Finite Group Databasebeta

← Group #13172109

Character table — Group #13172109

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size1111222222222222444444444444466888888888888888881212121212121212121212121212121212181824242424242424242424242424242424242436363636363636363636365454727272108
order12223336666666662333666666666443666666666666666624444661212121212121212121222666121212121212121212121212121212444446612121212441212124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-11-1111111-1-1-1-111-1-11111-11-11111111-1-1-1-1-11-1-11-1-1-1-111-1-11-1-1-1
χ3111111111111111111111111111111111111111111111111-111-11-1-111-1-1111111-1-1-1-1-11111-11111-1-111111-11-1-1-1-111-1-1-1-1-11-1-1
χ4111111111111111111111111111111111111111111111111-11-1-1-1-1-111-1-1-1-1-1-11111-1-1-11-11-1-11111-1-1-1-1-1-1-1-1-11-111-1-1-1-111-1-111
χ511111111111111111111111111111-1-1111111111111111111-111111-1-1111111-1-111111-11-111-1-1-1-1111111-1-1-11-111-1-1-1-1-1-1-1-11-1
χ611111111111111111111111111111-1-1111111111111111111-1-11-111-1-111-1-1-1-1-1-1-1-1111-1-1-1-11-1-1-1-111-1-1-1-11-11-1-1-1-111-1-111-11-11
χ711111111111111111111111111111-1-111111111111111111-1-11-11-1-1-1-1-1-11111-1-1-1-1-1-1-1-11-11-1-1-1-1-1-1-11111-11-1-11-1-1-1-111111-1-11
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
χ91111111111111111-1111111111111111-1-1-1-1-1-1-1-1-1111-1-1-1-11-11-1-11111-1-1-1-1111111111-1-1-11-111-1-1-1-111-1-11-1-1-1111111111-1-1-1-1
χ101111111111111111-1111111111111111-1-1-1-1-1-1-1-1-1111-1-1-1-11-1-1-111111-1-111-1-111-1-1111-11-1-1-111-1-1-1-1-1-111-1-1111-1-1-1-111-1-1-1111
χ111111111111111111-1111111111111111-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-111-1-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-111-11-1-1-111-1-1-1-11-111
χ121111111111111111-1111111111111111-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-111-1-1111111-1-11111-1-1-1-11-1-1111-1-111-1-111-111-1-111-1-1-1-11111-1-1
χ131111111111111111-1111111111111-1-11-1-1-1-1-1-1-1-1-1111-1-1-1-1111-1-111-1-1-1-1-1-111-1-1111111-111-1-1-111-1-111-1-1-111-1-111-1-1-1-1-1-111-11
χ141111111111111111-1111111111111-1-11-1-1-1-1-1-1-1-1-1111-1-1-1-111-1-1111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-111-1-1-1-11111-11-1-1-111-1-1111-11-1
χ151111111111111111-1111111111111-1-11-1-1-1-1-1-1-1-1-1111-1-1-1-1-1111-1-1-1-1-111-1-111-1-1-1-1-1-1-11-1111-1-1111111-1-1-1-1111-1-1-1-11111-111-1
χ161111111111111111-1111111111111-1-11-1-1-1-1-1-1-1-1-1111-1-1-1-1-11-111-1-1-1-11111-1-1-1-111-1-1-1111-11-1-11111-1-1111-1-1-11111111-1-1-1-1-11
χ17222222-1-122-1222-1222-1-12-1-1-122-1-1-100-122-122-1-1-1-1-1-1-1-1-1-1-1202222200-1-1-1-1220022-1-1-1020-120000-1-1-1-1-1-100020-1-100000000-10
χ18222222-1-122-1222-1222-1-12-1-1-122-1-1-100-122-122-1-1-1-1-1-1-1-1-1-1-120-22-22200-1-111-2-200-2-2-1-1-10-20120000-1-11111000-20110000000010
