-2-24-2-24-2-2-2-2441-2-2441-2-2-2-211-2-21-2-211-2-2-2-211111110000-4-4000022220000000000220000-1-1-1-1000000000000000000
χ4344444-2-24-2-24-2-2-2-24-41-2-2-4-41-2-2-2-211-2-2122-1-12222111-1-1-1-100004-40000-2-2220000000000-22000011-1-1000000000000000000
χ4444444-2-24-2-24-2-2-2-24-41-2-2-4-41-2-2-2-211-2-2122-1-12222111-1-1-1-10000-44000022-2-200000000002-20000-1-111000000000000000000
χ454444-24-2-24-2-24-24-2-24-2-21-2-2-2-2-211-2-2-2114-2-2-2-2-211111111104040000-2-200000-2-2001100-20000110000000000000000000000
χ464444-24-2-24-2-24-24-2-24-2-21-2-2-2-2-211-2-2-2114-2-2-2-2-21111111110-40-4000022000002200-1-10020000-1-10000000000000000000000
χ474444-24-2-24-2-24-24-2-2-4-2-2122-2-2-211-2-2-211-422222-1-1111-1-1-1-1040-400002200000-2-200110020000-1-10000000000000000000000
χ484444-24-2-24-2-24-24-2-2-4-2-2122-2-2-211-2-2-211-422222-1-1111-1-1-1-10-4040000-2-2000002200-1-100-20000110000000000000000000000
χ494444-2-24-2-24-2-24-24-24-21-2-2-2-211-2-2-2-21-21-24-2-211-2-21111111404000-2-2000000-2001100-2-200011000000000000000000000000
χ504444-2-24-2-24-2-24-24-24-21-2-2-2-211-2-2-2-21-21-24-2-211-2-21111111-40-400022000000200-1-10022000-1-1000000000000000000000000
χ514444-2-24-2-24-2-24-24-2-4-21-222-211-2-2-2-21-212-422-1-122111-1-1-1-140-4000-2-2000000-200110022000-1-1000000000000000000000000
χ524444-2-24-2-24-2-24-24-2-4-21-222-211-2-2-2-21-212-422-1-122111-1-1-1-1-40400022000000200-1-100-2-200011000000000000000000000000
χ5344-4-4444-4-4-4444-4-4-4044400-4-4-4-4-44-4444000000004-4-400000000000000000000000000000000000000000000000000000000
χ5444-4-444-2-4-4244-2-42-40-24-2002-4-422-224-2-200000000-222000000000000−2i32i3000000000000000000−2i32i30000000000000000000000
χ5544-4-444-2-4-4244-2-42-40-24-2002-4-422-224-2-200000000-2220000000000002i3−2i30000000000000000002i3−2i30000000000000000000000
χ5644-4-44-24-42-44-242-4-40-2-2400222-4-4-22-24-200000000-2220000000000−2i32i3000000000−2i32i3000000000000000000000000000000000
χ5744-4-44-24-42-44-242-4-40-2-2400222-4-4-22-24-200000000-22200000000002i3−2i30000000002i3−2i3000000000000000000000000000000000
χ5844-4-4-2442-4-4-244-4-4204-2-2−2i32i3-422224-4-2-2-20000−2i32i3−2i32i3-222−2i3−2i32i32i30000000000000000000000000000000000000000000000000000
χ5944-4-4-2442-4-4-244-4-4204-2-22i3−2i3-422224-4-2-2-200002i3−2i32i3−2i3-2222i32i3−2i3−2i30000000000000000000000000000000000000000000000000000
χ6044-4-4-24-22-42-24-2-4220-2-21−2i32i3222-1-1-22-2110000−2i32i3i3−i31-1-1i3i3−i3−i300000000−2i32i30000000003-30000000i3−i30000000000000000000000
χ6144-4-4-24-22-42-24-2-4220-2-21−2i32i3222-1-1-22-2110000−2i32i3i3−i31-1-1i3i3−i3−i3000000002i3−2i3000000000-330000000−i3i30000000000000000000000
χ6244-4-4-24-22-42-24-2-4220-2-212i3−2i3222-1-1-22-21100002i3−2i3−i3i31-1-1−i3−i3i3i300000000−2i32i3000000000-330000000i3−i30000000000000000000000
χ6344-4-4-24-22-42-24-2-4220-2-212i3−2i3222-1-1-22-21100002i3−2i3−i3i31-1-1−i3−i3i3i3000000002i3−2i30000000003-30000000−i3i30000000000000000000000
χ6444-4-4-2-2422-4-2-242-420-21-2−2i32i32-1-122-221-210000i3−i3−2i32i31-1-1i3i3−i3−i3000000−2i32i3000000000i3−i300000003-3000000000000000000000000
χ6544-4-4-2-2422-4-2-242-420-21-2−2i32i32-1-122-221-210000i3−i3−2i32i31-1-1i3i3−i3−i30000002i3−2i3000000000−i3i30000000-33000000000000000000000000
χ6644-4-4-2-2422-4-2-242-420-21-22i3−2i32-1-122-221-210000−i3i32i3−2i31-1-1−i3−i3i3i3000000−2i32i3000000000i3−i30000000-33000000000000000000000000
χ6744-4-4-2-2422-4-2-242-420-21-22i3−2i32-1-122-221-210000−i3i32i3−2i31-1-1−i3−i3i3i30000002i3−2i3000000000−i3i300000003-3000000000000000000000000
χ684-44-44444-4-4-4-4-444-4044400-44-44-4-44-4-4400000000-44-400000000000000000000000000000000000000000000000000000000
χ694-44-444-24-42-4-424-2-40-24-20024-4-222-2-42-2000000002-2200000000000000000000000000000000000000000000−2i32i30000000000
