Finite Group Databasebeta

← Group #13172921

Character table — Group #13172921

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111122222222222244444444444444488888888888888881212121212121212121212121212181818181818242424242424242424242424242424242424242436363636363636363636367272108108
order12223336666666662333666666666663666666666666666224444661212121212122244446666666121212121212121212121212122446612121212121261244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111-1-11111-1-1-1-1-1-111-1-11111111111-1-11111-1-1-1-1-11-1-1-1-1-11111-1-1-1-1
χ3111111111111111111111111111111111111111111111111-11-11111-1-11111-1-1-1-1111-1-111-1-111-11111-1-111111-1-1-1-111-1-1-1-11-1-1-1
χ4111111111111111111111111111111111111111111111111-11-1-1-111-1-1-1-1-1-111-1-1-1-11-1-111-1-111-1-1-111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1111
χ511111111111111111111111111111111111111111111111-11-1111-1-111111111-1-1-1-1-111-1-111-1-1111-1-1111111-1-1111-1-1-1-1-1-1-11-1-1
χ611111111111111111111111111111111111111111111111-11-11-1-1-1-111-1-1-1-1-1-1-1-111-111-1-111-1-11-1-1-1-111-1-1-1-11-1-1-1-111-1-1-1-11-111
χ711111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-11-1-1-1-1-11111-1-111
χ811111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1
χ91111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-111-1-11-111-1-111-1-1-1-111-1-11111111-1-1-11-1-1-1-1-111-1-11-11-1-1-1-111-1-1111-1
χ101111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-111-1-1-1111-1-1-1-1111111111111111-1-1-1-11-1-1-1-1-1-111-1-1-1111111-1-1-1-1-11
χ111111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-11-1-111-1111111-1-111-1-1-1-11-1-111-1-1-1-111-1-1-11111-1-111-111-1-1-1-1111-1-11
χ121111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-11-1-11-111111-1-111-1-1-1-1111-1-111-1-1-1-11-11-1-111-1-111-111-1-111-1-111-111-1
χ131111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-1-111-11-1-1-1-1-111-1-1-1-1-1-111-111-1-11111-11-111-1-111-1-1-111-1-111-1-111-11-11
χ141111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-1-111-1-11-1-1-1-1-1-11111-1-1-1-1-111-1-11111-1-1111-1-1-1-11111-111-1-1-1-1111-11-1
χ151111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1111-1-1-11111-1-1111111-1-1-1-1-1-1-11111-1111111-1-1-1-1-1111111-1-1-1-11-1
χ161111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-111-11-1-111-1-111-1-111-1-1-1-1-1-1-1-1-1111-111111-1-1111-11-1-1-1-111-1-111-11
χ17222222-122-122-12-122-12-122-122-1-1-1-12-1-12-1-1-122-1-1-1-1-1-1-1-1-102022200-1-1-1-12222000002-100-1-10022-100-1-1-1-1-1-1002-1-10000000-100
χ18222222-122-122-12-122-12-122-122-1-1-1-12-1-12-1-1-122-1-1-1-1-1-1-1-1-10202-2-200-1-111-2-2-2-2000002-100-1-1002-2100-1-1111100-2110000000100
χ19222222-122-122-12-122-12-122-122-1-1-1-12-1-12-1-1-122-1-1-1-1-1-1-1-1-10-20-2220011-1-122-2-200000-21001100-22-10011-1-1-1-100-2110000000100
