Finite Group Databasebeta

← Group #13172160

Character table — Group #13172160

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size1111222222222222444444444444466888888888888888881212121212121212121212121212121212181824242424242424242424242424242424242436363636363636363636365454727272108
order12223336666666662333666666666443666666666666666624444661212121212121212121244666121212121212121212121212121212244446612121212441212124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111-1-111-1-1111111-1-1-1-111111-11-1111111-1-1-1-1-11-1-11-1-1-1-111-1-11-1-1-1
χ3111111111111111111111111111111111111111111111111-11-111-1-1111111-1-111-1-1-1-1-1111-111111-1-111111-11-1-111-1-1-1-1-1-1-11-1-1
χ4111111111111111111111111111111111111111111111111-11-1-1-1-1-1-1-11111-1-1-1-111-1-1-111-1-1-11111-1-1-1-1-1-1-1-1-11-1-1-111-1-111-1-111
χ511111111111111111111111111111-1-1111111111111111111-11111111-1-1-1-1111111111-1-1111-1-1-1-1111111-1-1-11-1-1-111-1-1-1-1-1-11-1
χ611111111111111111111111111111-1-1111111111111111111-11-1-111-1-1-1-1-1-111-1-1-1-1111-1-1-11-1-1-1-1-111-1-1-1-11-11-1-111-1-1-1-111-11-11
χ711111111111111111111111111111-1-111111111111111111-1-1-111-1-111-1-1-1-1-1-111-1-1-1-1-1-1-11-11-1-1-1-1-1-11111-11-1-11-1-1-1-111111-1-11
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
χ91111111111111111-1111111111111111-1-1-1-1-1-1-1-1-1111-1-1-1-11-1-11-111-1-11111-1-11111111-1-1-1-1111-1-1-1-111-1-111-1-1-111111111-1-1-1-1
χ101111111111111111-1111111111111111-1-1-1-1-1-1-1-1-1111-1-1-1-11-1-1-1111111111-1-1-1-1-1-1111-1-11-1-111-1-1-1-1-1-111-1111-1-1-1-1-111-1-1-1111
χ111111111111111111-1111111111111111-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-111-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-11111-1-11-1-11111-1-1-1-1-1-11-111
χ121111111111111111-1111111111111111-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-11-11-1-111111111-1-111-1-1-1-1-111-111-1-111-1-111-1-11-11-1-111-1-11111-1-1
χ131111111111111111-1111111111111-1-11-1-1-1-1-1-1-1-1-1111-1-1-1-111-11-111-1-1-1-1-1-1-1-1111111111-1-11-1-111-1-111-1-1-1-11-11-1-111-1-1-1-111-11
χ141111111111111111-1111111111111-1-11-1-1-1-1-1-1-1-1-1111-1-1-1-111-1-111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1111-1-11111-1-1-1-1111-11-1
χ151111111111111111-1111111111111-1-11-1-1-1-1-1-1-1-1-1111-1-1-1-1-1111-1-1-1-1-1-1-1-1-11111-1-1-1-1-111-111-1-1111111-1-1-1111-1-1-1-1-11111-111-1
χ161111111111111111-1111111111111-1-11-1-1-1-1-1-1-1-1-1111-1-1-1-1-111-11-1-111-1-1-1-111-1-111-1-1-11111-1-1-11111-1-11111-1-1-1111111-1-1-1-1-11
χ17222222-122-1-12222-12-1-12-1-122-1-1-1-1222-122-1-1-1-1-122-1-1-1-1-1-1-102022002222-1-100-1-1000002-1-102-1-1-1-100-1-1-1-120200-1-10000000-100
χ18222222-122-1-12222-12-1-12-1-122-1-1-1-1222-122-1-1-1-1-122-1-1-1-1-1-1-1020-2-200-2-222-1-10011000002-110-2-1-1-1-1001111-20-200110000000100
