Finite Group Databasebeta

← Group #13172336

Character table — Group #13172336

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99
size111122222222222244444444444444488888888888888881212121212121212121212121212242424242424242424242424242424242424242436363636363636363636363636367272108108
order122233366666666623336666666666636666666666666662244446666121212126666661212121212121212121212121212244444121212121212121261244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111-1-11111-1-1-1-1111111-1111-111111-1-1-1-1-1-1-111-1-1-1-1-11111-1-1-1-1
χ3111111111111111111111111111111111111111111111111-11-11111-1-111111-111-1-111-1-11111-1-11111-111-1-1-1-1-111-1-1-1-1-11-1-1
χ4111111111111111111111111111111111111111111111111-11-1-1-111-1-1-1-1-1-11-111-1-1-11-1-1-1111-1-1-1-1-1-11-1-1-1-1111-1-1-1-1-1-11-111
χ511111111111111111111111111111111111111111111111-11-1111-1-1111111-11-1-1111-1111-1-1-11111111-1-1-1-1111-1-1-1-1-1-11-1-1-1
χ611111111111111111111111111111111111111111111111-11-11-1-1-1-111-1-1-1-1-11-1-111-1-111-1-1-1-111-1-1-1-1-111-1-1-1-1-111-1-1-1-1-1111
χ711111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-11-1-1-11-1-1-1-1-11111-1-1-111-1-1-1-1-11111-1-111
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
χ91111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-111-1-11-11111-1-111111111-1-1-1-11-1-1-1-1-111-1-11-111-1-1-1-11111-1-11-1-11
χ101111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-111-1-1-11111111-1-11111111-1-1-1-1-1-1-1-1-1-1-111-11-11-1111-1-111-1-1-111-1
χ111111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-11-1-111-111-1-1-1-1111-111-1-1-1-1111-1-1-11111-1-1-1-11-1111111-1-111-1-11-1
χ121111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-11-1-11-1111-1-111-1-11-111-1-11-111-1-1-1-111-1-11111-1-11-1-1-1-1-1-1-11111-11
χ131111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-1-111-11-1-1-111-1-111-11-1-111-11-1-11111-1-111-1-111-1-11-1-1-1-1-1-1-111111-1
χ141111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-1-111-1-11-1-11111-1-1-11-1-11111-1-1-1111-1-1-1-111-1-11-1111111-1-111-1-1-11
χ151111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1111-1-1-1-1-1-1-111-1-1-1-1-1-1-111111111111-1-1-11-11-1111-1-111-1-1-11-11
χ161111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-111-11-1-1-1-111-1-1-1-1-1-1-1-11111-111111-1-1111-111-1-1-1-11111-1-11-11-1
χ17222222-12-122-12-1222-12-122-122-1-1-1-12-1-12-1-1-122-1-1-1-1-1-1-1-1-102022200-1-1-1-1220200-1-1202-1-1000-1-1-1-1-1-1200002-1-1000000-1000
χ18222222-12-122-12-1222-12-122-122-1-1-1-12-1-12-1-1-122-1-1-1-1-1-1-1-1-10202-2-200-1-111-2-20200-1-1-202-11000-1-11111-20000-2110000001000
χ19222222-12-122-12-1222-12-122-122-1-1-1-12-1-12-1-1-122-1-1-1-1-1-1-1-1-10-20-2220011-1-1220-2001120-21-100011-1-1-1-1-20000-2110000001000
χ20222222-12-122-12-1222-12-122-122-1-1-1-12-1-12-1-1-122-1-1-1-1-1-1-1-1-10-20-2-2-2001111-2-20-20011-20-211000111111200002-1-1000000-1000
χ21222222-12-122-12-122-2-12-1-2-2-122-1-1-1-12-1-1-2111-2-211-1-1-11111020-22-200-1-111220200-1-1-20-21-100011-1-11120000-211000000-1000
χ22222222-12-122-12-122-2-12-1-2-2-122-1-1-1-12-1-1-2111-2-211-1-1-11111020-2-2200-1-1-1-1-2-20200-1-120-2110001111-1-1-200002-1-10000001000
χ23222222-12-122-12-122-2-12-1-2-2-122-1-1-1-12-1-1-2111-2-211-1-1-111110-2022-2001111220-20011-202-1-1000-1-1-1-111-200002-1-10000001000