χ19222222-1-122-1222-1222-1-12-1-1-122-1-1-100-122-122-1-1-1-1-1-1-1-1-1-1-1-202-22-2-20011-1-12200-2-2111020-1-2000011-1-1-1-1000-20110000000010
χ20222222-1-122-1222-1222-1-12-1-1-122-1-1-100-122-122-1-1-1-1-1-1-1-1-1-1-1-20-2-2-2-2-2001111-2-200221110-201-2000011111100020-1-100000000-10
χ21222222-1-122-1222-12-22-1-12-1-1-122-1-1-100-1-2-21-2-21111-1-1-11111202-2-222001111220022-1-1-10-20-1-2000011-1-111000-20-1-10000000010
χ22222222-1-122-1222-12-22-1-12-1-1-122-1-1-100-1-2-21-2-21111-1-1-1111120-2-22220011-1-1-2-200-2-2-1-1-10201-200001111-1-1000201100000000-10
χ23222222-1-122-1222-12-22-1-12-1-1-122-1-1-100-1-2-21-2-21111-1-1-11111-2022-2-2-200-1-1112200-2-21110-20-120000-1-1-1-111000201100000000-10
χ24222222-1-122-1222-12-22-1-12-1-1-122-1-1-100-1-2-21-2-21111-1-1-11111-20-222-2-200-1-1-1-1-2-20022111020120000-1-111-1-1000-20-1-10000000010
χ2522222-122-122-1222-12-12-1-12-1-1-1-122-122-12-12-1-122-1-1-1-1-1-1-1-1-122020-1-122220000-1-1002-1-1-1020-1-1-1-1-1-1-10000020020000-1-100-1000
χ2622222-122-122-1222-12-12-1-12-1-1-1-122-122-12-12-1-122-1-1-1-1-1-1-1-1-1-220-201122-2-20000-1-100-211-10201-1-1-1-11100000-200-2000011001000
χ2722222-122-122-1222-12-12-1-12-1-1-1-122-1-2-2-12-12-1-122-1-1-1-1-1-1-1-1-12-2020-1-1-2-222000011002-1-110-20-11111-1-100000-200-2000011001000
χ2822222-122-122-1222-12-12-1-12-1-1-1-122-1-2-2-12-12-1-122-1-1-1-1-1-1-1-1-1-2-20-2011-2-2-2-200001100-21110-2011111110000020020000-1-100-1000
χ2922222-122-122-1222-1-2-12-1-12-1-1-1-122-122-1-21-211-2-211-1-1-111112-20-20-1-122-2-20000-1-1002-1-110-201-1-1111100000-20020000-1-1001000
χ3022222-122-122-1222-1-2-12-1-12-1-1-1-122-122-1-21-211-2-211-1-1-11111-2-20201122220000-1-100-21110-20-1-1-111-1-100000200-200001100-1000
χ3122222-122-122-1222-1-2-12-1-12-1-1-1-122-1-2-2-1-21-211-2-211-1-1-11111220-20-1-1-2-2-2-2000011002-1-1-1020111-1-11100000200-200001100-1000
χ3222222-122-122-1222-1-2-12-1-12-1-1-1-122-1-2-2-1-21-211-2-211-1-1-11111-2202011-2-22200001100-211-1020-111-1-1-1-100000-20020000-1-1001000
χ332222-12222-122-1-1222-1-12-1-122-1-1-1-1222-1-122-1-1-1-122-1-1-1-1-1-1-10220200-1-10022-1-122000002-1-120-1-1-1-100-1-1-1-12020000-1-100000-100
χ342222-12222-122-1-1222-1-12-1-122-1-1-1-1222-1-122-1-1-1-122-1-1-1-1-1-1-102-20-200-1-100-2-211220000021-1-20-1-1-1-1001111-20-200001100000100
χ352222-12222-122-1-1222-1-12-1-122-1-1-1-12-2-2-1-122-1-1-1-122-1-1-1-1-1-1-10-220200110022-1-1-2-200000-2-1120111100-1-1-1-1-20-200001100000100
χ362222-12222-122-1-1222-1-12-1-122-1-1-1-12-2-2-1-122-1-1-1-122-1-1-1-1-1-1-10-2-20-2001100-2-211-2-200000-211-2011110011112020000-1-100000-100
χ372222-12222-122-1-122-2-1-12-1-122-1-1-1-1222-11-2-21111-2-2-1-1-111110-220-200-1-100-2-2-1-12200000-21120-1-11100-1-11120-20000-1-100000100
