Finite Group Databasebeta

← Group #13168547

Character table — Group #13168547

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size1111222222222222444444444444466888888888888888881212121212121212121212121212121212181824242424242424242424242424242424242436363636363636363636365454727272108
order1222333666666666333466666666644366612121212121212121212121212444441212121212121212121212124412121212121212121212121212121212121222444661212121244612122
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111-1-111111111-1-111-1-1-1-11-11-11111111111-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11-1
χ3111111111111111111111111111111111111111111111111-1111-111-1-1-1-1111111-1-111-111-111-1-111-1-111111-11-1-111-1-1-1-1-1-1-11-1-1
χ4111111111111111111111111111111111111111111111111-1-1-11-111-1-1-1-1-1-111-1-1111-1-1-11-111-1-111-1-1-1-1-1-1-11-1-1-1-1-111-1-1111-1-11
χ511111111111111111111111111111-1-111111111111111111111-11-1-1111111-1-11111-1111-11-1-111-1-1111111-11-1-1-1-1-111-1-1-1-11-1-1-1
χ611111111111111111111111111111-1-1111111111111111111-1-1-11-1-11111-1-1-1-1-1-1-1-1-1-11-1-11-1-111-1-111-1-1-1-11-11-1-111-1-1-1-111-11-11
χ711111111111111111111111111111-1-111111111111111111-111-1-1-1-1-1-1-1-111-1-111-1-1-11-11-1-1-1-1-1-1-1-1-1-11111-1-1-111-1-1-1-11111-1-111
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
χ91111111111111111111-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-11111-1-11111-1-1-1-1-1-111-1-11111-1-1-1-111-1-1-1111-1-1-1-1-111-1-111-11
χ101111111111111111111-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-11111-1-1-1-1111111-111-1-1-11111-1-1-1-1-1-1111-1-11-111111111-1-1-1-1
χ111111111111111111111-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-1111111-1-111-1-1-11-1111-1-1-1-11111-1-1-1-11-11-1-111-1-111-111-1
χ121111111111111111111-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1111-1-111-1-11111-1-1-11-1-1-1111-1-1-1-111-1-11111-1-1111-1-1-1-1-1-11-111
χ131111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-11-1-1-111-1-111-1-1-1-1-1-11-1111-1-1-11111-1-111-1-111-1-1111-1-1-1-1111-11-1
χ141111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-1-111-1-1-1-1-1-11111111-11-1-1-11111-1-1-1-111-1-11-11-1-111-1-1-1-1-1111
χ151111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-1-1-11111-1-1-1-1111-1-1111-1-1-1-1111111-1-11-1-11-1111111-1-1-1-1-11
χ161111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-111-1-1-1-111-1-111-1-111-1-1-1-11111-1-111-1111-1-1-1-1-1111111-1-1
χ17222222-12222-1-1-1222-1-122-1-1-12-12-1-100-1-1-1-12-12-1-122-1-1-1-1-1-1222020022-1-1-1-10022220-1-120200-1-100-1-1-1-1-1-10200000-1-10000-1000
χ18222222-12222-1-1-1222-1-122-1-1-12-12-1-100-1-1-1-12-12-1-122-1-1-1-1-1-12-2-2020022-1-11100-2-2-2-201-1-20200-1-100-1-111110-2000001100001000
