Finite Group Databasebeta

← Group #13172108

Character table — Group #13172108

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size1111222222222222444444444444466888888888888888881212121212121212121212121212121212181824242424242424242424242424242424242436363636363636363636365454727272108
order122233366666666623336666666664436666666666666666244446612121212121212121212226661212121212121212121212121212122244466121212124466124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111-111-11111-1-111-1-111-1-111111-11-1111111-1-1-1-11-1-1-11-1-111-1-1-1-1-11-1-1
χ3111111111111111111111111111111111111111111111111-111-11-1-11111-1-11111-1-1-1-1-11-11111111-1-11111-11-11-1-1-1-1-111-1-11-1-1-1
χ4111111111111111111111111111111111111111111111111-1-11-1-1-1-111-1-1-1-1-1-11111-1-1-11-1-11-11111-1-1-1-1-1-1-1-11-1-111-1-1-1-111-1-111
χ511111111111111111111111111111-1-11111111111111111111-11111-1-1111111-1-111111-111-11-1-1-1-1111111-1-11-1-111-1-1-1-1-1-1-1-11-1
χ611111111111111111111111111111-1-1111111111111111111-1-11-111-1-1-1-111-1-1-1-1-1-1111-11-1-1-1-1-1-1-111-1-1-1-1-11-11-1-1-1-1-111111-1-11
χ711111111111111111111111111111-1-111111111111111111-11-1-11-1-1-1-111-1-111-1-1-1-1-1-1-1-1-11-11-1-1-1-1-1-111111-1-1-11-1-111-1-111-11-11
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
χ91111111111111111-1111111111111111-1-1-1-1-1-1-1-1-1111-1-1-1-111-1-1-1111111-1-1-1-11111111-1-11-1-111-1-1-1-111-1-1-1-1-11111111111-1-1-1-1
χ101111111111111111-1111111111111111-1-1-1-1-1-1-1-1-1111-1-1-1-11-1-1-111111-1-1-1-11111-1-1111-1-1-1-1111-1-1-1-1-1-111-111-11-1-111-1-1-1-11-111
χ111111111111111111-1111111111111111-1-1-1-1-1-1-1-1-1111-1-1-1-1-11-11-1-1-1111111-1-111-1-1-1-1-1-111-1-111-1-11111-1-11-111-1-1-1-1-111-1-1-1111
χ121111111111111111-1111111111111111-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-111-1-111-1-111111111-1-1-1-11-1-1111-1-111-1-11111-1-1-111-1-1-1-11111-1-1
χ131111111111111111-1111111111111-1-11-1-1-1-1-1-1-1-1-1111-1-1-1-1111-1-111-1-111-1-1-1-1-1-1111111-111-1-1-111-1-111-1-111-1-1-111-1-1-1-1-1-111-11
χ141111111111111111-1111111111111-1-11-1-1-1-1-1-1-1-1-1111-1-1-1-11-11-1111-1-1-1-1-1-111-1-1-1-11111-1-111-1-111-1-1-1-1111-111-1-1-1-1-11111-111-1
χ151111111111111111-1111111111111-1-11-1-1-1-1-1-1-1-1-1111-1-1-1-1-1111-1-1-1-1-11111-1-1-1-1-1-1-1-1-11111-1-1-1111111-1-1-111-11-1-111-1-1111-11-1
χ161111111111111111-1111111111111-1-11-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1111-1-1-1-1-1-11111-1-111-1-1-111-111-1-11111-1-111-1-1-111111111-1-1-1-1-11
χ17222222-12-1222-12-1222-1-12-1-1-122-1-1-100-122-122-1-1-1-1-1-1-1-1-1-1-122022220022-1-1-1-10022-1-1-102-1020000-1-1-1-1-1-100200-1-100000000-10
χ18222222-12-1222-12-1222-1-12-1-1-122-1-1-100-122-122-1-1-1-1-1-1-1-1-1-1-12-202-22200-2-2-1-11100-2-2-1-1-10210-20000-1-1111100-200110000000010