χ24222222-12-122-12-122-2-12-1-2-2-122-1-1-1-12-1-1-2111-2-211-1-1-111110-202-220011-1-1-2-20-20011202-11000-1-111-1-120000-211000000-1000
χ2522222-12-122-12222-122-1-1-1-12-1-1-1-122-1-1-12222-1-1-1-1-1-1-1-1-1-1-122220022220000-1-1-1-1-1-10-1-1202-1-1-1-100000002200000-1-1-1-10000
χ2622222-12-122-12222-122-1-1-1-12-1-1-1-122-1-1-12222-1-1-1-1-1-1-1-1-1-1-12-22-20022-2-20000-11-1-1110-11-202-1-1110000000-2-20000011110000
χ2722222-12-122-12222-122-1-1-1-12-1-1-1-122-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-22-2200-2-22200001-111-1-101-120-211-1-10000000-2-20000011110000
χ2822222-12-122-12222-122-1-1-1-12-1-1-1-122-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-2-2-2-200-2-2-2-20000111111011-20-2111100000002200000-1-1-1-10000
χ2922222-12-122-12222-1-22-1-1112-1-1-1-122-1-1-1-2-2-2-21111-1-1-1111122-2-20022220000-1-1-1-1-1-1011-20-2111100000002-200000-1-1110000
χ3022222-12-122-12222-1-22-1-1112-1-1-1-122-1-1-1-2-2-2-21111-1-1-111112-2-220022-2-20000-11-1-11101-120-211-1-10000000-220000011-1-10000
χ3122222-12-122-12222-1-22-1-1112-1-1-1-122-1-1-1-2-2-2-21111-1-1-11111-222-200-2-22200001-111-1-10-11-202-1-1110000000-220000011-1-10000
χ3222222-12-122-12222-1-22-1-1112-1-1-1-122-1-1-1-2-2-2-21111-1-1-11111-2-22200-2-2-2-200001111110-1-1202-1-1-1-100000002-200000-1-1110000
χ332222-12222-122-12-122-1-1222-1-1-122-1-1-12-1-12-1-1-1-122-1-1-1-1-1-1-1202022-1-10022-1-120-1-100-12002-1-1-100-1-1-1-102200000-1-100000-100
χ342222-12222-122-12-122-1-1222-1-1-122-1-1-12-1-12-1-1-1-122-1-1-1-1-1-1-12020-2-2-1-100-2-21120-1-1001200-2-1-1-10011110-2-2000001100000100
χ352222-12222-122-12-122-1-1222-1-1-122-1-1-12-1-12-1-1-1-122-1-1-1-1-1-1-1-20-2022110022-1-1-201100-1-200211100-1-1-1-10-2-2000001100000100
χ362222-12222-122-12-122-1-1222-1-1-122-1-1-12-1-12-1-1-1-122-1-1-1-1-1-1-1-20-20-2-21100-2-211-2011001-200-211100111102200000-1-100000-100
χ372222-12222-122-12-12-2-1-12-2-2-1-1-122-1-1-12-11-21111-2-2-1-1-1111120-202-2-1-100-2-2-1-120-1-1001-200211100-1-1110-2200000-1-100000100
χ382222-12222-122-12-12-2-1-12-2-2-1-1-122-1-1-12-11-21111-2-2-1-1-1111120-20-22-1-100221120-1-100-1-200-21110011-1-102-2000001100000-100
χ392222-12222-122-12-12-2-1-12-2-2-1-1-122-1-1-12-11-21111-2-2-1-1-11111-20202-21100-2-2-1-1-20110012002-1-1-100-1-11102-2000001100000-100
χ402222-12222-122-12-12-2-1-12-2-2-1-1-122-1-1-12-11-21111-2-2-1-1-11111-2020-2211002211-201100-1200-2-1-1-10011-1-10-2200000-1-100000100
χ4144444-2-2-2-24-2-24-24-24-2-21-2-2-2-2-211-2-2-2114-2-2-2-2-211111111104040000-2-200000-2001100-2-20000110000000000000000000000
χ4244444-2-2-2-24-2-24-24-24-2-21-2-2-2-2-211-2-2-2114-2-2-2-2-21111111110-40-400002200000200-1-100220000-1-10000000000000000000000
χ4344444-2-2-2-24-2-24-24-2-4-2-2122-2-2-211-2-2-211-422222-1-1111-1-1-1-1040-40000-2-200000-2001100220000-1-10000000000000000000000
χ4444444-2-2-2-24-2-24-24-2-4-2-2122-2-2-211-2-2-211-422222-1-1111-1-1-1-10-40400002200000200-1-100-2-20000110000000000000000000000
χ454444-24-24-2-24-2-2-2-2441-2-2441-2-2-2-211-2-21-2-211-2-2-2-211111110000440000-2-2-2-2000000-2000-2000001111000000000000000000
χ464444-24-24-2-24-2-2-2-2441-2-2441-2-2-2-211-2-21-2-211-2-2-2-211111110000-4-4000022220000002000200000-1-1-1-1000000000000000000
χ474444-24-24-2-24-2-2-2-24-41-2-2-4-41-2-2-2-211-2-2122-1-12222111-1-1-1-100004-4000022-2-20000002000-20000011-1-1000000000000000000