χ19222222-12222-1-1-1222-1-122-1-1-12-12-1-100-1-1-1-12-12-1-122-1-1-1-1-1-1-2220-200-2-211-1-10022-2-20-1120-200110011-1-1-1-10-2000001100001000
χ20222222-12222-1-1-1222-1-122-1-1-12-12-1-100-1-1-1-12-12-1-122-1-1-1-1-1-1-2-2-20-200-2-2111100-2-222011-20-20011001111110200000-1-10000-1000
χ21222222-12222-1-1-1222-1-1-22-1-1-12-12-1-100-1-1-1-1-21-211-2-211111122-20-2002211-1-100-2-2-2-201-120-200-1-10011-1-1110200000110000-1000
χ22222222-12222-1-1-1222-1-1-22-1-1-12-12-1-100-1-1-1-1-21-211-2-21111112-220-2002211110022220-1-1-20-200-1-1001111-1-10-200000-1-100001000
χ23222222-12222-1-1-1222-1-1-22-1-1-12-12-1-100-1-1-1-1-21-211-2-2111111-22-20200-2-2-1-1-1-100-2-222011202001100-1-1-1-1110-200000-1-100001000
χ24222222-12222-1-1-1222-1-1-22-1-1-12-12-1-100-1-1-1-1-21-211-2-2111111-2-220200-2-2-1-1110022-2-20-11-202001100-1-111-1-10200000110000-1000
χ2522222-12-122-1222-12-12-12-12-1-1-12-12-122-1-1-1-1-122-1-1-1-122-1-1-1-10222022000022-1-1-1-100-120-120-1-100-1-100-1-1-1-120200-1-10000000-100
χ2622222-12-122-1222-12-12-12-12-1-1-12-12-122-1-1-1-1-122-1-1-1-122-1-1-1-10-2-220220000-2-2-1-11100-1-20120-1-100-1-1001111-20-200110000000100
χ2722222-12-122-1222-12-12-12-12-1-1-12-12-1-2-2-1-1-1-1-122-1-1-1-122-1-1-1-1022-20-2-200002211-1-100120-1-2011001100-1-1-1-1-20-200110000000100
χ2822222-12-122-1222-12-12-12-12-1-1-12-12-1-2-2-1-1-1-1-122-1-1-1-122-1-1-1-10-2-2-20-2-20000-2-21111001-201-2011001100111120200-1-10000000-100
χ2922222-12-122-1222-12-12-1-2-12-1-1-12-12-122-1-1-1-11-2-21111-2-2111102-2-2022000022-1-111001-20-1-20-1-1001100-1-111-20200110000000-100
χ3022222-12-122-1222-12-12-1-2-12-1-1-12-12-122-1-1-1-11-2-21111-2-211110-22-20220000-2-2-1-1-1-1001201-20-1-100110011-1-120-200-1-10000000100
χ3122222-12-122-1222-12-12-1-2-12-1-1-12-12-1-2-2-1-1-1-11-2-21111-2-2111102-220-2-2000022111100-1-20-1201100-1-100-1-11120-200-1-10000000100
χ3222222-12-122-1222-12-12-1-2-12-1-1-12-12-1-2-2-1-1-1-11-2-21111-2-211110-2220-2-20000-2-211-1-100-1201201100-1-10011-1-1-20200110000000-100
χ332222-1222-1-122222-1-1-122-1-122-1-1-1-1222-1-1-1-122-122-1-1-1-1-1-1-1-120022-1-1-1-122002200002020-1-1-1-1-1-1-1-1-1-10000000220000-1-10000-10
χ342222-1222-1-122222-1-1-122-1-122-1-1-1-1222-1-1-1-122-122-1-1-1-1-1-1-1-1-2002-2-1-111-2-20022000020-20-11-1-111-1-1110000000-2-2000011000010
χ352222-1222-1-122222-1-1-122-1-122-1-1-1-12-2-2-1-1-1-122-122-1-1-1-1-1-1-1-1200-2211-1-12200-2-20000-20201-111-1-111-1-10000000-2-2000011000010
χ362222-1222-1-122222-1-1-122-1-122-1-1-1-12-2-2-1-1-1-122-122-1-1-1-1-1-1-1-1-200-2-21111-2-200-2-20000-20-2011111111110000000220000-1-10000-10
χ372222-1222-1-122222-1-1-12-2-1-122-1-1-1-1222-1-1-1-1-2-21-2-211111111200-2-2-1-1-1-1-2-200220000-202011-1-1-1-1111100000002-20000-1-1000010