χ19222222-12-1222-12-1222-1-12-1-1-122-1-1-100-122-122-1-1-1-1-1-1-1-1-1-1-1-220-22-2-2002211-1-100-2-21110-2-102000011-1-1-1-100-200110000000010
χ20222222-12-1222-12-1222-1-12-1-1-122-1-1-100-122-122-1-1-1-1-1-1-1-1-1-1-1-2-20-2-2-2-200-2-2111100221110-210-2000011111100200-1-100000000-10
χ21222222-12-1222-12-12-22-1-12-1-1-122-1-1-100-1-2-21-2-21111-1-1-11111220-2-222002211110022-1-1-10-2-10-2000011-1-11100-200-1-10000000010
χ22222222-12-1222-12-12-22-1-12-1-1-122-1-1-100-1-2-21-2-21111-1-1-111112-20-222200-2-211-1-100-2-2-1-1-10-210200001111-1-1002001100000000-10
χ23222222-12-1222-12-12-22-1-12-1-1-122-1-1-100-1-2-21-2-21111-1-1-11111-2202-2-2-20022-1-11100-2-211102-10-20000-1-1-1-111002001100000000-10
χ24222222-12-1222-12-12-22-1-12-1-1-122-1-1-100-1-2-21-2-21111-1-1-11111-2-2022-2-200-2-2-1-1-1-10022111021020000-1-111-1-100-200-1-10000000010
χ2522222-12-1222-12-1222-12-1-12-1-1-1-122-122-12-12-1-122-1-1-1-1-1-1-1-1-120220-1-122002200-1-1002-1-1-1-1020-1-1-1-1-1-100002000200-1-100000-100
χ2622222-12-1222-12-1222-12-1-12-1-1-1-122-122-12-12-1-122-1-1-1-1-1-1-1-1-1-202-20112200-2-200-1-100-211-11020-1-1-1-1110000-2000-2001100000100
χ2722222-12-1222-12-1222-12-1-12-1-1-1-122-1-2-2-12-12-1-122-1-1-1-1-1-1-1-1-120-220-1-1-2-200220011002-1-11-10-201111-1-10000-2000-2001100000100
χ2822222-12-1222-12-1222-12-1-12-1-1-1-122-1-2-2-12-12-1-122-1-1-1-1-1-1-1-1-1-20-2-2011-2-200-2-2001100-211110-2011111100002000200-1-100000-100
χ2922222-12-1222-12-122-2-12-1-12-1-1-1-122-122-1-21-211-2-211-1-1-1111120-2-20-1-12200-2-200-1-1002-1-1110-20-1-111110000-2000200-1-100000100
χ3022222-12-1222-12-122-2-12-1-12-1-1-1-122-122-1-21-211-2-211-1-1-11111-20-2201122002200-1-100-2111-10-20-1-111-1-100002000-2001100000-100
χ3122222-12-1222-12-122-2-12-1-12-1-1-1-122-1-2-2-1-21-211-2-211-1-1-11111202-20-1-1-2-200-2-20011002-1-1-1102011-1-11100002000-2001100000-100
χ3222222-12-1222-12-122-2-12-1-12-1-1-1-122-1-2-2-1-21-211-2-211-1-1-11111-2022011-2-20022001100-211-1-102011-1-1-1-10000-2000200-1-100000100
χ332222-12222-1-12222-12-1-12-1-122-1-1-1-1222-1-122-1-1-1-122-1-1-1-1-1-1-10220200-1-1-1-100222200000202-1-1-1-1-1-100-1-1-1-1020200000-1-100-1000
χ342222-12222-1-12222-12-1-12-1-122-1-1-1-1222-1-122-1-1-1-122-1-1-1-1-1-1-10-220-200-1-11100-2-2220000020-2-11-1-1-1-10011110-20-20000011001000
χ352222-12222-1-12222-12-1-12-1-122-1-1-1-12-2-2-1-122-1-1-1-122-1-1-1-1-1-1-102-2020011-1-10022-2-200000-2021-1111100-1-1-1-10-20-20000011001000
χ362222-12222-1-12222-12-1-12-1-122-1-1-1-12-2-2-1-122-1-1-1-122-1-1-1-1-1-1-10-2-20-200111100-2-2-2-200000-20-2111111001111020200000-1-100-1000
χ372222-12222-1-12222-1-2-1-12-1-122-1-1-1-1222-11-2-21111-2-2-1-1-1111102-20-200-1-1-1-100-2-22200000-20211-1-11100-1-1110-20200000-1-1001000
