Finite Group Databasebeta

← Group #13169168

Character table — Group #13169168

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size1111222222222222444444444444466888888888888888881212121212121212121212121212121212181824242424242424242424242424242424242436363636363636363636365454727272108
order122233366666666633346666666664436661212121212121212121212121222444666612121212121212124466666612121212121212121212121222444661212121244612122
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111-111-111-1-1111111-1-1-1-1-1111-1-11-11111-1-111111-1-11-111-1-1-1-1-1-1-11-1-1
χ3111111111111111111111111111111111111111111111111-111-11-1-11111-1-11111-1-11-1-1-111-1111-1-1111111-111-1-1-1-111-1-1-1-11-1-1-1
χ4111111111111111111111111111111111111111111111111-1-11-1-1-1-1-1-111-1-111-1-111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11-1-1-1-11111-1-111
χ511111111111111111111111111111-1-11111111111111111111-1111111-1-111-1-1111111111111-1-11111-1-1-1-1-1-1-1-11-1-1-1-111-1-1-1-11-1
χ611111111111111111111111111111-1-1111111111111111111-1-11-111-1-1-1-111-1-1-1-1-1-1-1111-1-11-1-1-111-1-1-1-1-1-1-111-1-1-1-111-1-1111-1-11
χ711111111111111111111111111111-1-111111111111111111-11-1-11-1-111-1-1-1-1-1-111-1-11-1-1-111-11-1-1-1-111-1-1-1-11-1-11-111-1-1-1-111-11-11
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
χ91111111111111111111-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1111111-1-111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1111-1-111-1-1-1-1-1111
χ101111111111111111111-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1111-1-111-1-1111111-1111-1-1-11-1-1-1-11111-1-1-11-11-1-1-1-1-1111111-1-1
χ111111111111111111111-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-111111111-1-1111-1-1-1111-1-1-111-1-111-1-11-11-1-111111111-1-1-1-1
χ121111111111111111111-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1111111-1-111-1-1111-1-1-1-1-1-11-111
χ131111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-11111-1-1111-1-1-1-1111-11-1
χ141111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1111-1-1-1-1-1-1-1-11111-1111-1-1-1111-1-111-1-1111-11-1-1111111-1-1-1-1-11
χ151111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-111-1-111-1-1-1-1111-1-1-1111-11111-1-1-1-111-11-11-1-1-1-1-111-1-111-11
χ161111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-111111111-1-111-1-1111-1-111-1-111-111-1
χ17222222-122-122-1-122-12-12-12-1-12-12-1-122-1-1-1-122-122-1-1-1-1-1-1-1-1202202200-1-1-1-12200000-1-1-10020-12-1-100-1-1-1-120020-1-10000000-100
χ18222222-122-122-1-122-12-12-12-1-12-12-1-122-1-1-1-122-122-1-1-1-1-1-1-1-1-202-20-2-200-1-111220000011100-20-121100-1-1-1-1-200-20110000000100
χ19222222-122-122-1-122-12-12-12-1-12-12-1-1-2-2-1-1-1-122-122-1-1-1-1-1-1-1-120-220220011-1-1-2-200000-1-1-100201-2-1-1001111-200-20110000000100
