Finite Group Databasebeta

← Group #13172143

Character table — Group #13172143

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111122222222222244444444444444488888888888888881212121212121212121212121212181818181818242424242424242424242424242424242424242436363636363636363636367272108108
order12223336666666662333666666666663666666666666666244444121212121212121222444466661212121212121212121212121212121244466121212121212121244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-11-111-1-1-1-111-1-111-1-11111111-1-11111111-1-1-1-1-1-11-1-1-1-11111-1-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1111111111-1-111-1-1-1-11111-1-1-111111-1-1-1-11111-11-111-1-1-1-1-1-11-1-1-1
χ4111111111111111111111111111111111111111111111111-1-1-11-111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1111-1-1-1-1-1-1-1-11-1-1-1-111-1-1-1-1-1111
χ511111111111111111111111111111111111111111111111-1111-11-1-1111111-1-1-1-111-1-1-1-111111-1-1-1111111111-1-1-1-111-1-1-1-1-11-1-1
χ611111111111111111111111111111111111111111111111-111-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111-1-1-1-1-11111-1-1-1-1-11-111-1-1-1-1-1-11-111
χ711111111111111111111111111111111111111111111111-1-1-11-11-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-11111-1-11-1-1-1-11111-1-111
χ811111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1
χ91111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-111-11-1-1-1-111-1-11111111111111-1-11-1-1-1-111-1-111-1-1-1-1-1111111-1-1-1-1-11
χ101111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-111-1-1-11-1-1-1-11111-1-111-1-111111-1-1-11-1-1-111-1-1-1-11111-1-1-1-1-111-1-1111-1
χ111111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-11-111-1-1-1-111-1-1-1-111-1-1-1-11111-1111-1-1-1-1-1-11111-1-11-1111-1-1-1-111-111-1
χ121111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-11-11-1-11-1-1-1-111-1-1-1-1-1-1111111-111-11-1-1-1-1-111-1-111-111-1-111-1-1111-1-11
χ131111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-1-11-111-11111-1-111-1-1-1-111-1-1-1-11-1-11-111111-1-111-1-1-111-1-111-1-1111-11-1
χ141111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-1-11-1-11111-1-1111111-1-1-1-1-1-1-1-11-1-1-1111111-1-1-1-1111-1111-1-1-1-111-11-11
χ151111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1111-11111-1-1-1-1-1-111-1-1-1-1-1-1-1111-1111-1-11111-1-111-1-1-1-1-111-1-111-11
χ161111111111111111-1111-1-11111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-11-11111-1-111-1-1111111-1-1-1-1-111-11111-1-111-1-111-1-1-1111111-1-1-1-11-1
χ17222222-1-1222-122-1222-1-1222-1-1-122-1-1-1-12-122-1-1-1-1-1-1-1-1-1-1-1200222-1-122-1-1002200002-1-1-1000-122-1-10000-1-1-1-1020-1-1000000-1000
χ18222222-1-1222-122-1222-1-1222-1-1-122-1-1-1-12-122-1-1-1-1-1-1-1-1-1-1-1200-22-2-1-1-2-21100-2-200002-1-1-10001-22-1-1000011110-20110000001000