χ382222-12222-1-12222-1-2-1-12-1-122-1-1-1-1222-11-2-21111-2-2-1-1-111110-2-20200-1-11100222200000-20-21-1-1-1110011-1-1020-2000001100-1000
χ392222-12222-1-12222-1-2-1-12-1-122-1-1-1-12-2-2-11-2-21111-2-2-1-1-111110220-20011-1-100-2-2-2-200000202-1111-1-100-1-111020-2000001100-1000
χ402222-12222-1-12222-1-2-1-12-1-122-1-1-1-12-2-2-11-2-21111-2-2-1-1-111110-22020011110022-2-20000020-2-1-111-1-10011-1-10-20200000-1-1001000
χ4122-2-22222-22-2-2-2-22-202222-22-2-2-22-2-22i−2i20000000002-2-2000000000002i−2i0000002i−2i2-2000000002i−2i00000000000002-200002i−2i0000
χ4222-2-22222-22-2-2-2-22-202222-22-2-2-22-2-22i−2i20000000002-2-2000000000002i−2i0000002i−2i-22000000002i−2i0000000000000-220000−2i2i0000
χ4322-2-22222-22-2-2-2-22-202222-22-2-2-22-2-2−2i2i20000000002-2-200000000000−2i2i000000−2i2i2-200000000−2i2i00000000000002-20000−2i2i0000
χ4422-2-22222-22-2-2-2-22-202222-22-2-2-22-2-2−2i2i20000000002-2-200000000000−2i2i000000−2i2i-2200000000−2i2i0000000000000-2200002i−2i0000
χ4544444-2-2-2-244-2-2-2-244-2-21-2-211-2-2-2-210014-2-2-2-2-2-211111111140040-2-20000-2-2000000-2110-2000000011000000000000000000000
χ4644444-2-2-2-244-2-2-2-244-2-21-2-211-2-2-2-210014-2-2-2-2-2-2111111111-400-40220000220000002-1-1020000000-1-1000000000000000000000
χ4744444-2-2-2-244-2-2-2-24-4-2-21-2-211-2-2-2-21001-4222222-1-1111-1-1-1-1400-40-2-2000022000000-211020000000-1-1000000000000000000000
χ4844444-2-2-2-244-2-2-2-24-4-2-21-2-211-2-2-2-21001-4222222-1-1111-1-1-1-1-40040220000-2-20000002-1-10-2000000011000000000000000000000
χ494444-24-24-2-2-24-24-2-24-21-2-21-2-2-2-211-2001-24-2-2-211-2-21111111040040000-2-200-2-2000000000-20-2000000111100000000000000000
χ504444-24-24-2-2-24-24-2-24-21-2-21-2-2-2-211-2001-24-2-2-211-2-211111110-400-40000220022000000000202000000-1-1-1-100000000000000000
χ514444-24-24-2-2-24-24-2-2-4-21-2-21-2-2-2-211-20012-4222-1-122111-1-1-1-10400-40000-2-20022000000000-20200000011-1-100000000000000000
χ524444-24-24-2-2-24-24-2-2-4-21-2-21-2-2-2-211-20012-4222-1-122111-1-1-1-10-400400002200-2-200000000020-2000000-1-11100000000000000000
χ534444-2-24-24-2-2-24-24-241-2-21-2-2-211-2-2-2441-2-2411-2-2-2-211111110040000-2-2000000-2-200000-200-20111100000000000000000000000
χ544444-2-24-24-2-2-24-24-241-2-21-2-2-211-2-2-2-4-41-2-2411-2-2-2-2111111100-4000022000000220000020020-1-1-1-100000000000000000000000
χ554444-2-24-24-2-2-24-24-2-41-2-21-2-2-211-2-2-244122-4-1-12222111-1-1-1-100-40000-2-2000000-2-2000002002011-1-100000000000000000000000
χ564444-2-24-24-2-2-24-24-2-41-2-21-2-2-211-2-2-2-4-4122-4-1-12222111-1-1-1-10040000220000002200000-200-20-1-11100000000000000000000000
χ5744-4-444-2424-4-42-4-2-404-2-242-22-4-4-22200-2000000000-2220000000000000000000004-400000000000000000000000-220000000000
χ5844-4-444-2424-4-42-4-2-404-2-242-22-4-4-22200-2000000000-222000000000000000000000-44000000000000000000000002-20000000000