χ484444-24-24-2-24-2-2-2-24-41-2-2-4-41-2-2-2-211-2-2122-1-12222111-1-1-1-10000-440000-2-222000000-2000200000-1-111000000000000000000
χ494444-2-24-24-2-24-24-2-24-21-2-2-2-211-2-2-2-21-21-24-2-211-2-21111111404000-2-2000000-2011000-2000-211000000000000000000000000
χ504444-2-24-24-2-24-24-2-24-21-2-2-2-211-2-2-2-21-21-24-2-211-2-21111111-40-40002200000020-1-100020002-1-1000000000000000000000000
χ514444-2-24-24-2-24-24-2-2-4-21-222-211-2-2-2-21-212-422-1-122111-1-1-1-140-4000-2-2000000-201100020002-1-1000000000000000000000000
χ524444-2-24-24-2-24-24-2-2-4-21-222-211-2-2-2-21-212-422-1-122111-1-1-1-1-4040002200000020-1-1000-2000-211000000000000000000000000
χ5344-4-444444-4-4-44-4-4-404440044-44-4-4-4-4-44000000004-4-400000000000000000000000000000000000000000000000000000000
χ5444-4-444-24-2-4-4242-4-40-24-200-24-4-2222-42-200000000-2220000000000000023−230000000000000000000023−23000000000000000000
χ5544-4-444-24-2-4-4242-4-40-24-200-24-4-2222-42-200000000-22200000000000000−232300000000000000000000−2323000000000000000000
χ5644-4-44-24-24-42-44-4-4204-2-2004-22-22-4-422-200000000-2220000000000000000000000000000000000000000000000000023−230000
χ5744-4-44-24-24-42-44-4-4204-2-2004-22-22-4-422-200000000-22200000000000000000000000000000000000000000000000000−23230000
χ5844-4-4-244442-4-4-2-42-40-2-2400-2-224-4222-4-200000000-222000000000000000023−23000000000000000023−2300000000000000000000
χ5944-4-4-244442-4-4-2-42-40-2-2400-2-224-4222-4-200000000-2220000000000000000−23230000000000000000−232300000000000000000000
χ6044-4-4-24-24-22-42-222-401-2-2001-22-22-1-1221003-300001-1-133-3-3000000000023−2323−230000000000000000−33−33000000000000000000
χ6144-4-4-24-24-22-42-222-401-2-2001-22-22-1-1221003-300001-1-133-3-30000000000−2323−232300000000000000003−33−3000000000000000000
χ6244-4-4-24-24-22-42-222-401-2-2001-22-22-1-122100-3300001-1-1-3-333000000000023−23−232300000000000000003−3−33000000000000000000
χ6344-4-4-24-24-22-42-222-401-2-2001-22-22-1-122100-3300001-1-1-3-3330000000000−232323−230000000000000000−333−3000000000000000000
χ644-44-4444-4-4-444-4-44-4044400-4-4-4-4-44-444400000000-44-400000000000000000000000000000000000000000000000000000000
χ654-44-444-2-42-44-2-424-40-24-2002-4-422-224-2-2000000002-22000000000000−2i32i300000000−2i32i300000000000000000000000000000000
χ664-44-444-2-42-44-2-424-40-24-2002-4-422-224-2-2000000002-220000000000002i3−2i3000000002i3−2i300000000000000000000000000000000
χ674-44-44-242-4-4-24-4-44204-2-2−2i32i3-422224-4-2-2-20000−2i32i3−2i32i32-22−2i32i3−2i32i30000000000000000000000000000000000000000000000000000
χ684-44-44-242-4-4-24-4-44204-2-22i3−2i3-422224-4-2-2-200002i3−2i32i3−2i32-222i3−2i32i3−2i30000000000000000000000000000000000000000000000000000
χ694-44-44-2-222-4-2-2-42420-2-21−2i32i3222-1-1-22-2110000−2i32i3i3−i3-11-1i3−i3i3−i300000000−2i32i300000000i3−i3000000003-30000000000000000000000
χ704-44-44-2-222-4-2-2-42420-2-21−2i32i3222-1-1-22-2110000−2i32i3i3−i3-11-1i3−i3i3−i3000000002i3−2i300000000−i3i300000000-330000000000000000000000
χ714-44-44-2-222-4-2-2-42420-2-212i3−2i3222-1-1-22-21100002i3−2i3−i3i3-11-1−i3i3−i3i300000000−2i32i300000000i3−i300000000-330000000000000000000000
χ724-44-44-2-222-4-2-2-42420-2-212i3−2i3222-1-1-22-21100002i3−2i3−i3i3-11-1−i3i3−i3i3000000002i3−2i300000000−i3i3000000003-30000000000000000000000