χ19222222-1-1222-122-1222-1-1222-1-1-122-1-1-1-12-122-1-1-1-1-1-1-1-1-1-1-1-2002-221122-1-100-2-20000-2111000-12-2110000-1-1-1-10-20110000001000
χ20222222-1-1222-122-1222-1-1222-1-1-122-1-1-1-12-122-1-1-1-1-1-1-1-1-1-1-1-200-2-2-211-2-21100220000-21110001-2-21100001111020-1-1000000-1000
χ21222222-1-1222-122-12-22-1-1-2-22-1-1-122-1-1-1-1-21-2-21111-1-1-111112002-2-2112211002200002-1-1-1000-1-2-2110000-1-1110-20-1-10000001000
χ22222222-1-1222-122-12-22-1-1-2-22-1-1-122-1-1-1-1-21-2-21111-1-1-11111200-2-2211-2-2-1-100-2-200002-1-1-100012-211000011-1-102011000000-1000
χ23222222-1-1222-122-12-22-1-1-2-22-1-1-122-1-1-1-1-21-2-21111-1-1-11111-20022-2-1-1221100-2-20000-2111000-1-22-1-10000-1-11102011000000-1000
χ24222222-1-1222-122-12-22-1-1-2-22-1-1-122-1-1-1-1-21-2-21111-1-1-11111-200-222-1-1-2-2-1-100220000-2111000122-1-1000011-1-10-20-1-10000001000
χ2522222-122-1-122222-12-12-1-1-1-12-1-1-1-122-1-122-1-122-1-1-1-1-1-1-1-1-122202022000022002200-12-1-1-1-1200-1-1-1-1-1-1-100000020000-1-1-1-10000
χ2622222-122-1-122222-12-12-1-1-1-12-1-1-1-122-1-122-1-122-1-1-1-1-1-1-1-1-12-2-2020220000-2-200-2-200-12-1-111-200-1-1-11111000000-2000011110000
χ2722222-122-1-122222-12-12-1-1-1-12-1-1-1-122-1-122-1-122-1-1-1-1-1-1-1-1-1-2220-20-2-200002200-2-2001-211-1-1200111-1-1-1-1000000-2000011110000
χ2822222-122-1-122222-12-12-1-1-1-12-1-1-1-122-1-122-1-122-1-1-1-1-1-1-1-1-1-2-2-20-20-2-20000-2-20022001-21111-200111111100000020000-1-1-1-10000
χ2922222-122-1-122222-1-2-12-111-12-1-1-1-122-1-1-2-211-2-211-1-1-1111122-20-20-2-2000022002200-12-1-1-11-200111-1-111000000-20000-1-1110000
χ3022222-122-1-122222-1-2-12-111-12-1-1-1-122-1-1-2-211-2-211-1-1-111112-220-20-2-20000-2-200-2-200-12-1-11-120011111-1-10000002000011-1-10000
χ3122222-122-1-122222-1-2-12-111-12-1-1-1-122-1-1-2-211-2-211-1-1-11111-22-20202200002200-2-2001-211-11-200-1-1-1-1-1110000002000011-1-10000
χ3222222-122-1-122222-1-2-12-111-12-1-1-1-122-1-1-2-211-2-211-1-1-11111-2-22020220000-2-20022001-2111-1200-1-1-111-1-1000000-20000-1-1110000
χ332222-122222-12-1-1222-1-1222-1-122-1-1-1-12-1-12-1-1-1-122-1-1-1-1-1-1-102220200-1-122-1-1000022000022-12-1000-1-1-1-1-1-1-1-120000-1-100000-100
χ342222-122222-12-1-1222-1-1222-1-122-1-1-1-12-1-12-1-1-1-122-1-1-1-1-1-1-1022-20-20011-2-2-1-10000-2-2000022-1-21000-1-1-1-11111-200001100000100
χ352222-122222-12-1-1222-1-1222-1-122-1-1-1-12-1-12-1-1-1-122-1-1-1-1-1-1-10-2-220200-1-122110000-2-20000-2-212-10001111-1-1-1-1-200001100000100
χ362222-122222-12-1-1222-1-1222-1-122-1-1-1-12-1-12-1-1-1-122-1-1-1-1-1-1-10-2-2-20-20011-2-2110000220000-2-21-210001111111120000-1-100000-100
χ372222-122222-12-1-122-2-1-12-2-2-1-122-1-1-1-12-11-21111-2-2-1-1-1111102-220-200-1-1-2-2-1-100002200002-2121000-1-111-1-111-20000-1-100000100
χ382222-122222-12-1-122-2-1-12-2-2-1-122-1-1-1-12-11-21111-2-2-1-1-1111102-2-202001122-1-10000-2-200002-21-2-1000-1-11111-1-1200001100000-100