χ5944-4-44-24-2-44-42-424-40-24-2-2-4-22224-424i−4i-2000000000-222000000000004i−4i000000−2i2i0000000000−2i2i0000000000000000000000000
χ6044-4-44-24-2-44-42-424-40-24-2-2-4-22224-42−4i4i-2000000000-22200000000000−4i4i0000002i−2i00000000002i−2i0000000000000000000000000
χ6144-4-4-2444-4-22-4-4-4420-2-24-224-422-22-44i−4i-2000000000-22200000000000−2i2i0000004i−4i0000000000−2i2i0000000000000000000000000
χ6244-4-4-2444-4-22-4-4-4420-2-24-224-422-22-4−4i4i-2000000000-222000000000002i−2i000000−4i4i00000000002i−2i0000000000000000000000000
χ6344-4-4-2-24-2-4-222-424201-2-212-22-1-1-2224i−4i10003-300001-1-133-3-30000000−2i2i000000−2i2i0000000000i−i3i−3i00000000000000000000000
χ6444-4-4-2-24-2-4-222-424201-2-212-22-1-1-2224i−4i1000-3300001-1-1-3-3330000000−2i2i000000−2i2i0000000000i−i−3i3i00000000000000000000000
χ6544-4-4-2-24-2-4-222-424201-2-212-22-1-1-222−4i4i10003-300001-1-133-3-300000002i−2i0000002i−2i0000000000−ii−3i3i00000000000000000000000
χ6644-4-4-2-24-2-4-222-424201-2-212-22-1-1-222−4i4i1000-3300001-1-1-3-33300000002i−2i0000002i−2i0000000000−ii3i−3i00000000000000000000000
χ674-44-4444-4-4-4-444-4-440444-4-4-4-44-4-444004000000000-44-40000000000000000000000000000000000000000000000000000000000
χ684-44-444-2-42-4-44-2-42404-2-2-42224-42-2-200-20000000002-22000000000000000−2i32i3000000000000000000−2i32i3000000000000000000000
χ694-44-444-2-42-4-44-2-42404-2-2-42224-42-2-200-20000000002-220000000000000002i3−2i30000000000000000002i3−2i3000000000000000000000
χ704-44-44-242-4-4-4-242-440-24-22-422-22-44-200-20000000002-22000000000−2i32i30000000000000−2i32i300000000000000000000000000000000
χ714-44-44-242-4-4-4-242-440-24-22-422-22-44-200-20000000002-220000000002i3−2i300000000000002i3−2i300000000000000000000000000000000
χ724-44-44-2-222-4-4-2-22240-2-2122-1-1-222-2100100000003-3-11-13-33-300000−2i32i30000−2i32i30000000i3−i3000000000i3−i3000000000000000000000
χ734-44-44-2-222-4-4-2-22240-2-2122-1-1-222-2100100000003-3-11-13-33-3000002i3−2i300002i3−2i30000000−i3i3000000000−i3i3000000000000000000000
χ744-44-44-2-222-4-4-2-22240-2-2122-1-1-222-210010000000-33-11-1-33-3300000−2i32i300002i3−2i30000000i3−i3000000000−i3i3000000000000000000000
χ754-44-44-2-222-4-4-2-22240-2-2122-1-1-222-210010000000-33-11-1-33-33000002i3−2i30000−2i32i30000000−i3i3000000000i3−i3000000000000000000000
χ764-44-4-244-4-42244-4-4-20-2-2422-4-4-222-2400-20000000002-2200000000000000000000000000000000000000000000000000−2i32i3000000
χ774-44-4-244-4-42244-4-4-20-2-2422-4-4-222-2400-20000000002-22000000000000000000000000000000000000000000000000002i3−2i3000000
χ784-4-44444-44-44-4-44-4-40444-44-44-44-4-4-4004000000000-4-440000000000000000000000000000000000000000000000000000000000
χ794-4-4444-2-4-2-44-4242-404-2-2-4-22-2-4422200-200000000022-20000000000000000023−230000000000000000000023−2300000000000000000