χ704-44-444-24-42-4-424-2-40-24-20024-4-222-2-42-2000000002-22000000000000000000000000000000000000000000002i3−2i30000000000
χ714-44-44-2442-4-42-4-24-40-2-24002-224-42-22-4-2000000002-220000000000000000000000000000000000000000000000−2i32i300000000
χ724-44-44-2442-4-42-4-24-40-2-24002-224-42-22-4-2000000002-2200000000000000000000000000000000000000000000002i3−2i300000000
χ734-44-4-244-2-4-42-4-444204-2-200-4-22-22-4422-2000000002-220000000000000000000000000000000000000000000000000023−230000
χ744-44-4-244-2-4-42-4-444204-2-200-4-22-22-4422-2000000002-2200000000000000000000000000000000000000000000000000−23230000
χ754-4-44444-444-4-4-4-4-440444004-44-44-4-4-4-4400000000-4-4400000000000000000000000000000000000000000000000000000000
χ764-4-4444-2-44-2-4-42-4240-24-200-2-442-222-42-20000000022-20000000000000023−2300000000000000000023−2300000000000000000000
χ774-4-4444-2-44-2-4-42-4240-24-200-2-442-222-42-20000000022-200000000000000−2323000000000000000000−232300000000000000000000
χ784-4-444-24-4-24-42-42-440-2-2400-22-2-44222-4-20000000022-2000000000000000023−2300000000000000000023−23000000000000000000
χ794-4-444-24-4-24-42-42-440-2-2400-22-2-44222-4-20000000022-20000000000000000−2323000000000000000000−2323000000000000000000
χ804-4-444-2-2-4-2-2-42222401-2-20012-22-2-1-1221003-30000-1-113-33-3000000000023−2323−230000000000000000−33−33000000000000000000
χ814-4-444-2-2-4-2-2-42222401-2-20012-22-2-1-1221003-30000-1-113-33-30000000000−2323−232300000000000000003−33−3000000000000000000
χ824-4-444-2-2-4-2-2-42222401-2-20012-22-2-1-122100-330000-1-11-33-33000000000023−23−23230000000000000000−333−3000000000000000000
χ834-4-444-2-2-4-2-2-42222401-2-20012-22-2-1-122100-330000-1-11-33-330000000000−232323−2300000000000000003−3−33000000000000000000
χ844-4-44-2442442-4-4-4-4-204-2-20042-22-2-4-422-20000000022-2000000000000000000000000000000000000000000000000−2i32i3000000
χ854-4-44-2442442-4-4-4-4-204-2-20042-22-2-4-422-20000000022-20000000000000000000000000000000000000000000000002i3−2i3000000
χ868888-4-4-4-4-4-4-4-4-4-4-4-48222-4-4222222222-1-4-4222222-1-1-1-1-1-1-10000000000000000000000000000000000000000000000000000
χ878888-4-4-4-4-4-4-4-4-4-4-4-4-822244222222222-144-2-2-2-2-2-2-1-1-111110000000000000000000000000000000000000000000000000000
χ8888-8-88-4-4-8448-4-444-802-4-400-244442-2-4-42000000002-2-200000000000000000000000000000000000000000000000000000000
χ8988-8-8-4-4-4444-4-4-44440222−4i34i3-2-2-2-2-22-222-100002i3−2i32i3−2i3-111−i3−i3i3i30000000000000000000000000000000000000000000000000000
χ9088-8-8-4-4-4444-4-4-444402224i3−4i3-2-2-2-2-22-222-10000−2i32i3−2i32i3-111i3i3−i3−i30000000000000000000000000000000000000000000000000000
χ918-88-88-4-4844-844-4-4-802-4-400-2-44-44-2244200000000-22-200000000000000000000000000000000000000000000000000000000
χ928-88-8-48-4-4-844-848-440-4-42004-442-24-44-2200000000-22-200000000000000000000000000000000000000000000000000000000
χ938-88-8-4-48-44-844-8-4840-42-40042-2-444-4-24200000000-22-200000000000000000000000000000000000000000000000000000000
χ948-88-8-4-4-4-444444-4-44022200-22-22-2-22-2-2-1000000001-11−3i33i33i3−3i30000000000000000000000000000000000000000000000000000
χ958-88-8-4-4-4-444444-4-44022200-22-22-2-22-2-2-1000000001-113i3−3i3−3i33i30000000000000000000000000000000000000000000000000000
χ968-8-88-48-448-44-84-84-40-4-4200-44-4-22444-2200000000-2-2200000000000000000000000000000000000000000000000000000000
χ978-8-88-4-484-4844-84-8-40-42-400-4-224-444-24200000000-2-2200000000000000000000000000000000000000000000000000000000
χ988-8-88-4-4-44-4-444444-40222002-22-22-2-2-2-2-1006-6000011-1-33-330000000000000000000000000000000000000000000000000000
χ998-8-88-4-4-44-4-444444-40222002-22-22-2-2-2-2-100-66000011-13-33-30000000000000000000000000000000000000000000000000000

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