χ19222222-122-1-12222-12-1-12-1-122-1-1-1-12-2-2-122-1-1-1-1-122-1-1-1-1-1-1-10-20220022-2-21100-1-100000-21-102111100-1-1-1-1-20-200110000000100
χ20222222-122-1-12222-12-1-12-1-122-1-1-1-12-2-2-122-1-1-1-1-122-1-1-1-1-1-1-10-20-2-200-2-2-2-211001100000-2110-2111100111120200-1-10000000-100
χ21222222-122-1-12222-1-2-1-12-1-122-1-1-1-1222-1-2-211111-2-2-1-1-111110-202-200-2-222-1-100-1-100000-21102-1-11100-1-11120-200-1-10000000100
χ22222222-122-1-12222-1-2-1-12-1-122-1-1-1-1222-1-2-211111-2-2-1-1-111110-20-22002222-1-1001100000-21-10-2-1-1110011-1-1-20200110000000-100
χ23222222-122-1-12222-1-2-1-12-1-122-1-1-1-12-2-2-1-2-211111-2-2-1-1-111110202-200-2-2-2-21100-1-1000002-110211-1-100-1-111-20200110000000-100
χ24222222-122-1-12222-1-2-1-12-1-122-1-1-1-12-2-2-1-2-211111-2-2-1-1-11111020-220022-2-2110011000002-1-10-211-1-10011-1-120-200-1-10000000100
χ2522222-122-1222-12-1222-1-12-1-1-122-1-1-100-12-1222-1-1-1-1-1-1-1-1-1-1-12022222-1-10000-1-12222-1-1-10022-10000-1-1-1-1-1-10002000-1-1000000-10
χ2622222-122-1222-12-1222-1-12-1-1-122-1-1-100-12-1222-1-1-1-1-1-1-1-1-1-1-1202-2-222110000-1-1-2-2-2-2-1-1-100-2210000-1-11111000-20001100000010
χ2722222-122-1222-12-1222-1-12-1-1-122-1-1-100-12-1222-1-1-1-1-1-1-1-1-1-1-1-20-222-2-2-1-100001122-2-2111002-2-1000011-1-1-1-1000-20001100000010
χ2822222-122-1222-12-1222-1-12-1-1-122-1-1-100-12-1222-1-1-1-1-1-1-1-1-1-1-1-20-2-2-2-2-211000011-2-22211100-2-2100001111110002000-1-1000000-10
χ2922222-122-1222-12-12-22-1-12-1-1-122-1-1-100-1-21-2-2-21111-1-1-1111120-22-222110000112222-1-1-100-2-2-1000011-1-111000-2000-1-100000010
χ3022222-122-1222-12-12-22-1-12-1-1-122-1-1-100-1-21-2-2-21111-1-1-1111120-2-2222-1-1000011-2-2-2-2-1-1-1002-2100001111-1-1000200011000000-10
χ3122222-122-1222-12-12-22-1-12-1-1-122-1-1-100-1-21-2-2-21111-1-1-11111-2022-2-2-2110000-1-122-2-211100-22-10000-1-1-1-111000200011000000-10
χ3222222-122-1222-12-12-22-1-12-1-1-122-1-1-100-1-21-2-2-21111-1-1-11111-202-22-2-2-1-10000-1-1-2-222111002210000-1-111-1-1000-2000-1-100000010
χ332222-122-1222-12-1222-12-1-12-1-1-1-122-122-1-122-1-122-1-1-1-1-1-1-1-1-122200-1-100-1-1222200002-1-1-120-10-1-1-1-1-1-10000020020000-1-100-1000
χ342222-122-1222-12-1222-12-1-12-1-1-1-122-122-1-122-1-122-1-1-1-1-1-1-1-1-1-22-2001100-1-122-2-20000-211-12010-1-1-1-11100000-200-2000011001000
χ352222-122-1222-12-1222-12-1-12-1-1-1-122-1-2-2-1-122-1-122-1-1-1-1-1-1-1-1-12-2200-1-10011-2-22200002-1-11-20-101111-1-100000-200-2000011001000
χ362222-122-1222-12-1222-12-1-12-1-1-1-122-1-2-2-1-122-1-122-1-1-1-1-1-1-1-1-1-2-2-200110011-2-2-2-20000-2111-20101111110000020020000-1-100-1000
χ372222-122-1222-12-122-2-12-1-12-1-1-1-122-122-11-2-211-2-211-1-1-111112-2-200-1-100-1-122-2-200002-1-11-2010-1-1111100000200-20000-1-1001000
χ382222-122-1222-12-122-2-12-1-12-1-1-1-122-122-11-2-211-2-211-1-1-11111-2-22001100-1-122220000-2111-20-10-1-111-1-100000-200200001100-1000