χ20222222-122-122-1-122-12-12-12-1-12-12-1-1-2-2-1-1-1-122-122-1-1-1-1-1-1-1-1-20-2-20-2-2001111-2-20000011100-201-21100111120020-1-10000000-100
χ21222222-122-122-1-122-12-1-2-12-1-12-12-1-122-1-1-1-1-2-21-2-21111111120-2-202200-1-1112200000-1-1-100-201-21100-1-111-20020110000000-100
χ22222222-122-122-1-122-12-1-2-12-1-12-12-1-122-1-1-1-1-2-21-2-211111111-20-220-2-200-1-1-1-1220000011100201-2-1-100-1-111200-20-1-10000000100
χ23222222-122-122-1-122-12-1-2-12-1-12-12-1-1-2-2-1-1-1-1-2-21-2-211111111202-2022001111-2-200000-1-1-100-20-12110011-1-1200-20-1-10000000100
χ24222222-122-122-1-122-12-1-2-12-1-12-12-1-1-2-2-1-1-1-1-2-21-2-211111111-20220-2-20011-1-1-2-2000001110020-12-1-10011-1-1-20020110000000-100
χ2522222-122-122-122-12-1-122-1-12-1-12-12-122-1-1-1-12-12-1-122-1-1-1-1-1-10220200-1-12200-1-122002000-1-10-12-100-1-1-1-1-1-10220000-1-10000-1000
χ2622222-122-122-122-12-1-122-1-12-1-12-12-122-1-1-1-12-12-1-122-1-1-1-1-1-10-220-200112200-1-1-2-200-200011012-10011-1-1-1-10-2-200001100001000
χ2722222-122-122-122-12-1-122-1-12-1-12-12-1-2-2-1-1-1-12-12-1-122-1-1-1-1-1-102-20200-1-1-2-2001122002000-1-10-1-2100-1-111110-2-200001100001000
χ2822222-122-122-122-12-1-122-1-12-1-12-12-1-2-2-1-1-1-12-12-1-122-1-1-1-1-1-10-2-20-20011-2-20011-2-200-20001101-21001111110220000-1-10000-1000
χ2922222-122-122-122-12-1-12-2-1-12-1-12-12-122-1-1-1-1-21-211-2-211111102-20-200-1-12200-1-1-2-2002000-1-101-210011-1-1110-220000-1-100001000
χ3022222-122-122-122-12-1-12-2-1-12-1-12-12-122-1-1-1-1-21-211-2-21111110-2-20200112200-1-12200-2000110-1-2100-1-1-1-11102-20000110000-1000
χ3122222-122-122-122-12-1-12-2-1-12-1-12-12-1-2-2-1-1-1-1-21-211-2-21111110220-200-1-1-2-20011-2-2002000-1-1012-1001111-1-102-20000110000-1000
χ3222222-122-122-122-12-1-12-2-1-12-1-12-12-1-2-2-1-1-1-1-21-211-2-21111110-22020011-2-200112200-2000110-12-100-1-111-1-10-220000-1-100001000
χ332222-122-122-12222-12-1-122-1-12-1-1-1-1200-1-1-1-1-122-1-1-1-122-1-1-1-122022-1-122002200-1-122-12-1-1-1-1-1200-1-1-1-10000000020000-1-10000-10
χ342222-122-122-12222-12-1-122-1-12-1-1-1-1200-1-1-1-1-122-1-1-1-122-1-1-1-12-202-2-1-1-2-200220011-2-212-1-111-1-200-1-11100000000-2000011000010
χ352222-122-122-12222-12-1-122-1-12-1-1-1-1200-1-1-1-1-122-1-1-1-122-1-1-1-1-220-22112200-2-200-1-1-2-2-1-211-1-1120011-1-100000000-2000011000010
χ362222-122-122-12222-12-1-122-1-12-1-1-1-1200-1-1-1-1-122-1-1-1-122-1-1-1-1-2-20-2-211-2-200-2-20011221-211111-20011110000000020000-1-10000-10
χ372222-122-122-12222-12-1-1-22-1-12-1-1-1-1200-1-1-1-11-2-21111-2-21111220-2-2-1-12200-2-20011-2-2-12-1-1-1-11-20011110000000020000110000-10
χ382222-122-122-12222-12-1-1-22-1-12-1-1-1-1200-1-1-1-11-2-21111-2-211112-20-22-1-1-2-200-2-200-1-12212-1-111120011-1-100000000-20000-1-1000010
χ392222-122-122-12222-12-1-1-22-1-12-1-1-1-1200-1-1-1-11-2-21111-2-21111-2202-211220022001122-1-211-1-1-1-200-1-11100000000-20000-1-1000010