χ382222-1222-1-122222-1-1-12-2-1-122-1-1-1-1222-1-1-1-1-2-21-2-211111111-200-22-1-1112200220000-20-201-1-1-11111-1-10000000-220000110000-10
χ392222-1222-1-122222-1-1-12-2-1-122-1-1-1-12-2-2-1-1-1-1-2-21-2-2111111112002-211-1-1-2-200-2-200002020-1111-1-1-1-1110000000-220000110000-10
χ402222-1222-1-122222-1-1-12-2-1-122-1-1-1-12-2-2-1-1-1-1-2-21-2-211111111-2002211112200-2-2000020-20-1-11111-1-1-1-100000002-20000-1-1000010
χ412-22-2222-22-2-2-22-22-22220-22-2-22-2-2-222-222-2-20000000000000000002-20000002-2002i−2i0000002-2000000000000000002i−2i002i−2i0000
χ422-22-2222-22-2-2-22-22-22220-22-2-22-2-2-222-222-2-20000000000000000002-20000002-200−2i2i0000002-200000000000000000−2i2i00−2i2i0000
χ432-22-2222-22-2-2-22-22-22220-22-2-22-2-2-22-2222-2-2000000000000000000-22000000-22002i−2i000000-22000000000000000002i−2i00−2i2i0000
χ442-22-2222-22-2-2-22-22-22220-22-2-22-2-2-22-2222-2-2000000000000000000-22000000-2200−2i2i000000-2200000000000000000−2i2i002i−2i0000
χ4544444-2-2-244-2-2-2-2-24-2-214-2-211-2-2-2-21001111-2-2411-2-2-2-2111104400000000-2-200-2-2000-20-20000000000111100000000000000000
χ4644444-2-2-244-2-2-2-2-24-2-214-2-211-2-2-2-21001111-2-2411-2-2-2-211110-4-4000000002200220002020000000000-1-1-1-100000000000000000
χ4744444-2-2-244-2-2-2-2-24-2-21-4-2-211-2-2-2-2100111122-4-1-12222-1-1-1-104-400000000-2-2002200020-2000000000011-1-100000000000000000
χ4844444-2-2-244-2-2-2-2-24-2-21-4-2-211-2-2-2-2100111122-4-1-12222-1-1-1-10-44000000002200-2-2000-2020000000000-1-11100000000000000000
χ494444-24-24-2-24-2-2-24-2-21-24-21-2-2-21-21-20011114-2-2-2-2-2-21111114000400-2-2-2-20000000000-200-200110011000000000000000000000
χ504444-24-24-2-24-2-2-24-2-21-24-21-2-2-21-21-20011114-2-2-2-2-2-2111111-4000-40022220000000000200200-1-100-1-1000000000000000000000
χ514444-24-24-2-24-2-2-24-2-21-2-4-21-2-2-21-21-2001111-4222222-1-1-1-1-1-14000-400-2-2220000000000-2002001100-1-1000000000000000000000
χ524444-24-24-2-24-2-2-24-2-21-2-4-21-2-2-21-21-2001111-4222222-1-1-1-1-1-1-400040022-2-20000000000200-200-1-10011000000000000000000000
χ534444-2-24-2-2-2-2444-2-21-2-241-2-2-21-21-2-2441111-24-2-2-211-2-2111100040-2-2000000-2-20000-2000-2011001100000000000000000000000
χ544444-2-24-2-2-2-2444-2-21-2-241-2-2-21-21-2-2-4-41111-24-2-2-211-2-21111000-4022000000220000200020-1-100-1-100000000000000000000000
χ554444-2-24-2-2-2-2444-2-21-2-2-41-2-2-21-21-2-24411112-4222-1-122-1-1-1-1000-40-2-2000000-2-200002000201100-1-100000000000000000000000
χ564444-2-24-2-2-2-2444-2-21-2-2-41-2-2-21-21-2-2-4-411112-4222-1-122-1-1-1-10004022000000220000-2000-20-1-1001100000000000000000000000
χ5744-4-44444-44-4-4-44-4-444404-44-4-44-4-4-4004-44-40000000000000000000000000000000000000000000000000000000000000000000
χ5844-4-444-24-44-422-2-4-44-2-2042-22-4-2-42200-22-22000000000000000000000023−230000000000000000000023−23000000000000000000000