χ20222222-122-122-12-122-12-122-122-1-1-1-12-1-12-1-1-122-1-1-1-1-1-1-1-1-10-20-2-2-2001111-2-22200000-21001100-2-2100111111002-1-10000000-100
χ21222222-122-122-12-12-2-12-1-2-2-122-1-1-1-12-1-1-2111-2-211-1-1-11111020-22-20011-1-1-2-2-2-2000002-100-1-100-2210011-1-111002110000000-100
χ22222222-122-122-12-12-2-12-1-2-2-122-1-1-1-12-1-1-2111-2-211-1-1-11111020-2-220011112222000002-100-1-100-2-2-1001111-1-100-2-1-10000000100
χ23222222-122-122-12-12-2-12-1-2-2-122-1-1-1-12-1-1-2111-2-211-1-1-111110-2022-200-1-1-1-1-2-22200000-2100110022100-1-1-1-11100-2-1-10000000100
χ24222222-122-122-12-12-2-12-1-2-2-122-1-1-1-12-1-1-2111-2-211-1-1-111110-202-2200-1-11122-2-200000-210011002-2-100-1-111-1-1002110000000-100
χ2522222-122-122-12-1222-1-1222-1-1-122-1-1-12-1-12-1-1-1-122-1-1-1-1-1-1-1202022-1-10022-1-1000022200-1-1002-10-12-1-100-1-1-1-120000-1-10000-1000
χ2622222-122-122-12-1222-1-1222-1-1-122-1-1-12-1-12-1-1-1-122-1-1-1-1-1-1-12020-2-2-1-100-2-2110000-2-2200-1-1002-101-2-1-1001111-200001100001000
χ2722222-122-122-12-1222-1-1222-1-1-122-1-1-12-1-12-1-1-1-122-1-1-1-1-1-1-1-20-2022110022-1-10000-2-2-2001100-210-121100-1-1-1-1-200001100001000
χ2822222-122-122-12-1222-1-1222-1-1-122-1-1-12-1-12-1-1-1-122-1-1-1-1-1-1-1-20-20-2-21100-2-211000022-2001100-2101-21100111120000-1-10000-1000
χ2922222-122-122-12-122-2-1-12-2-2-1-1-122-1-1-12-11-21111-2-2-1-1-1111120-202-2-1-10022110000-2-2200-1-100-210-1-21100-1-11120000110000-1000
χ3022222-122-122-12-122-2-1-12-2-2-1-1-122-1-1-12-11-21111-2-2-1-1-1111120-20-22-1-100-2-2-1-1000022200-1-100-21012110011-1-1-20000-1-100001000
χ3122222-122-122-12-122-2-1-12-2-2-1-1-122-1-1-12-11-21111-2-2-1-1-11111-20202-211002211000022-20011002-10-1-2-1-100-1-111-20000-1-100001000
χ3222222-122-122-12-122-2-1-12-2-2-1-1-122-1-1-12-11-21111-2-2-1-1-11111-2020-221100-2-2-1-10000-2-2-20011002-1012-1-10011-1-120000110000-1000
χ332222-122-122-12222-122-1-1-1-12-1-1-1-122-1-1-12222-1-1-1-1-1-1-1-1-1-1-122220022220000002200-1-12-1-1-1-1-12-100-1-1-1-100000200000-1-1-1-10000
χ342222-122-122-12222-122-1-1-1-12-1-1-1-122-1-1-12222-1-1-1-1-1-1-1-1-1-1-12-22-20022-2-2000000-2-200-11-2-1-111-12100-1-11100000-20000011110000
χ352222-122-122-12222-122-1-1-1-12-1-1-1-122-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-22-2200-2-222000000-2-2001-1211-1-11-2-10011-1-100000-20000011110000
χ362222-122-122-12222-122-1-1-1-12-1-1-1-122-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-2-2-2-200-2-2-2-2000000220011-211111-2100111100000200000-1-1-1-10000
χ372222-122-122-12222-1-22-1-1112-1-1-1-122-1-1-1-2-2-2-21111-1-1-1111122-2-20022-2-20000002200-1-12-1-1-1-11-2100111100000-200000-1-1110000
χ382222-122-122-12222-1-22-1-1112-1-1-1-122-1-1-1-2-2-2-21111-1-1-111112-2-22002222000000-2-200-11-2-1-1111-2-10011-1-10000020000011-1-10000