χ402222-122-122-12222-12-1-1-22-1-12-1-1-1-1200-1-1-1-11-2-21111-2-21111-2-202211-2-2002200-1-1-2-21-21111-1200-1-1-1-10000000020000110000-10
χ412-22-2222222-2-2-2-2-2-22220-2-2-2222-2-2-22i−2i2-2-2200000000000000000000002i−2i002i−2i002i−2i000000000000002i−2i000000000002i−2i2-20000
χ422-22-2222222-2-2-2-2-2-22220-2-2-2222-2-2-22i−2i2-2-2200000000000000000000002i−2i002i−2i00−2i2i000000000000002i−2i00000000000−2i2i-220000
χ432-22-2222222-2-2-2-2-2-22220-2-2-2222-2-2-2−2i2i2-2-220000000000000000000000−2i2i00−2i2i002i−2i00000000000000−2i2i000000000002i−2i-220000
χ442-22-2222222-2-2-2-2-2-22220-2-2-2222-2-2-2−2i2i2-2-220000000000000000000000−2i2i00−2i2i00−2i2i00000000000000−2i2i00000000000−2i2i2-20000
χ4544444-2-24-2-24-2-2-2-241-2-241-2-21-2-2-2-214411114-2-2-2-2-2-2111111004000000-2-200-2-2000000000000-2-20000111100000000000000000
χ4644444-2-24-2-24-2-2-2-241-2-241-2-21-2-2-2-21-4-411114-2-2-2-2-2-211111100-4000000220022000000000000220000-1-1-1-100000000000000000
χ4744444-2-24-2-24-2-2-2-241-2-2-41-2-21-2-2-2-21441111-4222222-1-1-1-1-1-100-4000000-2-200-2-200000000000022000011-1-100000000000000000
χ4844444-2-24-2-24-2-2-2-241-2-2-41-2-21-2-2-2-21-4-41111-4222222-1-1-1-1-1-1004000000220022000000000000-2-20000-1-11100000000000000000
χ494444-24-2-24-2-24-2-24-2-2-214-2-21-2-21-21-2001111-24-2-2-211-2-2111140040-2-20000-2-20000000-21100-20001100000000000000000000000
χ504444-24-2-24-2-24-2-24-2-2-214-2-21-2-21-21-2001111-24-2-2-211-2-21111-400-402200002200000002-1-1002000-1-100000000000000000000000
χ514444-24-2-24-2-24-2-24-2-2-21-4-2-21-2-21-21-20011112-4222-1-122-1-1-1-1400-40-2-20000220000000-211002000-1-100000000000000000000000
χ524444-24-2-24-2-24-2-24-2-2-21-4-2-21-2-21-21-20011112-4222-1-122-1-1-1-1-40040220000-2-200000002-1-100-20001100000000000000000000000
χ534444-2-24-2-24-2-244-2-2-21-24-21-2-21-21-2-2001111-2-2411-2-2-2-211110400400-2-2000000-2-200-2000110-2000011000000000000000000000
χ544444-2-24-2-24-2-244-2-2-21-24-21-2-21-21-2-2001111-2-2411-2-2-2-211110-400-4002200000022002000-1-1020000-1-1000000000000000000000
χ554444-2-24-2-24-2-244-2-2-21-2-4-21-2-21-21-2-200111122-4-1-12222-1-1-1-10400-400-2-20000002200-200011020000-1-1000000000000000000000
χ564444-2-24-2-24-2-244-2-2-21-2-4-21-2-21-21-2-200111122-4-1-12222-1-1-1-10-40040022000000-2-2002000-1-10-2000011000000000000000000000
χ5744-4-4444-4-4-44-44-44-44440-44-4-4-4-4-4440044-4-40000000000000000000000000000000000000000000000000000000000000000000
χ5844-4-444-2-4-424-4-224-4-24-202422-42-4-2-200-2-2220000000000000000000000000000000000000000000000000000000−2i32i30000000000
χ5944-4-444-2-4-424-4-224-4-24-202422-42-4-2-200-2-22200000000000000000000000000000000000000000000000000000002i3−2i30000000000
χ6044-4-44-24-42-4424-4-2-4-2-2402-2-422-424-200-2-22200000000000000000000−2i32i300000000000000−2i32i300000000000000000000000000000