χ382222-12222-122-1-122-2-1-12-1-122-1-1-1-1222-11-2-21111-2-2-1-1-111110-2-20200-1-10022112200000-2-11-20-1-1110011-1-1-20200001100000-100
χ392222-12222-122-1-122-2-1-12-1-122-1-1-1-12-2-2-11-2-21111-2-2-1-1-111110220-2001100-2-2-1-1-2-20000021-12011-1-100-1-111-20200001100000-100
χ402222-12222-122-1-122-2-1-12-1-122-1-1-1-12-2-2-11-2-21111-2-2-1-1-1111102-2020011002211-2-2000002-1-1-2011-1-10011-1-120-20000-1-100000100
χ412-22-2222-2-2-2-222-22-202222-22-2-2-22-2-22i−2i20000000002-2-2000000000002i−2i0000002i−2i2-2000000002i−2i00000000000002-200002i−2i0000
χ422-22-2222-2-2-2-222-22-202222-22-2-2-22-2-22i−2i20000000002-2-2000000000002i−2i0000002i−2i-22000000002i−2i0000000000000-220000−2i2i0000
χ432-22-2222-2-2-2-222-22-202222-22-2-2-22-2-2−2i2i20000000002-2-200000000000−2i2i000000−2i2i2-200000000−2i2i00000000000002-20000−2i2i0000
χ442-22-2222-2-2-2-222-22-202222-22-2-2-22-2-2−2i2i20000000002-2-200000000000−2i2i000000−2i2i-2200000000−2i2i0000000000000-2200002i−2i0000
χ4544444-2-2-2-24-2-244-2-24-2-21-2-211-2-2-2-210014-2-2-2-2-2-211111111140040-2-200-2-200000000-2110000-2000011000000000000000000000
χ4644444-2-2-2-24-2-244-2-24-2-21-2-211-2-2-2-210014-2-2-2-2-2-2111111111-400-40220022000000002-1-1000020000-1-1000000000000000000000
χ4744444-2-2-2-24-2-244-2-2-4-2-21-2-211-2-2-2-21001-4222222-1-1111-1-1-1-1400-40-2-2002200000000-211000020000-1-1000000000000000000000
χ4844444-2-2-2-24-2-244-2-2-4-2-21-2-211-2-2-2-21001-4222222-1-1111-1-1-1-1-400402200-2-2000000002-1-10000-2000011000000000000000000000
χ494444-24-2-24-2-24-2-2-244-21-2-21-2-2-2-211-2001-24-2-2-211-2-2111111100404000000-2-2-2-200000000-20-20000000111100000000000000000
χ504444-24-2-24-2-24-2-2-244-21-2-21-2-2-2-211-2001-24-2-2-211-2-2111111100-40-40000002222000000002020000000-1-1-1-100000000000000000
χ514444-24-2-24-2-24-2-2-24-4-21-2-21-2-2-2-211-20012-4222-1-122111-1-1-1-10040-400000022-2-20000000020-2000000011-1-100000000000000000
χ524444-24-2-24-2-24-2-2-24-4-21-2-21-2-2-2-211-20012-4222-1-122111-1-1-1-100-404000000-2-22200000000-2020000000-1-11100000000000000000
χ534444-2-244-2-24-2-2-24-241-2-21-2-2-211-2-2-2441-2-2411-2-2-2-211111110400000-2-2000000-2-200000-20-200111100000000000000000000000
χ544444-2-244-2-24-2-2-24-241-2-21-2-2-211-2-2-2-4-41-2-2411-2-2-2-211111110-40000022000000220000020200-1-1-1-100000000000000000000000
χ554444-2-244-2-24-2-2-24-2-41-2-21-2-2-211-2-2-244122-4-1-12222111-1-1-1-10-400000-2-2000000-2-2000002020011-1-100000000000000000000000
χ564444-2-244-2-24-2-2-24-2-41-2-21-2-2-211-2-2-2-4-4122-4-1-12222111-1-1-1-10400000220000002200000-20-200-1-11100000000000000000000000
χ5744-4-444444-4-4-4-44-4-40444-44-444-4-4-4-4004000000000-44-40000000000000000000000000000000000000000000000000000000000
χ5844-4-444-2-24-42-4-442-404-2-2-4-22-24-422200-20000000002-2200000000000000023−23000000000000000000000023−2300000000000000000