χ392222-122222-12-1-122-2-1-12-2-2-1-122-1-1-1-12-11-21111-2-2-1-1-111110-2220-200-1-1-2-2110000-2-20000-22-12100011-1-1-1-111200001100000-100
χ402222-122222-12-1-122-2-1-12-2-2-1-122-1-1-1-12-11-21111-2-2-1-1-111110-22-202001122110000220000-22-1-2-100011-1-111-1-1-20000-1-100000100
χ412-22-2222-22-22-2-2-22-2022200-2-22-22-22-2-22000000002-2-20000000000000000002-22i−2i2i−2i000000000000000000000002-22i−2i2i−2i000000
χ422-22-2222-22-22-2-2-22-2022200-2-22-22-22-2-22000000002-2-20000000000000000002-2−2i2i−2i2i000000000000000000000002-2−2i2i−2i2i000000
χ432-22-2222-22-22-2-2-22-2022200-2-22-22-22-2-22000000002-2-2000000000000000000-222i−2i−2i2i00000000000000000000000-22−2i2i2i−2i000000
χ442-22-2222-22-22-2-2-22-2022200-2-22-22-22-2-22000000002-2-2000000000000000000-22−2i2i2i−2i00000000000000000000000-222i−2i−2i2i000000
χ4544444-2-2-2-2-24-244-2-24-2-21-2-2-2-211-2-2-2-2114-2-2-2-2-2111111111400040-2-2000000000000-2-21100000-21100000000000000000000000
χ4644444-2-2-2-2-24-244-2-24-2-21-2-2-2-211-2-2-2-2114-2-2-2-2-2111111111-4000-402200000000000022-1-1000002-1-100000000000000000000000
χ4744444-2-2-2-2-24-244-2-2-4-2-2122-2-211-2-2-2-211-422222-1-1111-1-1-1-14000-4022000000000000-2-211000002-1-100000000000000000000000
χ4844444-2-2-2-2-24-244-2-2-4-2-2122-2-211-2-2-2-211-422222-1-1111-1-1-1-1-400040-2-200000000000022-1-100000-21100000000000000000000000
χ494444-24-2-244-2-2-2-2-244-21-244-21-2-2-2-211-21-2-2-2-211-2-2111111100040400-2-2-2-2000000000000000-2-200000001111000000000000000
χ504444-24-2-244-2-2-2-2-244-21-244-21-2-2-2-211-21-2-2-2-211-2-21111111000-40-4002222000000000000000220000000-1-1-1-1000000000000000
χ514444-24-2-244-2-2-2-2-24-4-21-2-4-4-21-2-2-2-211-212222-1-122111-1-1-1-100040-400-2-222000000000000000-22000000011-1-1000000000000000
χ524444-24-2-244-2-2-2-2-24-4-21-2-4-4-21-2-2-2-211-212222-1-122111-1-1-1-1000-4040022-2-20000000000000002-20000000-1-111000000000000000
χ534444-2-244-2-2-24-2-24-241-2-2-2-21-2-2-211-2-2-21-2411-2-2-2-21111111044000000000-2-20000000000-2-2-20000011110000000000000000000
χ544444-2-244-2-2-24-2-24-241-2-2-2-21-2-2-211-2-2-21-2411-2-2-2-211111110-4-400000000022000000000022200000-1-1-1-10000000000000000000
χ554444-2-244-2-2-24-2-24-2-41-2-2221-2-2-211-2-2-212-4-1-12222111-1-1-1-104-4000000000-2-20000000000-2220000011-1-10000000000000000000
χ564444-2-244-2-2-24-2-24-2-41-2-2221-2-2-211-2-2-212-4-1-12222111-1-1-1-10-440000000002200000000002-2-200000-1-1110000000000000000000
χ5744-4-44444-44-4-44-4-4-4044400-44-44-44-4-4-4400000000-44-400000000000000000000000000000000000000000000000000000000000
χ5844-4-444-2-2-44-424-42-404-2-200-4-22-2-44222-2000000002-220000000000000023−230000000000000000000000000023−23000000000000000
χ5944-4-444-2-2-44-424-42-404-2-200-4-22-2-44222-2000000002-2200000000000000−232300000000000000000000000000−2323000000000000000