χ392222-122-1222-12-122-2-12-1-12-1-1-1-122-1-2-2-11-2-211-2-211-1-1-1111122-200-1-10011-2-2-2-200002-1-1-1201011-1-11100000-200200001100-1000
χ402222-122-1222-12-122-2-12-1-12-1-1-1-122-1-2-2-11-2-211-2-211-1-1-11111-22200110011-2-2220000-211-120-1011-1-1-1-100000200-20000-1-1001000
χ412-2-22222-222-22-2-2-2-202222-22-2-2-22-2-22i−2i20000000002-2-200000000000002i−2i2i−2i00002i−2i000000002i−2i0000000000000002i−2i002-20000
χ422-2-22222-222-22-2-2-2-202222-22-2-2-22-2-22i−2i20000000002-2-200000000000002i−2i2i−2i0000−2i2i000000002i−2i000000000000000−2i2i00-220000
χ432-2-22222-222-22-2-2-2-202222-22-2-2-22-2-2−2i2i20000000002-2-20000000000000−2i2i−2i2i00002i−2i00000000−2i2i0000000000000002i−2i00-220000
χ442-2-22222-222-22-2-2-2-202222-22-2-2-22-2-2−2i2i20000000002-2-20000000000000−2i2i−2i2i0000−2i2i00000000−2i2i000000000000000−2i2i002-20000
χ4544444-2-24-2-2-24-24-2-24-21-2-21-2-2-2-211-20014-2-2-2-211-2-211111110004400-2-2000000-2-20000000-20-2000000111100000000000000000
χ4644444-2-24-2-2-24-24-2-24-21-2-21-2-2-2-211-20014-2-2-2-211-2-21111111000-4-40022000000220000000202000000-1-1-1-100000000000000000
χ4744444-2-24-2-2-24-24-2-2-4-21-2-21-2-2-2-211-2001-42222-1-122111-1-1-1-10004-40022000000-2-2000000020-200000011-1-100000000000000000
χ4844444-2-24-2-2-24-24-2-2-4-21-2-21-2-2-2-211-2001-42222-1-122111-1-1-1-1000-4400-2-2000000220000000-202000000-1-11100000000000000000
χ494444-24-2-24-2-2-24-24-241-2-21-2-2-211-2-2-2441-24-211-2-2-2-21111111040000000-2-2-2-2000000000-2-2000111100000000000000000000000
χ504444-24-2-24-2-2-24-24-241-2-21-2-2-211-2-2-2-4-41-24-211-2-2-2-211111110-40000000222200000000022000-1-1-1-100000000000000000000000
χ514444-24-2-24-2-2-24-24-2-41-2-21-2-2-211-2-2-24412-42-1-12222111-1-1-1-10-40000000-2-2-2-20000000002200011-1-100000000000000000000000
χ524444-24-2-24-2-2-24-24-2-41-2-21-2-2-211-2-2-2-4-412-42-1-12222111-1-1-1-10400000002222000000000-2-2000-1-11100000000000000000000000
χ534444-2-24-2-244-2-2-2-244-2-21-2-211-2-2-2-21001-2-24-2-2-2-211111111140400-2-2000000-2-20000-211000-20000011000000000000000000000
χ544444-2-24-2-244-2-2-2-244-2-21-2-211-2-2-2-21001-2-24-2-2-2-2111111111-40-400220000002200002-1-1000200000-1-1000000000000000000000
χ554444-2-24-2-244-2-2-2-24-4-2-21-2-211-2-2-2-2100122-42222-1-1111-1-1-1-140-400-2-2000000220000-211000200000-1-1000000000000000000000
χ564444-2-24-2-244-2-2-2-24-4-2-21-2-211-2-2-2-2100122-42222-1-1111-1-1-1-1-4040022000000-2-200002-1-1000-20000011000000000000000000000
χ5744-4-44444-4-44-44-4-4-40444-44-444-4-4-4-4004000000000-44-40000000000000000000000000000000000000000000000000000000000
χ5844-4-444-24-42-2-44-4-420-2-242-2-44-2222-400-20000000002-22000000000000000000023−23000000000000000023−230000000000000000000
χ5944-4-444-24-42-2-44-4-420-2-242-2-44-2222-400-20000000002-220000000000000000000−23230000000000000000−23230000000000000000000