χ5944-4-444-2-24-42-4-442-404-2-2-4-22-24-422200-20000000002-22000000000000000−23230000000000000000000000−232300000000000000000
χ6044-4-44-244-2-4-42-44-420-24-2242-2-22-4-4200-20000000002-220000000000000000000000000000000000000000000000000023−23000000
χ6144-4-44-244-2-4-42-44-420-24-2242-2-22-4-4200-20000000002-2200000000000000000000000000000000000000000000000000−2323000000
χ6244-4-4-244442-4-42-2-4-40-2-242-2-44-2222-400-20000000002-220000000000000000023−2300000000000000000023−230000000000000000000
χ6344-4-4-244442-4-42-2-4-40-2-242-2-44-2222-400-20000000002-2200000000000000000−2323000000000000000000−23230000000000000000000
χ6444-4-4-24-2-2422-42-22-40-21-2212-2-22-1-12001000003-300-11-133-3-30000000000023−2323−23000000000000000000−33−3300000000000000000
χ6544-4-4-24-2-2422-42-22-40-21-2212-2-22-1-12001000003-300-11-133-3-300000000000−2323−23230000000000000000003−33−300000000000000000
χ6644-4-4-24-2-2422-42-22-40-21-2212-2-22-1-1200100000-3300-11-1-3-3330000000000023−23−23230000000000000000003−3−3300000000000000000
χ6744-4-4-24-2-2422-42-22-40-21-2212-2-22-1-1200100000-3300-11-1-3-33300000000000−232323−23000000000000000000−333−300000000000000000
χ684-44-444-22-4-4244-4-2-404-2-242-22-4-4-22200-2000000000-2220000000000000000000004-400000000000000000000000-220000000000
χ694-44-444-22-4-4244-4-2-404-2-242-22-4-4-22200-2000000000-222000000000000000000000-44000000000000000000000002-20000000000
χ704-44-44-24-42-4-4-24-4420-24-2-2-4-22224-424i−4i-2000000000-222000000000004i−4i000000−2i2i0000000000−2i2i0000000000000000000000000
χ714-44-44-24-42-4-4-24-4420-24-2-2-4-22224-42−4i4i-2000000000-22200000000000−4i4i0000002i−2i00000000002i−2i0000000000000000000000000
χ724-44-4-244-4-42-44-224-40-2-24-224-422-22-44i−4i-2000000000-22200000000000−2i2i0000004i−4i0000000000−2i2i0000000000000000000000000
χ734-44-4-244-4-42-44-224-40-2-24-224-422-22-4−4i4i-2000000000-222000000000002i−2i000000−4i4i00000000002i−2i0000000000000000000000000
χ744-44-4-2-24-422-4-2-224201-2-212-22-1-1-2224i−4i10003-300001-1-13-33-30000000−2i2i000000−2i2i0000000000i−i3i−3i00000000000000000000000
χ754-44-4-2-24-422-4-2-224201-2-212-22-1-1-2224i−4i1000-3300001-1-1-33-330000000−2i2i000000−2i2i0000000000i−i−3i3i00000000000000000000000
χ764-44-4-2-24-422-4-2-224201-2-212-22-1-1-222−4i4i10003-300001-1-13-33-300000002i−2i0000002i−2i0000000000−ii−3i3i00000000000000000000000
χ774-44-4-2-24-422-4-2-224201-2-212-22-1-1-222−4i4i1000-3300001-1-1-33-3300000002i−2i0000002i−2i0000000000−ii3i−3i00000000000000000000000
χ784-4-44444-4-444-4-4-4-440444-4-4-4-4-44-444004000000000-4-440000000000000000000000000000000000000000000000000000000000
χ794-4-4444-22-44-2-4-4-42404-2-2-4222-442-2-200-200000000022-20000000000000−2i32i300000000000000000000−2i32i3000000000000000000000
