Finite Group Databasebeta

← Group #13172356

Character table — Group #13172356

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99
size111122222222222244444444444444488888888888888881212121212121212121212121212242424242424242424242424242424242424242436363636363636363636363636367272108108
order1222333666666666233366666666666366666666666666624444412121212121212126666121212121212121212121212121212122224446666661212121224
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111-1-1111111-1-111111-1-1-111111111-1-1-1-11-1-11-1-111-1-1-1-1-1-11-1-1-1
χ31111111111111111111111111111111111111111111111111-1-11111-1-1-1-11111111111-1-111-1-1-1-11111-111-1-1-1-1-11111-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-111111-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1111
χ511111111111111111111111111111111111111111111111-1-11111-1-1111111-1-1-1-1-111111-1-111111111-1-1-1-111-1-1-1-1-1-111-11-1-1
χ611111111111111111111111111111111111111111111111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-111-1-1-1-1-11111-1-1-1-111
χ711111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1111-1-1-1-1-1-1-1-111111-1-11-1-111-1-1-1-1-1-11-111
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
χ91111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-11-11-11-1-1-111-1-1-1-11111-11-111-1-1-111-1-111-1-111-1-1-111111-1-1-1-1-11-11
χ101111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-11-11-1-11-1-111-1-1111111-1-11-11-1-1-111-1-1-1-1111-11-11-111-1-11111-1-11-1
χ111111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-11-1-111-1-1-1-1-111-1-11111-11-11-11-1-1-1-11111-1-1-11-111-1-1-111-1-1111-11-1
χ121111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-11-1-11-11-1-1-1-111111111-1-11-1-11-1-1-1-111-1-111-1-111-11-1-1-1-111-1-111-11
χ131111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-1-111-11-11111-1-1-1-1-1-1-1-111-111-11111-1-111-1-1-1-111-11-1-1-1-111-1-1111-1
χ141111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-1-111-1-111111-1-111-1-1-1-11-11-11-11111-1-1-1-111-11-111-1-1-111-1-1111-1-11
χ151111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-1-11-111-111-1-111-1-1-1-1-1-111-11-1111-1-11111-1-11-11-11-111-1-11111-1-1-11
χ161111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-1-11-11-1111-1-11111-1-1-1-11-11-1-1111-1-111-1-11111-1-1-111111-1-1-1-1-111-1
χ17222222-12-1-1-12222222-1-1-1-12-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1220022220000222-1-1-1-1-1-1200-1-10000-1-1-1-102200000-1-1-1-1000000
χ18222222-12-1-1-12222222-1-1-1-12-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-12200-2-2220000-2-22-1-1-1-111-200-1-1000011110-2-2000001111000000
χ19222222-12-1-1-12222222-1-1-1-12-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-2-20022-2-2000022-21111-1-1200110000-1-1-1-10-2-2000001111000000
χ20222222-12-1-1-12222222-1-1-1-12-1-1-122-1-1-1-12222-1-1-1-1-1-1-1-1-1-1-1-2-200-2-2-2-20000-2-2-2111111-200110000111102200000-1-1-1-1000000
χ21222222-12-1-1-122222-22-1-1112-1-1-122-1-1-1-1-2-2-2-21111-1-1-111112-2002-2-2-20000-2-22-1-1-11-11200110000-1-11102-200000-1-111000000
χ22222222-12-1-1-122222-22-1-1112-1-1-122-1-1-1-1-2-2-2-21111-1-1-111112-200-22-2-20000222-1-1-111-1-20011000011-1-10-220000011-1-1000000
χ23222222-12-1-1-122222-22-1-1112-1-1-122-1-1-1-1-2-2-2-21111-1-1-11111-22002-2220000-2-2-2111-1-11200-1-10000-1-1110-220000011-1-1000000