χ6044-4-44-2442-44-4-2-42-404-2-2-4-22-24-422200-20000000002-220000000000023−230000000000000000000000000023−2300000000000000000
χ6144-4-44-2442-44-4-2-42-404-2-2-4-22-24-422200-20000000002-2200000000000−232300000000000000000000000000−232300000000000000000
χ6244-4-44-2-2422-2-4-2-4220-21-2212-2-22-1-12001000003-300-11-133-3-3000000023−2300000023−230000000000000000−33−3300000000000000000
χ6344-4-44-2-2422-2-4-2-4220-21-2212-2-22-1-12001000003-300-11-133-3-30000000−2323000000−232300000000000000003−33−300000000000000000
χ6444-4-44-2-2422-2-4-2-4220-21-2212-2-22-1-1200100000-3300-11-1-3-333000000023−23000000−232300000000000000003−3−3300000000000000000
χ6544-4-44-2-2422-2-4-2-4220-21-2212-2-22-1-1200100000-3300-11-1-3-3330000000−232300000023−230000000000000000−333−300000000000000000
χ6644-4-4-244-2-4-44242-4-40-24-2242-2-22-4-4200-20000000002-220000000000000000000000000000000000000000000000000023−23000000
χ6744-4-4-244-2-4-44242-4-40-24-2242-2-22-4-4200-20000000002-2200000000000000000000000000000000000000000000000000−2323000000
χ684-44-4444-4-4-4-4-4-44440444-4-4-4-4-44-444004000000000-4-440000000000000000000000000000000000000000000000000000000000
χ694-44-444-2-4-422-4-444-20-2-2422-4-42-22-2400-200000000022-20000000000000000000000000000000000000000000000−2i32i30000000000
χ704-44-444-2-4-422-4-444-20-2-2422-4-42-22-2400-200000000022-200000000000000000000000000000000000000000000002i3−2i30000000000
χ714-44-44-24-42-4-4-424-2404-2-2-4222-442-2-200-200000000022-200000000000000000−2i32i30000000000000000−2i32i3000000000000000000000
χ724-44-44-24-42-4-4-424-2404-2-2-4222-442-2-200-200000000022-2000000000000000002i3−2i300000000000000002i3−2i3000000000000000000000
χ734-44-4-2442-4-4-42-4-2440-24-22-4222-2-44-200-200000000022-2000000000−2i32i30000000000000−2i32i300000000000000000000000000000000
χ744-44-4-2442-4-4-42-4-2440-24-22-4222-2-44-200-200000000022-20000000002i3−2i300000000000002i3−2i300000000000000000000000000000000
χ754-44-4-2-2422-4-422-2-240-2-2122-1-12-22-2100100000003-3-1-113-33-300000−2i32i3000000−2i32i300000i3−i3000000000i3−i3000000000000000000000
χ764-44-4-2-2422-4-422-2-240-2-2122-1-12-22-2100100000003-3-1-113-33-3000002i3−2i30000002i3−2i300000−i3i3000000000−i3i3000000000000000000000
χ774-44-4-2-2422-4-422-2-240-2-2122-1-12-22-210010000000-33-1-11-33-3300000−2i32i30000002i3−2i300000i3−i3000000000−i3i3000000000000000000000
χ784-44-4-2-2422-4-422-2-240-2-2122-1-12-22-210010000000-33-1-11-33-33000002i3−2i3000000−2i32i300000−i3i3000000000i3−i3000000000000000000000
χ794-4-4444-2-44-224-4-4-420-2-24-224-422-22-44i−4i-2000000000-22200000000000004i−4i−2i2i00000000000000−2i2i0000000000000000000000000
χ804-4-4444-2-44-224-4-4-420-2-24-224-422-22-4−4i4i-2000000000-2220000000000000−4i4i2i−2i000000000000002i−2i0000000000000000000000000