χ734-44-4-244-4-42442-4-2-40-2-2400222-4-4-22-24-2000000002-220000000000−2i32i300000000−2i32i30000000000000000000000000000000000
χ744-44-4-244-4-42442-4-2-40-2-2400222-4-4-22-24-2000000002-2200000000002i3−2i3000000002i3−2i30000000000000000000000000000000000
χ754-44-4-2-242-42-242-4-220-21-2−2i32i32-1-122-221-210000i3−i3−2i32i3-11-1i3−i3i3−i3000000−2i32i300000000i3−i3000000003-3000000000000000000000000
χ764-44-4-2-242-42-242-4-220-21-2−2i32i32-1-122-221-210000i3−i3−2i32i3-11-1i3−i3i3−i30000002i3−2i300000000−i3i300000000-33000000000000000000000000
χ774-44-4-2-242-42-242-4-220-21-22i3−2i32-1-122-221-210000−i3i32i3−2i3-11-1−i3i3−i3i3000000−2i32i300000000i3−i300000000-33000000000000000000000000
χ784-44-4-2-242-42-242-4-220-21-22i3−2i32-1-122-221-210000−i3i32i3−2i3-11-1−i3i3−i3i30000002i3−2i300000000−i3i3000000003-3000000000000000000000000
χ794-4-44444-4-44-4-4-44-44044400-4-44-44-44-4-4400000000-4-4400000000000000000000000000000000000000000000000000000000
χ804-4-4444-2-424-42-4-2-440-24-2002-442-22-2-42-20000000022-200000000000000000000000000000000000000000000−2i32i30000000000
χ814-4-4444-2-424-42-4-2-440-24-2002-442-22-2-42-20000000022-2000000000000000000000000000000000000000000002i3−2i30000000000
χ824-4-444-242-442-4-44-4-204-2-200-42-22-2-4422-20000000022-2000000000000000000000000000000000000000000000000−2i32i3000000
χ834-4-444-242-442-4-44-4-204-2-200-42-22-2-4422-20000000022-20000000000000000000000000000000000000000000000002i3−2i3000000
χ844-4-44-244-4-4-2-4-424240-2-240022-2-442-22-4-20000000022-2000000000000000000000000000000000000000000000023−2300000000
χ854-4-44-244-4-4-2-4-424240-2-240022-2-442-22-4-20000000022-20000000000000000000000000000000000000000000000−232300000000
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
χ8888-8-88-4-4-4-4-84484-840-4-4200-4-442-2444-22000000002-2-200000000000000000000000000000000000000000000000000000000
χ8988-8-8-4-48-4844-8-4-8440-42-400-42-2-4444-242000000002-2-200000000000000000000000000000000000000000000000000000000
χ9088-8-8-4-4-4-4-4444-444402220022-22-2-2-2-2-2-1006-60000-111-3-3330000000000000000000000000000000000000000000000000000
χ9188-8-8-4-4-4-4-4444-444402220022-22-2-2-2-2-2-100-660000-11133-3-30000000000000000000000000000000000000000000000000000
χ928-88-8-48-4-8448-444-4-802-4-400-244442-2-4-4200000000-22-200000000000000000000000000000000000000000000000000000000
χ938-88-8-4-4-4444-4-444-440222−4i34i3-2-2-2-2-22-222-100002i3−2i32i3−2i31-11−i3i3−i3i30000000000000000000000000000000000000000000000000000
χ948-88-8-4-4-4444-4-444-4402224i3−4i3-2-2-2-2-22-222-10000−2i32i3−2i32i31-11i3−i3i3−i30000000000000000000000000000000000000000000000000000
χ958-8-888-4-444844-8-4-8-40-4-420044-4-224-44-2200000000-2-2200000000000000000000000000000000000000000000000000000000
χ968-8-88-48-4-84-4-844-44802-4-400-24-44-4-2244200000000-2-2200000000000000000000000000000000000000000000000000000000
χ978-8-88-4-484-8-44-8484-40-42-4004-224-44-4-24200000000-2-2200000000000000000000000000000000000000000000000000000000
χ988-8-88-4-4-444-4444-44-4022200-2-22-22-22-2-2-10000000011-1−3i33i33i3−3i30000000000000000000000000000000000000000000000000000
χ998-8-88-4-4-444-4444-44-4022200-2-22-22-22-2-2-10000000011-13i3−3i3−3i33i30000000000000000000000000000000000000000000000000000

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