χ24222222-12-1-1-122222-22-1-1112-1-1-122-1-1-1-1-2-2-2-21111-1-1-11111-2200-2222000022-2111-11-1-200-1-1000011-1-102-200000-1-111000000
χ2522222-12-12222-122-12-12-122-12-1-1-1-122-1-12-1-1-122-1-1-1-1-1-1-1-1-1222200-1-122-1-100-12-1-12000-12-1-1-1-1-1-10000200200-1-1000000-1000
χ2622222-12-12222-122-12-12-122-12-1-1-1-122-1-12-1-1-122-1-1-1-1-1-1-1-1-122-2-200-1-1-2-21100-12-1-120001-2-1-111110000-200-200110000001000
χ2722222-12-12222-122-12-12-122-12-1-1-1-122-1-12-1-1-122-1-1-1-1-1-1-1-1-1-2-222001122-1-1001-211-2000-1211-1-1-1-10000-200-200110000001000
χ2822222-12-12222-122-12-12-122-12-1-1-1-122-1-12-1-1-122-1-1-1-1-1-1-1-1-1-2-2-2-20011-2-211001-211-20001-21111110000200200-1-1000000-1000
χ2922222-12-12222-122-1-2-12-1-2-2-12-1-1-1-122-1-1-2111-2-211-1-1-111112-22-20011221100-12-1-1-2000-1-211-1-1110000200-200-1-10000001000
χ3022222-12-12222-122-1-2-12-1-2-2-12-1-1-1-122-1-1-2111-2-211-1-1-111112-2-220011-2-2-1-100-12-1-1-2000121111-1-10000-20020011000000-1000
χ3122222-12-12222-122-1-2-12-1-2-2-12-1-1-1-122-1-1-2111-2-211-1-1-11111-222-200-1-12211001-2112000-1-2-1-1-1-1110000-20020011000000-1000
χ3222222-12-12222-122-1-2-12-1-2-2-12-1-1-1-122-1-1-2111-2-211-1-1-11111-22-2200-1-1-2-2-1-1001-211200012-1-111-1-10000200-200-1-10000001000
χ332222-1222222-12-1-122-1-1222-1-122-1-1-1-12-1-12-1-1-1-122-1-1-1-1-1-1-100222200-1-122-1-10000022-12-100-1-1-1-1-1-1-1-1000022000000-1-10-100
χ342222-1222222-12-1-122-1-1222-1-122-1-1-1-12-1-12-1-1-1-122-1-1-1-1-1-1-10022-2-200-1-1221100000-2-212-100-1-1-1-111110000-2-2000000110100
χ352222-1222222-12-1-122-1-1222-1-122-1-1-1-12-1-12-1-1-1-122-1-1-1-1-1-1-100-2-2220011-2-2-1-10000022-1-21001111-1-1-1-10000-2-2000000110100
χ362222-1222222-12-1-122-1-1222-1-122-1-1-1-12-1-12-1-1-1-122-1-1-1-1-1-1-100-2-2-2-20011-2-21100000-2-21-210011111111000022000000-1-10-100
χ372222-1222222-12-1-12-2-1-12-2-2-1-122-1-1-1-12-11-21111-2-2-1-1-11111002-22-200-1-1-2-211000002-2-12100-1-111-1-1110000-22000000110-100
χ382222-1222222-12-1-12-2-1-12-2-2-1-122-1-1-1-12-11-21111-2-2-1-1-11111002-2-2200-1-1-2-2-1-100000-2212100-1-11111-1-100002-2000000-1-10100
χ392222-1222222-12-1-12-2-1-12-2-2-1-122-1-1-1-12-11-21111-2-2-1-1-1111100-222-200112211000002-2-1-2-10011-1-1-1-11100002-2000000-1-10100
χ402222-1222222-12-1-12-2-1-12-2-2-1-122-1-1-1-12-11-21111-2-2-1-1-1111100-22-22001122-1-100000-221-2-10011-1-111-1-10000-22000000110-100
χ4144444-2-2-2-2-2-24-244-24-2-21-2-2-2-211-2-2-2-2114-2-2-2-2-2111111111440000-2-2000000-2-211-2000001100000000000000000000000000
χ4244444-2-2-2-2-2-24-244-24-2-21-2-2-2-211-2-2-2-2114-2-2-2-2-2111111111-4-400002200000022-1-1200000-1-100000000000000000000000000
χ4344444-2-2-2-2-2-24-244-2-4-2-2122-2-211-2-2-2-211-422222-1-1111-1-1-1-14-4000022000000-2-211200000-1-100000000000000000000000000
χ4444444-2-2-2-2-2-24-244-2-4-2-2122-2-211-2-2-2-211-422222-1-1111-1-1-1-1-440000-2-200000022-1-1-2000001100000000000000000000000000
χ454444-24-24-2-2-2-24-2-244-21-2-2-2-21-2-2-2-211-21-24-2-211-2-21111111000044000000-2-200000-2-2-2000000001111000000000000000000
χ464444-24-24-2-2-2-24-2-244-21-2-2-2-21-2-2-2-211-21-24-2-211-2-211111110000-4-4000000220000022200000000-1-1-1-1000000000000000000
χ474444-24-24-2-2-2-24-2-24-4-21-222-21-2-2-2-211-212-422-1-122111-1-1-1-100004-40000002200000-22-20000000011-1-1000000000000000000