χ6044-4-44-2442-2-4-44-4-420-24-200242-22-2-4-42-2000000002-220000000000000000000000000000000000000000000000000000023−230000
χ6144-4-44-2442-2-4-44-4-420-24-200242-22-2-4-42-2000000002-2200000000000000000000000000000000000000000000000000000−23230000
χ6244-4-4-2444-442-4-22-4-40-2-24002-2-442-222-4-2000000002-2200000000000023−230000000000000000000000000023−2300000000000000000
χ6344-4-4-2444-442-4-22-4-40-2-24002-2-442-222-4-2000000002-22000000000000−232300000000000000000000000000−232300000000000000000
χ6444-4-4-24-2-2-4422-222-40-21-200212-22-2-1-12100003-300-11-133-3-30000000023−2323−23000000000000000000000000−33−33000000000000000
χ6544-4-4-24-2-2-4422-222-40-21-200212-22-2-1-12100003-300-11-133-3-300000000−2323−23230000000000000000000000003−33−3000000000000000
χ6644-4-4-24-2-2-4422-222-40-21-200212-22-2-1-1210000-3300-11-1-3-3330000000023−23−2323000000000000000000000000−333−3000000000000000
χ6744-4-4-24-2-2-4422-222-40-21-200212-22-2-1-1210000-3300-11-1-3-33300000000−232323−230000000000000000000000003−3−33000000000000000
χ684-44-444-224-442-4-4-2-404-2-200-42-224-4-222-200000000-2220000000000000000004-4000000000000000000000000000-220000000000
χ694-44-444-224-442-4-4-2-404-2-200-42-224-4-222-200000000-222000000000000000000-440000000000000000000000000002-20000000000
χ704-44-44-24-4-224-4-4-4420-24-2002-4-22-224-42-200000000-222000000000000000000004i−4i00000000000000000000000000000−2i2i000000
χ714-44-44-24-4-224-4-4-4420-24-2002-4-22-224-42-200000000-22200000000000000000000−4i4i000000000000000000000000000002i−2i000000
χ724-44-4-244-44-4-2-4224-40-2-2400224-4-22-22-4-200000000-22200000000000000000000004i−4i0000000000000000000000000−2i2i00000000
χ734-44-4-244-44-4-2-4224-40-2-2400224-4-22-22-4-200000000-2220000000000000000000000−4i4i00000000000000000000000002i−2i00000000
χ744-4-44444-4-4-4-44-44-440444004-4-4-4-4-4-444400000000-4-4400000000000000000000000000000000000000000000000000000000000
χ754-4-4444-22-4-4-4-2-442404-2-2004222-4-42-2-2-20000000022-20000000000−2i32i30000000000000000000000−2i32i300000000000000000000000
χ764-4-4444-22-4-4-4-2-442404-2-2004222-4-42-2-2-20000000022-200000000002i3−2i300000000000000000000002i3−2i300000000000000000000000
χ774-4-444-24-422-44-44-4-20-24-2−2i32i3-2-42222-44-2-200−2i32i300−2i32i322-2−2i32i3−2i32i30000000000000000000000000000000000000000000000000000000
χ784-4-444-24-422-44-44-4-20-24-22i3−2i3-2-42222-44-2-2002i3−2i3002i3−2i322-22i3−2i32i3−2i30000000000000000000000000000000000000000000000000000000
χ794-4-444-2-2222-4-2-442-20-2-21−2i32i3-22-1-1222-21100−2i32i300i3−i3-1-11i3−i3i3−i3000000−2i32i3000000000000003-3000000i3−i300000000000000000000000
χ804-4-444-2-2222-4-2-442-20-2-21−2i32i3-22-1-1222-21100−2i32i300i3−i3-1-11i3−i3i3−i30000002i3−2i300000000000000-33000000−i3i300000000000000000000000
χ814-4-444-2-2222-4-2-442-20-2-212i3−2i3-22-1-1222-211002i3−2i300−i3i3-1-11−i3i3−i3i3000000−2i32i300000000000000-33000000i3−i300000000000000000000000