χ392222-122-122-12222-1-22-1-1112-1-1-1-122-1-1-1-2-2-2-21111-1-1-11111-222-200-2-2-2-2000000-2-2001-1211-1-1-12100-1-1110000020000011-1-10000
χ402222-122-122-12222-1-22-1-1112-1-1-1-122-1-1-1-2-2-2-21111-1-1-11111-2-22200-2-222000000220011-21111-12-100-1-1-1-100000-200000-1-1110000
χ412-2-22222-2-2-2-2-2-2222022200-22-22-22-2-2-22000000002-2-20000000000000000002-22-22-2000000000000000000000002-22-22-2000000
χ422-2-22222-2-2-2-2-2-2222022200-22-22-22-2-2-22000000002-2-20000000000000000002-2-22-22000000000000000000000002-2-22-22000000
χ432-2-22222-2-2-2-2-2-2222022200-22-22-22-2-2-22000000002-2-2000000000000000000-222-2-2200000000000000000000000-22-222-2000000
χ442-2-22222-2-2-2-2-2-2222022200-22-22-22-2-2-22000000002-2-2000000000000000000-22-222-200000000000000000000000-222-2-22000000
χ4544444-2-24-2-24-2-2-2-2441-2-2441-2-2-2-211-2-21-2-211-2-2-2-211111110000440000-2-2-2-20000000000000000-2-200001111000000000000000
χ4644444-2-24-2-24-2-2-2-2441-2-2441-2-2-2-211-2-21-2-211-2-2-2-211111110000-4-4000022220000000000000000220000-1-1-1-1000000000000000
χ4744444-2-24-2-24-2-2-2-24-41-2-2-4-41-2-2-2-211-2-2122-1-12222111-1-1-1-100004-40000-2-2220000000000000000-22000011-1-1000000000000000
χ4844444-2-24-2-24-2-2-2-24-41-2-2-4-41-2-2-2-211-2-2122-1-12222111-1-1-1-10000-44000022-2-200000000000000002-20000-1-111000000000000000
χ494444-24-2-24-2-24-24-2-24-2-21-2-2-2-2-211-2-2-2114-2-2-2-2-211111111104040000-2-200000000000-2-2001100-20000110000000000000000000
χ504444-24-2-24-2-24-24-2-24-2-21-2-2-2-2-211-2-2-2114-2-2-2-2-21111111110-40-4000022000000000002200-1-10020000-1-10000000000000000000
χ514444-24-2-24-2-24-24-2-2-4-2-2122-2-2-211-2-2-211-422222-1-1111-1-1-1-1040-400002200000000000-2-200110020000-1-10000000000000000000
χ524444-24-2-24-2-24-24-2-2-4-2-2122-2-2-211-2-2-211-422222-1-1111-1-1-1-10-4040000-2-2000000000002200-1-100-20000110000000000000000000
χ534444-2-24-2-24-2-24-24-24-21-2-2-2-211-2-2-2-21-21-24-2-211-2-21111111404000-2-2000000000000-2001100-2-200011000000000000000000000
χ544444-2-24-2-24-2-24-24-24-21-2-2-2-211-2-2-2-21-21-24-2-211-2-21111111-40-400022000000000000200-1-10022000-1-1000000000000000000000
χ554444-2-24-2-24-2-24-24-2-4-21-222-211-2-2-2-21-212-422-1-122111-1-1-1-140-4000-2-2000000000000-200110022000-1-1000000000000000000000
χ564444-2-24-2-24-2-24-24-2-4-21-222-211-2-2-2-21-212-422-1-122111-1-1-1-1-40400022000000000000200-1-100-2-200011000000000000000000000
χ5744-4-4444444-4-4-4-4-4-40444004-44-44-4-4-4-4400000000-44-400000000000000000000000000000000000000000000000000000000000
χ5844-4-444-244-2-4-42-42-40-24-200-2-442-222-42-2000000002-220000000000000023−2300000000000000000000000023−2300000000000000000
χ5944-4-444-244-2-4-42-42-40-24-200-2-442-222-42-2000000002-2200000000000000−2323000000000000000000000000−232300000000000000000
χ6044-4-44-244-24-42-42-4-40-2-2400-22-2-44222-4-2000000002-22000000000000000023−2300000000000000000000000023−23000000000000000