χ484444-24-24-2-2-2-24-2-24-4-21-222-21-2-2-2-211-212-422-1-122111-1-1-1-10000-44000000-2-2000002-2200000000-1-111000000000000000000
χ494444-2-24-2444-2-2-2-2-241-2-2441-2-2-211-2-2-21-2-211-2-2-2-2111111100440000-2-2-2-20000000000-2-20011110000000000000000000000
χ504444-2-24-2444-2-2-2-2-241-2-2441-2-2-211-2-2-21-2-211-2-2-2-2111111100-4-40000222200000000002200-1-1-1-10000000000000000000000
χ514444-2-24-2444-2-2-2-2-2-41-2-2-4-41-2-2-211-2-2-2122-1-12222111-1-1-1-1004-40000-2-2220000000000-220011-1-10000000000000000000000
χ524444-2-24-2444-2-2-2-2-2-41-2-2-4-41-2-2-211-2-2-2122-1-12222111-1-1-1-100-44000022-2-200000000002-200-1-1110000000000000000000000
χ5344-4-4444-44-4-44-4-4-44044400-4-44-44-44-4-44000000004-4-400000000000000000000000000000000000000000000000000000000
χ5444-4-444-2-4-2224-4-4-4404-2-200-42-224-4-222-200000000-2220000000000000000000000000000000000000000000000−2i32i300000000
χ5544-4-444-2-4-2224-4-4-4404-2-200-42-224-4-222-200000000-22200000000000000000000000000000000000000000000002i3−2i300000000
χ5644-4-44-2424-4-442-4-4-20-24-2002-4-22-224-42-200000000-22200000000000000000000000000000000000000000000−2i32i30000000000
χ5744-4-44-2424-4-442-4-4-20-24-2002-4-22-224-42-200000000-222000000000000000000000000000000000000000000002i3−2i30000000000
χ5844-4-4-244-44-4-4-2-42240-2-2400224-4-22-22-4-200000000-2220000000000000000000000000000000000000000000000000023−230000
χ5944-4-4-244-44-4-4-2-42240-2-2400224-4-22-22-4-200000000-22200000000000000000000000000000000000000000000000000−23230000
χ604-44-4444-4-44-4-444-4-4044400-44-4-4-44-4-44400000000-44-400000000000000000000000000000000000000000000000000000000
χ614-44-444-2-42-22-444-4-404-2-2−2i32i3-4-222-4422-2-20000−2i32i3−2i32i32-22−2i3−2i32i32i30000000000000000000000000000000000000000000000000000
χ624-44-444-2-42-22-444-4-404-2-22i3−2i3-4-222-4422-2-200002i3−2i32i3−2i32-222i32i3−2i3−2i30000000000000000000000000000000000000000000000000000
χ634-44-44-242-44-4-4-24-420-24-20024222-2-4-4-2-2000000002-220000000000−2i32i30000000000000000−2i32i300000000000000000000000000
χ644-44-44-242-44-4-4-24-420-24-20024222-2-4-4-2-2000000002-2200000000002i3−2i300000000000000002i3−2i300000000000000000000000000
χ654-44-44-2-222-22-4-24-420-2-21−2i32i32-2-1-12-222110000−2i32i3i3−i3-11-1i3i3−i3−i3000000−2i32i3000000003-3000000i3−i300000000000000000000000000
χ664-44-44-2-222-22-4-24-420-2-21−2i32i32-2-1-12-222110000−2i32i3i3−i3-11-1i3i3−i3−i30000002i3−2i300000000-33000000−i3i300000000000000000000000000
χ674-44-44-2-222-22-4-24-420-2-212i3−2i32-2-1-12-2221100002i3−2i3−i3i3-11-1−i3−i3i3i3000000−2i32i300000000-33000000i3−i300000000000000000000000000
χ684-44-44-2-222-22-4-24-420-2-212i3−2i32-2-1-12-2221100002i3−2i3−i3i3-11-1−i3−i3i3i30000002i3−2i3000000003-3000000−i3i300000000000000000000000000
χ694-44-4-244-4-44-424-22-40-2-24002-2-4-42-2224-2000000002-22000000000000000023−2300000000000000000023−23000000000000000000
χ704-44-4-244-4-44-424-22-40-2-24002-2-4-42-2224-2000000002-220000000000000000−2323000000000000000000−2323000000000000000000
χ714-44-4-24-2-42-2224-22-40-21-2−2i32i321222-2-1-1-210000i3−i3−2i32i3-11-1i3i3−i3−i300000000000023−2300000000000000003i−3i−33000000000000000000
χ724-44-4-24-2-42-2224-22-40-21-2−2i32i321222-2-1-1-210000i3−i3−2i32i3-11-1i3i3−i3−i3000000000000−23230000000000000000−3i3i3−3000000000000000000