χ6144-4-44-24-42-4424-4-2-4-2-2402-2-422-424-200-2-222000000000000000000002i3−2i3000000000000002i3−2i300000000000000000000000000000
χ6244-4-4-2442-4-4-2-44-4424-2-20-4-22-4222-2400-2-222000000000000000000000000000023−230000000000000023−23000000000000000000000
χ6344-4-4-2442-4-4-2-44-4424-2-20-4-22-4222-2400-2-2220000000000000000000000000000−232300000000000000−2323000000000000000000000
χ6444-4-4-2-2422-4-224-4-22-21-202122-12-1-2-20011-1-10003i−3i00003i3i−3i−3i0000000−2i32i300000023−23000000i3−i3000000−33000000000000000000000
χ6544-4-4-2-2422-4-224-4-22-21-202122-12-1-2-20011-1-10003i−3i00003i3i−3i−3i00000002i3−2i3000000−2323000000−i3i30000003−3000000000000000000000
χ6644-4-4-2-2422-4-224-4-22-21-202122-12-1-2-20011-1-1000−3i3i0000−3i−3i3i3i0000000−2i32i3000000−2323000000i3−i30000003−3000000000000000000000
χ6744-4-4-2-2422-4-224-4-22-21-202122-12-1-2-20011-1-1000−3i3i0000−3i−3i3i3i00000002i3−2i300000023−23000000−i3i3000000−33000000000000000000000
χ684-44-444-244-2-4-422-4-4-24-202-42-24-2-4224i−4i-222-20000000000000000000000−2i2i004i−4i000000000000000000−2i2i0000000000000000000
χ694-44-444-244-2-4-422-4-4-24-202-42-24-2-422−4i4i-222-200000000000000000000002i−2i00−4i4i0000000000000000002i−2i0000000000000000000
χ704-44-44-244-24-42-4-42-4-2-24022-4-2-242-424i−4i-222-200000000000000000000004i−4i00−2i2i000000000000000000−2i2i0000000000000000000
χ714-44-44-244-24-42-4-42-4-2-24022-4-2-242-42−4i4i-222-20000000000000000000000−4i4i002i−2i0000000000000000002i−2i0000000000000000000
χ724-44-44-2-24-2-2-42222-41-2-20-1221-2-222-14i−4i1-1-1100000003-33-33-3000000000−2i2i00−2i2i000000000000000000i−i3i−3i00000000000000000
χ734-44-44-2-24-2-2-42222-41-2-20-1221-2-222-14i−4i1-1-110000000-33-33-33000000000−2i2i00−2i2i000000000000000000i−i−3i3i00000000000000000
χ744-44-44-2-24-2-2-42222-41-2-20-1221-2-222-1−4i4i1-1-1100000003-33-33-30000000002i−2i002i−2i000000000000000000−ii−3i3i00000000000000000
χ754-44-44-2-24-2-2-42222-41-2-20-1221-2-222-1−4i4i1-1-110000000-33-33-330000000002i−2i002i−2i000000000000000000−ii3i−3i00000000000000000
χ764-44-4-244-2442-4-4-4-424-2-20-4224-2-222-400-222-20000000000000000000000000000004i−4i000000000000000000000000000−2i2i000000
χ774-44-4-244-2442-4-4-4-424-2-20-4224-2-222-400-222-2000000000000000000000000000000−4i4i0000000000000000000000000002i−2i000000
χ784-4-44444-4-4-4-44-44-4444404-44-4-4-44-4-4004-44-40000000000000000000000000000000000000000000000000000000000000000000
χ794-4-4444-2-4-42-442-2-44-24-20-2-4-22-4242200-22-2200000000000000000000000023−23000000000000000023−2300000000000000000000000
χ804-4-4444-2-4-42-442-2-44-24-20-2-4-22-4242200-22-22000000000000000000000000−23230000000000000000−232300000000000000000000000
χ814-4-444-24-42-4-4-2-4424-2-240-22422-4-2-4200-22-2200000000000000000000000000000000000000000000000000000000023−2300000000