χ6144-4-44-244-24-42-42-4-40-2-2400-22-2-44222-4-2000000002-220000000000000000−2323000000000000000000000000−2323000000000000000
χ6244-4-44-2-24-2-2-42222-401-2-20012-22-2-1-1221003-30000-11-133-3-3000000000023−2323−230000000000000000000000−33−33000000000000000
χ6344-4-44-2-24-2-2-42222-401-2-20012-22-2-1-1221003-30000-11-133-3-30000000000−2323−232300000000000000000000003−33−3000000000000000
χ6444-4-44-2-24-2-2-42222-401-2-20012-22-2-1-122100-330000-11-1-3-333000000000023−23−23230000000000000000000000−333−3000000000000000
χ6544-4-44-2-24-2-2-42222-401-2-20012-22-2-1-122100-330000-11-1-3-3330000000000−232323−2300000000000000000000003−3−33000000000000000
χ6644-4-4-244-2442-4-4-4-4204-2-20042-22-2-4-422-2000000002-220000000000000000000000000000000000000000000000000000023−230000
χ6744-4-4-244-2442-4-4-4-4204-2-20042-22-2-4-422-2000000002-2200000000000000000000000000000000000000000000000000000−23230000
χ684-44-4444-4-4-4444-4-4-4044400-4-4-4-4-4-4444400000000-4-4400000000000000000000000000000000000000000000000000000000000
χ694-44-444-2-4-4244-2-42-40-24-2002-4-4222-24-2-20000000022-2000000000000−2i32i3000000000000000000000000−2i32i30000000000000000000
χ704-44-444-2-4-4244-2-42-40-24-2002-4-4222-24-2-20000000022-20000000000002i3−2i30000000000000000000000002i3−2i30000000000000000000
χ714-44-44-24-42-44-242-4-40-2-2400222-4-42-2-24-20000000022-20000000000−2i32i3000000000000000−2i32i3000000000000000000000000000000
χ724-44-44-24-42-44-242-4-40-2-2400222-4-42-2-24-20000000022-200000000002i3−2i30000000000000002i3−2i3000000000000000000000000000000
χ734-44-4-2442-4-4-244-4-4204-2-2−2i32i3-42222-44-2-2-20000−2i32i3−2i32i322-2−2i32i3−2i32i30000000000000000000000000000000000000000000000000000000
χ744-44-4-2442-4-4-244-4-4204-2-22i3−2i3-42222-44-2-2-200002i3−2i32i3−2i322-22i3−2i32i3−2i30000000000000000000000000000000000000000000000000000000
χ754-44-4-24-22-42-24-2-4220-2-21−2i32i3222-1-12-2-2110000−2i32i3i3−i3-1-11i3−i3i3−i300000000−2i32i30000000000000003-30000000i3−i30000000000000000000
χ764-44-4-24-22-42-24-2-4220-2-21−2i32i3222-1-12-2-2110000−2i32i3i3−i3-1-11i3−i3i3−i3000000002i3−2i3000000000000000-330000000−i3i30000000000000000000
χ774-44-4-24-22-42-24-2-4220-2-212i3−2i3222-1-12-2-21100002i3−2i3−i3i3-1-11−i3i3−i3i300000000−2i32i3000000000000000-330000000i3−i30000000000000000000
χ784-44-4-24-22-42-24-2-4220-2-212i3−2i3222-1-12-2-21100002i3−2i3−i3i3-1-11−i3i3−i3i3000000002i3−2i30000000000000003-30000000−i3i30000000000000000000
χ794-44-4-2-2422-4-2-242-420-21-2−2i32i32-1-1222-21-210000i3−i3−2i32i3-1-11i3−i3i3−i3000000−2i32i3000000000000000i3−i300000003-3000000000000000000000
χ804-44-4-2-2422-4-2-242-420-21-2−2i32i32-1-1222-21-210000i3−i3−2i32i3-1-11i3−i3i3−i30000002i3−2i3000000000000000−i3i30000000-33000000000000000000000