χ804-4-4444-2-4-2-44-4242-404-2-2-4-22-2-4422200-200000000022-200000000000000000−232300000000000000000000−232300000000000000000
χ814-4-444-2424-442-4-2-4-40-24-2242-22-2-4-4200-200000000022-2000000000000000000000000000000000000000000000000−2i32i300000000
χ824-4-444-2424-442-4-2-4-40-24-2242-22-2-4-4200-200000000022-20000000000000000000000000000000000000000000000002i3−2i300000000
χ834-4-44-244-442-2-4-44-420-2-242-2-442-222-400-200000000022-2000000000000023−23000000000000000000000023−230000000000000000000
χ844-4-44-244-442-2-4-44-420-2-242-2-442-222-400-200000000022-20000000000000−23230000000000000000000000−23230000000000000000000
χ854-4-44-24-2-4-22-2-424220-21-2212-22-2-1-12001000003-300-1-113-3-3300000000023−230023−23000000000000000000−33−3300000000000000000
χ864-4-44-24-2-4-22-2-424220-21-2212-22-2-1-12001000003-300-1-113-3-33000000000−232300−23230000000000000000003−33−300000000000000000
χ874-4-44-24-2-4-22-2-424220-21-2212-22-2-1-1200100000-3300-1-11-333-300000000023−2300−2323000000000000000000−333−300000000000000000
χ884-4-44-24-2-4-22-2-424220-21-2212-22-2-1-1200100000-3300-1-11-333-3000000000−23230023−230000000000000000003−3−3300000000000000000
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
χ9188-8-88-4-4-448-8444-4-80-4-42-442-244-44-20020000000002-2-20000000000000000000000000000000000000000000000000000000000
χ9288-8-8-48-484-44-84-8-440-42-4-4-2-44442-240020000000002-2-20000000000000000000000000000000000000000000000000000000000
χ9388-8-8-4-4-4-44-44444-4402222-22-2-2-22-2-200-10006-60000-111-3-333000000000000000000000000000000000000000000000000000000
χ9488-8-8-4-4-4-44-44444-4402222-22-2-2-22-2-200-1000-660000-11133-3-3000000000000000000000000000000000000000000000000000000
χ958-88-8-48-4-84448-4-84-40-42-44-244-44-22-4002000000000-22-20000000000000000000000000000000000000000000000000000000000
χ968-88-8-4-484-844-484-8-402-4-4-24442-24-4-4002000000000-22-20000000000000000000000000000000000000000000000000000000000
χ978-88-8-4-4-44444-4-444-40222-2-2-2-22-2-22200-100000006-61-11-33-33000000000000000000000000000000000000000000000000000000
χ988-88-8-4-4-44444-4-444-40222-2-2-2-22-2-22200-10000000-661-113-33-3000000000000000000000000000000000000000000000000000000
χ998-8-888-4-44-4-8844-44-80-4-424-4-224-444-2002000000000-2-220000000000000000000000000000000000000000000000000000000000
χ1008-8-88-4-48484-44-8-4-8402-4-4-2-44-4-22444002000000000-2-220000000000000000000000000000000000000000000000000000000000
χ1018-8-88-4-4-44-44-444-4440222-22-22-22-2-2-200-1000006-60011-1-333-3000000000000000000000000000000000000000000000000000000
χ1028-8-88-4-4-44-44-444-4440222-22-22-22-2-2-200-100000-660011-13-3-33000000000000000000000000000000000000000000000000000000

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