χ824-4-444-24-42-4-4-2-4424-2-240-22422-4-2-4200-22-22000000000000000000000000000000000000000000000000000000000−232300000000
χ834-4-44-2442-4-424-44-4-24-2-2042-2-422-22-400-22-22000000000000000000−2i32i300000000000000−2i32i30000000000000000000000000000000
χ844-4-44-2442-4-424-44-4-24-2-2042-2-422-22-400-22-220000000000000000002i3−2i3000000000000002i3−2i30000000000000000000000000000000
χ854-4-44-24-22-42242-2-4-2-2-210-22122-1-2-12001-11-1000003i−3i003i−3i−3i3i00000−2i32i3000023−2300000000i3−i3000000−3300000000000000000000000
χ864-4-44-24-22-42242-2-4-2-2-210-22122-1-2-12001-11-1000003i−3i003i−3i−3i3i000002i3−2i30000−232300000000−i3i30000003−300000000000000000000000
χ874-4-44-24-22-42242-2-4-2-2-210-22122-1-2-12001-11-100000−3i3i00−3i3i3i−3i00000−2i32i30000−232300000000i3−i30000003−300000000000000000000000
χ884-4-44-24-22-42242-2-4-2-2-210-22122-1-2-12001-11-100000−3i3i00−3i3i3i−3i000002i3−2i3000023−2300000000−i3i3000000−3300000000000000000000000
χ898888-4-4-4-4-4-4-4-4-4-4-4-4222822222222200-1-1-1-1-4-4-4222222-1-1-1-1000000000000000000000000000000000000000000000000000000
χ908888-4-4-4-4-4-4-4-4-4-4-4-4222-822222222200-1-1-1-1444-2-2-2-2-2-21111000000000000000000000000000000000000000000000000000000
χ9188-8-88-4-4-84484-44-4-82-4-40-2-44-2444-420022-2-20000000000000000000000000000000000000000000000000000000000000000000
χ9288-8-8-48-44-84-4-8-4484-4-4204-4-244-242-40022-2-20000000000000000000000000000000000000000000000000000000000000000000
χ9388-8-8-4-4-4444-44-44-442220-22-2-2-2-2-22200-1-1110006i−6i0000−3i−3i3i3i000000000000000000000000000000000000000000000000000000
χ9488-8-8-4-4-4444-44-44-442220-22-2-2-2-2-22200-1-111000−6i6i00003i3i−3i−3i000000000000000000000000000000000000000000000000000000
χ958-88-8-48-4-48-44-844-84-4-42044-2-4-424-24002-2-220000000000000000000000000000000000000000000000000000000000000000000
χ968-88-8-4-48-4-4844-8-844-42-404-24-42-4-244002-2-220000000000000000000000000000000000000000000000000000000000000000000
χ978-88-8-4-4-4-4-4-44444442220-2-2-2222-2-2-200-111-100000006-6-33-33000000000000000000000000000000000000000000000000000000
χ988-88-8-4-4-4-4-4-44444442220-2-2-2222-2-2-200-111-10000000-663-33-3000000000000000000000000000000000000000000000000000000
χ998-8-888-4-4-844-8-44-4482-4-4024-4-244-44-2002-22-20000000000000000000000000000000000000000000000000000000000000000000
χ1008-8-88-4-4844-84-4-884-4-42-40-4-2-44-24244002-22-20000000000000000000000000000000000000000000000000000000000000000000
χ1018-8-88-4-4-44444-44-44-422202-22-2-2-22-2-200-11-11000006i−6i00−3i3i3i−3i000000000000000000000000000000000000000000000000000000
χ1028-8-88-4-4-44444-44-44-422202-22-2-2-22-2-200-11-1100000−6i6i003i−3i−3i3i000000000000000000000000000000000000000000000000000000

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