χ5944-4-444-24-44-422-2-4-44-2-2042-22-4-2-42200-22-220000000000000000000000−232300000000000000000000−2323000000000000000000000
χ6044-4-44-24-2-442-4-442-4-24-20-2-4-22242-4200-22-220000000000000000000000000000000000000000000000000000000−2i32i30000000000
χ6144-4-44-24-2-442-4-442-4-24-20-2-4-22242-4200-22-2200000000000000000000000000000000000000000000000000000002i3−2i30000000000
χ6244-4-4-24442-2-4-4-44-42-2-240-224-42-222-400-22-2200000000000000000000−2i32i3000000000000000000−2i32i30000000000000000000000000
χ6344-4-4-24442-2-4-4-44-42-2-240-224-42-222-400-22-22000000000000000000002i3−2i30000000000000000002i3−2i30000000000000000000000000
χ6444-4-4-24-242-2-422-2-42-21-20-2-1-22212-12001-11-100000003i−3i3i3i−3i−3i0000000−2i32i323−230000000000000000i3−i300−33000000000000000000000
χ6544-4-4-24-242-2-422-2-42-21-20-2-1-22212-12001-11-100000003i−3i3i3i−3i−3i00000002i3−2i3−23230000000000000000−i3i3003−3000000000000000000000
χ6644-4-4-24-242-2-422-2-42-21-20-2-1-22212-12001-11-10000000−3i3i−3i−3i3i3i0000000−2i32i3−23230000000000000000i3−i3003−3000000000000000000000
χ6744-4-4-24-242-2-422-2-42-21-20-2-1-22212-12001-11-10000000−3i3i−3i−3i3i3i00000002i3−2i323−230000000000000000−i3i300−33000000000000000000000
χ684-44-444-2-44-4-42-224-44-2-20-4-22242-42-200-2-2220000000000000000000000000000004i−4i0000000000000000000000000−2i2i00000000
χ694-44-444-2-44-4-42-224-44-2-20-4-22242-42-200-2-222000000000000000000000000000000−4i4i00000000000000000000000002i−2i00000000
χ704-44-44-2424-42-44-4-2-4-24-202422-2-42-4-24-4-2-2220000000000000000004-4000000-220000000000-22000000000000000000000000000
χ714-44-44-2424-42-44-4-2-4-24-202422-2-42-4-2-44-2-222000000000000000000-440000002-200000000002-2000000000000000000000000000
χ724-44-4-244-4-22-4-44-442-2-2402-2-4-4-222244-4-2-222000000000000000000-220000004-40000000000-22000000000000000000000000000
χ734-44-4-244-4-22-4-44-442-2-2402-2-4-4-22224-44-2-2220000000000000000002-2000000-4400000000002-2000000000000000000000000000
χ744-44-4-2-242-222-44-4-221-2-20-1-22212-12-24-411-1-1000003i−3i003i−3i3i−3i00000-22000000-2200000000001-1003i−3i00000000000000000000000
χ754-44-4-2-242-222-44-4-221-2-20-1-22212-12-24-411-1-100000−3i3i00−3i3i−3i3i00000-22000000-2200000000001-100−3i3i00000000000000000000000
χ764-44-4-2-242-222-44-4-221-2-20-1-22212-12-2-4411-1-1000003i−3i003i−3i3i−3i000002-20000002-20000000000-1100−3i3i00000000000000000000000
χ774-44-4-2-242-222-44-4-221-2-20-1-22212-12-2-4411-1-100000−3i3i00−3i3i−3i3i000002-20000002-20000000000-11003i−3i00000000000000000000000
χ784-4-44444-4-4-444-4-4-444440-4-4-44-4-444-4004-4-440000000000000000000000000000000000000000000000000000000000000000000
χ794-4-4444-2-4-4-44-222-444-2-20-422-2-424-2200-222-200000000000000000000000023−230000000000000000000023−230000000000000000000