χ824-4-444-2-2222-4-2-442-20-2-212i3−2i3-22-1-1222-211002i3−2i300−i3i3-1-11−i3i3−i3i30000002i3−2i3000000000000003-3000000−i3i300000000000000000000000
χ834-4-44-244-4-4-4242-2-440-2-2400-22-4-4222-24-20000000022-2000000000000000023−2300000000000000000023−23000000000000000000000
χ844-4-44-244-4-4-4242-2-440-2-2400-22-4-4222-24-20000000022-20000000000000000−2323000000000000000000−2323000000000000000000000
χ854-4-44-2-24-422242-2-4-201-2-2−2i32i31222-1-12-2-2100i3−i300−2i32i3-1-11i3−i3i3−i300000000000023−23000000000000000000−333i−3i0000000000000000000
χ864-4-44-2-24-422242-2-4-201-2-2−2i32i31222-1-12-2-2100i3−i300−2i32i3-1-11i3−i3i3−i3000000000000−23230000000000000000003−3−3i3i0000000000000000000
χ874-4-44-2-24-422242-2-4-201-2-22i3−2i31222-1-12-2-2100−i3i3002i3−2i3-1-11−i3i3−i3i300000000000023−23000000000000000000−33−3i3i0000000000000000000
χ884-4-44-2-24-422242-2-4-201-2-22i3−2i31222-1-12-2-2100−i3i3002i3−2i3-1-11−i3i3−i3i3000000000000−23230000000000000000003−33i−3i0000000000000000000
χ898888-4-4-4-4-4-4-4-4-4-4-4-48222-4-4222222222-1-4-4222222-1-1-1-1-1-1-10000000000000000000000000000000000000000000000000000000
χ908888-4-4-4-4-4-4-4-4-4-4-4-4-822244222222222-144-2-2-2-2-2-2-1-1-111110000000000000000000000000000000000000000000000000000000
χ9188-8-88-4-4-44-4-848-8440-4-42004-4-224-444-2200000000-22-200000000000000000000000000000000000000000000000000000000000
χ9288-8-8-4-4884-44-8-44-8402-4-400-2-44-4-22444200000000-22-200000000000000000000000000000000000000000000000000000000000
χ9388-8-8-4-4-4-44-444-4444022200-22-22-22-2-2-2-100006-6001-11-3-3330000000000000000000000000000000000000000000000000000000
χ9488-8-8-4-4-4-44-444-4444022200-22-22-22-2-2-2-10000-66001-1133-3-30000000000000000000000000000000000000000000000000000000
χ958-88-88-4-44-4484-8-8-440-4-4200442-2-44-44-22000000002-2-200000000000000000000000000000000000000000000000000000000000
χ968-88-8-48-448-8-4444-4-80-42-4004-2-44-442-242000000002-2-200000000000000000000000000000000000000000000000000000000000
χ978-88-8-4-48-8-44-4-8448402-4-400-24-442-2-4442000000002-2-200000000000000000000000000000000000000000000000000000000000
χ988-88-8-4-4-44-44-4444-44022200-2-22-22-22-2-2-100000000-111−3i33i33i3−3i30000000000000000000000000000000000000000000000000000000
χ998-88-8-4-4-44-44-4444-44022200-2-22-22-22-2-2-100000000-1113i3−3i3−3i33i30000000000000000000000000000000000000000000000000000000
χ1008-8-88-48-44-8-84-44-4480-42-400-4-24444-22-4200000000-2-2200000000000000000000000000000000000000000000000000000000000
χ1018-8-88-4-4-44444-44-44-40222−4i34i32-2-2-2-2-2-222-1002i3−2i3002i3−2i311-1−i3i3−i3i30000000000000000000000000000000000000000000000000000000
χ1028-8-88-4-4-44444-44-44-402224i3−4i32-2-2-2-2-2-222-100−2i32i300−2i32i311-1i3−i3i3−i30000000000000000000000000000000000000000000000000000000

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