χ814-44-4-2-2422-4-2-242-420-21-22i3−2i32-1-1222-21-210000−i3i32i3−2i3-1-11−i3i3−i3i3000000−2i32i3000000000000000i3−i30000000-33000000000000000000000
χ824-44-4-2-2422-4-2-242-420-21-22i3−2i32-1-1222-21-210000−i3i32i3−2i3-1-11−i3i3−i3i30000002i3−2i3000000000000000−i3i300000003-3000000000000000000000
χ834-4-4444-2-4-42-4-424-240-24-20024-4-22-22-42-200000000-2220000000000000000004-4000000000000000000000000000-220000000000
χ844-4-4444-2-4-42-4-424-240-24-20024-4-22-22-42-200000000-222000000000000000000-440000000000000000000000000002-20000000000
χ854-4-444-24-42-4-42-4-2440-2-24002-224-4-222-4-200000000-22200000000000000000000004-40000000000000000000000000-2200000000
χ864-4-444-24-42-4-42-4-2440-2-24002-224-4-222-4-200000000-2220000000000000000000000-4400000000000000000000000002-200000000
χ874-4-44-2442-4-42-4-444-204-2-200-4-22-224-422-200000000-222000000000000000000004-400000000000000000000000000000-22000000
χ884-4-44-2442-4-42-4-444-204-2-200-4-22-224-422-200000000-22200000000000000000000-44000000000000000000000000000002-2000000
χ898888-4-4-4-4-4-4-4-4-4-4-4-48222-4-4222222222-1-4-4222222-1-1-1-1-1-1-10000000000000000000000000000000000000000000000000000000
χ908888-4-4-4-4-4-4-4-4-4-4-4-4-822244222222222-144-2-2-2-2-2-2-1-1-111110000000000000000000000000000000000000000000000000000000
χ9188-8-8-48-4-48-44-84-8440-4-4200-44-4-22444-2200000000-22-200000000000000000000000000000000000000000000000000000000000
χ9288-8-8-4-48-4-4844-84-840-42-400-4-224-444-24200000000-22-200000000000000000000000000000000000000000000000000000000000
χ9388-8-8-4-4-4-4-4-44444440222002-22-22-2-2-2-2-1006-600001-11-3-3330000000000000000000000000000000000000000000000000000000
χ9488-8-8-4-4-4-4-4-44444440222002-22-22-2-2-2-2-100-6600001-1133-3-30000000000000000000000000000000000000000000000000000000
χ958-88-88-4-4-8448-4-444-802-4-400-24444-22-4-4200000000-2-2200000000000000000000000000000000000000000000000000000000000
χ968-88-8-4-4-4444-4-4-44440222−4i34i3-2-2-2-2-2-2222-100002i3−2i32i3−2i311-1−i3i3−i3i30000000000000000000000000000000000000000000000000000000
χ978-88-8-4-4-4444-4-4-444402224i3−4i3-2-2-2-2-2-2222-10000−2i32i3−2i32i311-1i3−i3i3−i30000000000000000000000000000000000000000000000000000000
χ988-8-888-4-4-844-844-4-4802-4-400-2-44-442-2442000000002-2-200000000000000000000000000000000000000000000000000000000000
χ998-8-88-48-44-844-848-4-40-4-42004-442-2-444-22000000002-2-200000000000000000000000000000000000000000000000000000000000
χ1008-8-88-4-4844-844-8-48-40-42-40042-2-44-44-242000000002-2-200000000000000000000000000000000000000000000000000000000000
χ1018-8-88-4-4-4444444-4-4-4022200-22-22-22-2-2-2-100000000-111−3i33i33i3−3i30000000000000000000000000000000000000000000000000000000
χ1028-8-88-4-4-4444444-4-4-4022200-22-22-22-2-2-2-100000000-1113i3−3i3−3i33i30000000000000000000000000000000000000000000000000000000

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