χ804-4-4444-2-4-4-44-222-444-2-20-422-2-424-2200-222-2000000000000000000000000−232300000000000000000000−23230000000000000000000
χ814-4-444-242-4-4-24-4-424-24-202-42-22-4-24200-222-2000000000000000000000000000023−2300000000000000000023−2300000000000000000
χ824-4-444-242-4-4-24-4-424-24-202-42-22-4-24200-222-20000000000000000000000000000−2323000000000000000000−232300000000000000000
χ834-4-444-2-22-4-4-2-22224-2-21022-1122-2-2-1001-1-110003-300003-3-330000000000023−230023−230000000000000000−33−3300000000000000000
χ844-4-444-2-22-4-4-2-22224-2-21022-1122-2-2-1001-1-110003-300003-3-3300000000000−232300−232300000000000000003−33−300000000000000000
χ854-4-444-2-22-4-4-2-22224-2-21022-1122-2-2-1001-1-11000-330000-333-30000000000023−2300−23230000000000000000−333−300000000000000000
χ864-4-444-2-22-4-4-2-22224-2-21022-1122-2-2-1001-1-11000-330000-333-300000000000−23230023−2300000000000000003−3−3300000000000000000
χ874-4-44-244-42244-4-4-4-2-2-24022-4422-2-2-400-222-200000000000000000000000000000000000000000000000000000000000−2i32i3000000
χ884-4-44-244-42244-4-4-4-2-2-24022-4422-2-2-400-222-2000000000000000000000000000000000000000000000000000000000002i3−2i3000000
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
χ9188-8-88-4-4-4-88444-44-8-4-420-442-24-444-2002-22-20000000000000000000000000000000000000000000000000000000000000000000
χ9288-8-8-4-48-44-44-8-88442-4-4024-44-2-4-244002-22-20000000000000000000000000000000000000000000000000000000000000000000
χ9388-8-8-4-4-4-44-4444-44422202-22-2-22-2-2-200-11-1100000006i−6i−3i−3i3i3i000000000000000000000000000000000000000000000000000000
χ9488-8-8-4-4-4-44-4444-44422202-22-2-22-2-2-200-11-110000000−6i6i3i3i−3i−3i000000000000000000000000000000000000000000000000000000
χ958-88-88-4-448-844-44-4-8-4-4204-4-2-2-444420022-2-20000000000000000000000000000000000000000000000000000000000000000000
χ968-88-8-48-4-8-44-84-4484-42-404244-4-24-2-40022-2-20000000000000000000000000000000000000000000000000000000000000000000
χ978-88-8-4-4-44-4444-44-442220-22-2-22-2-2-2200-1-111000006i−6i00−3i3i−3i3i000000000000000000000000000000000000000000000000000000
χ988-88-8-4-4-44-4444-44-442220-22-2-22-2-2-2200-1-11100000−6i6i003i−3i3i−3i000000000000000000000000000000000000000000000000000000
χ998-8-88-48-4-8448-444-8-4-42-404-24-44-2-424002-2-220000000000000000000000000000000000000000000000000000000000000000000
χ1008-8-88-4-48444-48-8-84-42-4-40-244-4-242-44002-2-220000000000000000000000000000000000000000000000000000000000000000000
χ1018-8-88-4-4-4444-4-4444-42220-2-2-22-2-222-200-111-10006-60000-333-3000000000000000000000000000000000000000000000000000000
χ1028-8-88-4-4-4444-4-4444-42220-2-2-22-2-222-200-111-1000-6600003-3-33000000000000000000000000000000000000000000000000000000

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