χ734-44-4-24-2-42-2224-22-40-21-22i3−2i321222-2-1-1-210000−i3i32i3−2i3-11-1−i3−i3i3i300000000000023−230000000000000000−3i3i−33000000000000000000
χ744-44-4-24-2-42-2224-22-40-21-22i3−2i321222-2-1-1-210000−i3i32i3−2i3-11-1−i3−i3i3i3000000000000−232300000000000000003i−3i3−3000000000000000000
χ754-4-444444-4-44-4-4-44-40444004-4-44-4-4-44-4400000000-4-4400000000000000000000000000000000000000000000000000000000
χ764-4-4444-2422-2-4-4-44-404-2-200422-2-4-42-22-20000000022-2000000000000000000000000000000000000000000000000−2i32i3000000
χ774-4-4444-2422-2-4-4-44-404-2-200422-2-4-42-22-20000000022-20000000000000000000000000000000000000000000000002i3−2i3000000
χ784-4-444-24-2-4-44-42-4420-24-200-2-42-222-442-20000000022-20000000000000023−23000000000000000023−230000000000000000000000
χ794-4-444-24-2-4-44-42-4420-24-200-2-42-222-442-20000000022-200000000000000−23230000000000000000−23230000000000000000000000
χ804-4-44-2444-4-442-42-2-40-2-2400-22-44222-2-4-20000000022-200000000000023−23000000000000000023−23000000000000000000000000
χ814-4-44-2444-4-442-42-2-40-2-2400-22-44222-2-4-20000000022-2000000000000−23230000000000000000−2323000000000000000000000000
χ824-4-44-2-24-2-4-44222-2201-2-200122-2-1-12-221003-30000-1-113-33-30000000023−2323−2300000000000000−33−330000000000000000000000
χ834-4-44-2-24-2-4-44222-2201-2-200122-2-1-12-221003-30000-1-113-33-300000000−2323−2323000000000000003−33−30000000000000000000000
χ844-4-44-2-24-2-4-44222-2201-2-200122-2-1-12-22100-330000-1-11-33-330000000023−23−232300000000000000−333−30000000000000000000000
χ854-4-44-2-24-2-4-44222-2201-2-200122-2-1-12-22100-330000-1-11-33-3300000000−232323−23000000000000003−3−330000000000000000000000
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
χ8888-8-88-4-44-44484-8-8-40-4-4200442-2-44-44-22000000002-2-200000000000000000000000000000000000000000000000000000000
χ8988-8-8-48-4-8-444-4-84480-42-4004-2-44-442-242000000002-2-200000000000000000000000000000000000000000000000000000000
χ9088-8-8-4-4848-8-8-4444-402-4-400-24-442-2-4442000000002-2-200000000000000000000000000000000000000000000000000000000
χ9188-8-8-4-4-44-444-4444-4022200-2-22-22-22-2-2-100000000-111−3i33i33i3−3i30000000000000000000000000000000000000000000000000000
χ9288-8-8-4-4-44-444-4444-4022200-2-22-22-22-2-2-100000000-1113i3−3i3−3i33i30000000000000000000000000000000000000000000000000000
χ938-88-8-4-484-88-84-4-44402-4-400-2-444-2244-4200000000-22-200000000000000000000000000000000000000000000000000000000
χ948-88-8-4-4-444-444-4-4440222−4i34i3-22-2-2-22-2-22-100002i3−2i32i3−2i31-11−i3−i3i3i30000000000000000000000000000000000000000000000000000
χ958-88-8-4-4-444-444-4-44402224i3−4i3-22-2-2-22-2-22-10000−2i32i3−2i32i31-11i3i3−i3−i30000000000000000000000000000000000000000000000000000
χ968-8-888-4-4-444-4-84-8840-4-4200-44-22444-4-2200000000-2-2200000000000000000000000000000000000000000000000000000000
χ978-8-88-48-4844-44-84-4-80-42-400-4-24-444-224200000000-2-2200000000000000000000000000000000000000000000000000000000
χ988-8-88-4-4-4-444-4444-440222002-2-22-2-2-22-2-1006-6000011-1-33-330000000000000000000000000000000000000000000000000000
χ998-8-88-4-4-4-444-4444-440222002-2-22-2-2-22-2-100-66000011-13-33-30000000000000000000000000000000000000000000000000000

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