χ804-4-4444-22-44-2-4-4-42404-2-2-4222-442-2-200-200000000022-200000000000002i3−2i3000000000000000000002i3−2i3000000000000000000000
χ814-4-444-24-42442-4-4-4-20-24-22-4222-2-44-200-200000000022-2000000000−2i32i30000000000000−2i32i300000000000000000000000000000000
χ824-4-444-24-42442-4-4-4-20-24-22-4222-2-44-200-200000000022-20000000002i3−2i300000000000002i3−2i300000000000000000000000000000000
χ834-4-444-2-2224-22-4-42-20-2-2122-1-12-22-2100100000003-3-1-113-3-3300000−2i32i300−2i32i3000000000i3−i3000000000i3−i3000000000000000000000
χ844-4-444-2-2224-22-4-42-20-2-2122-1-12-22-2100100000003-3-1-113-3-33000002i3−2i3002i3−2i3000000000−i3i3000000000−i3i3000000000000000000000
χ854-4-444-2-2224-22-4-42-20-2-2122-1-12-22-210010000000-33-1-11-333-300000−2i32i3002i3−2i3000000000i3−i3000000000−i3i3000000000000000000000
χ864-4-444-2-2224-22-4-42-20-2-2122-1-12-22-210010000000-33-1-11-333-3000002i3−2i300−2i32i3000000000−i3i3000000000i3−i3000000000000000000000
χ874-4-44-244-4-4-24-422-440-2-2422-4-42-22-2400-200000000022-200000000000000000000000000000000000000000000000023−2300000000
χ884-4-44-244-4-4-24-422-440-2-2422-4-42-22-2400-200000000022-2000000000000000000000000000000000000000000000000−232300000000
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
χ9188-8-88-4-4-4-4-844-88440-4-424-4-22-4444-2002000000000-22-20000000000000000000000000000000000000000000000000000000000
χ9288-8-8-4-488-44-844-4-8402-4-4-2-44-42-2444002000000000-22-20000000000000000000000000000000000000000000000000000000000
χ9388-8-8-4-4-4-4-44444-4440222-22-222-2-2-2-200-1000006-6001-11-3-333000000000000000000000000000000000000000000000000000000
χ9488-8-8-4-4-4-4-44444-4440222-22-222-2-2-2-200-100000-66001-1133-3-3000000000000000000000000000000000000000000000000000000
χ958-88-88-4-444-84-48-8-440-4-42-442-244-44-20020000000002-2-20000000000000000000000000000000000000000000000000000000000
χ968-88-8-48-44-8448-44-4-80-42-4-4-2-44442-240020000000002-2-20000000000000000000000000000000000000000000000000000000000
χ978-88-8-4-4-44444-4-44-4402222-22-2-2-22-2-200-10006-60000-111-33-33000000000000000000000000000000000000000000000000000000
χ988-88-8-4-4-44444-4-44-4402222-22-2-2-22-2-200-1000-660000-1113-33-3000000000000000000000000000000000000000000000000000000
χ998-8-88-48-44-8-4-4-844480-42-44-2444-4-22-4002000000000-2-220000000000000000000000000000000000000000000000000000000000
χ1008-8-88-4-48-84-48444-8-402-4-4-2444-224-4-4002000000000-2-220000000000000000000000000000000000000000000000000000000000
χ1018-8-88-4-4-444-4-44444-40222-2-2-2-2-22-22200-100000006-611-1-333-3000000000000000000000000000000000000000000000000000000
χ1028-8-88-4-4-444-4-44444-40222-2-2-2-2-22-22200-10000000-6611-13-3-33000000000000000000000000000000000000000000000000000000

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