χ814-4-444-24-4-24-442-42-404-2-242-22-4-4-22200-2000000000-2220000000000000000000004i−4i0000000000000000000000000−2i2i00000000
χ824-4-444-24-4-24-442-42-404-2-242-22-4-4-22200-2000000000-222000000000000000000000−4i4i00000000000000000000000002i−2i00000000
χ834-4-44-244244-4-2-42-4-40-24-2-2-4-22224-424i−4i-2000000000-2220000000000000−2i2i4i−4i00000000000000−2i2i0000000000000000000000000
χ844-4-44-244244-4-2-42-4-40-24-2-2-4-22224-42−4i4i-2000000000-22200000000000002i−2i−4i4i000000000000002i−2i0000000000000000000000000
χ854-4-44-24-224-22-2-42-4201-2-212-22-1-1-2224i−4i10003-300001-1-13-3-33000000000−2i2i−2i2i00000000000000i−i3i−3i00000000000000000000000
χ864-4-44-24-224-22-2-42-4201-2-212-22-1-1-2224i−4i1000-3300001-1-1-333-3000000000−2i2i−2i2i00000000000000i−i−3i3i00000000000000000000000
χ874-4-44-24-224-22-2-42-4201-2-212-22-1-1-222−4i4i10003-300001-1-13-3-330000000002i−2i2i−2i00000000000000−ii−3i3i00000000000000000000000
χ884-4-44-24-224-22-2-42-4201-2-212-22-1-1-222−4i4i1000-3300001-1-1-333-30000000002i−2i2i−2i00000000000000−ii3i−3i00000000000000000000000
χ898888-4-4-4-4-4-4-4-4-4-4-4-4822222222222200-1-4-4-4222222-1-1-1-1-1-1-1000000000000000000000000000000000000000000000000000000
χ908888-4-4-4-4-4-4-4-4-4-4-4-4-822222222222200-1444-2-2-2-2-2-2-1-1-11111000000000000000000000000000000000000000000000000000000
χ9188-8-8-48-4-4-84-4484-8402-4-4-2-44-42-2444002000000000-22-20000000000000000000000000000000000000000000000000000000000
χ9288-8-8-4-48-44-884-444-80-4-424-4-22-4444-2002000000000-22-20000000000000000000000000000000000000000000000000000000000
χ9388-8-8-4-4-4-444-44-44440222-22-222-2-2-2-200-1000006-6001-11-3-333000000000000000000000000000000000000000000000000000000
χ9488-8-8-4-4-4-444-44-44440222-22-222-2-2-2-200-100000-66001-1133-3-3000000000000000000000000000000000000000000000000000000
χ958-88-88-4-4-8444-848-4-40-42-44-2444-4-22-4002000000000-2-220000000000000000000000000000000000000000000000000000000000
χ968-88-8-48-44-8444-8-48-402-4-4-2444-224-4-4002000000000-2-220000000000000000000000000000000000000000000000000000000000
χ978-88-8-4-4-4444444-4-4-40222-2-2-2-2-22-22200-100000006-611-1-33-33000000000000000000000000000000000000000000000000000000
χ988-88-8-4-4-4444444-4-4-40222-2-2-2-2-22-22200-10000000-6611-13-33-3000000000000000000000000000000000000000000000000000000
χ998-8-888-4-4-8-4-4484-8440-42-4-4-2-44442-240020000000002-2-20000000000000000000000000000000000000000000000000000000000
χ1008-8-88-4-484-48-8-4444-80-4-42-442-244-44-20020000000002-2-20000000000000000000000000000000000000000000000000000000000
χ1018-8-88-4-4-44-4-44-4444402222-22-2-2-22-2-200-10006-60000-111-333-3000000000000000000000000000000000000000000000000000000
χ1028-8-88-4-4-44-4-44-4444402222-22-2-2-22-2-200-1000-660000-1113-3-33000000000000000000000000000000000000000000000000000000

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