Finite Group Databasebeta

← Group #13169459

Character table — Group #13169459

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size1111222222222222444444444444466888888888888888881212121212121212121212121212121212181824242424242424242424242424242424242436363636363636363636365454727272108
order1222333666666666333466666666644366612121212121212121212121212444441212121212121212121212124412121212121212121212121212121212121244444121212121212441212122
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-11-111-1-1-1-1111111-1-1111-11-111-1-111-1-11111-11-11-111-1-1-1-1-1-11-1-1-1
χ31111111111111111111111111111111111111111111111111-11-11-1-1111111-1-111-1-1-11-1111-1-111-1-11111111-1-1-11-1-111-1-1-1-1-11-1-1
χ41111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-11111-11-1-11-1-1-1-1-1-1-1-1-11111-1-11-1-1-1-1-1-11111-1-111
χ511111111111111111111111111111-1-111111111111111111-11111111111-1-111-1-1111-111-1111111111-1-1-1-1-1-11-1-1-1-1-1-111-1-1-1-11-1
χ611111111111111111111111111111-1-111111111111111111-11-11-111-1-1-1-1-1-111-1-1-1-11-11-1-1-111-1-111-1-1-1-1-1-11-1-1-11-1-111-1-111-11-11
χ711111111111111111111111111111-1-111111111111111111-1-11-11-1-11111-1-1-1-1-1-1-1-1-1-1-11-11-1-111-1-111-1-1-1-1-11-11-111-1-1-1-1111-1-11
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
χ91111111111111111111-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-111-1-111-1-1-1-11-1-111111-1-1-1-111-1-1-1-1111-1-111-1-1-1-11-111
χ101111111111111111111-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111-1-11111-1-11111-1-111-1-111-1-1-1-11111-1-11-1-11-1-1-1-1-1111111-1-1
χ111111111111111111111-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-111-1-1111111111-1-1-1-11-1-11111-1-111-1-1-11-1-1111111111-1-1-1-1
χ121111111111111111111-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-11-1-11-1-1-1-1-1-1111111-1-1111-1-111-1-1-1-1-1-1-1111
χ131111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-11111-1-1-1-1-1-1-1-1-1-1-111-1111111-1-1-1-1-1-111111-1-111-1-1-1-111-111-1
χ141111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111-1-111-1-1-1-1-1-111-11111-111-1-1-1-111-1-111-11-1-11111111-1-1-1-1-11
χ151111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-1-111-1-1-1-111-1-11111-1-111-1-11111-1-1-1-1111-1-11-1-1-1-1-111-1-111-11
χ161111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-1-1-111-1-111-1-1-1-111-111-1-1-1-1-11111-1-111-1-1111-1-111-1-1111-11-1
χ17222222-1222-1-12-1222-1-122-1-1-12-12-1-122-1-1-1-122-1-1-122-1-1-1-1-1-122020220000-1-1-1-122002-1-1020-1-100-1-100-1-1-1-102020-1-1000000-1000
χ18222222-1222-1-12-1222-1-122-1-1-12-12-1-122-1-1-1-122-1-1-122-1-1-1-1-1-12-20-20-2-20000-1-1112200-2-1102011001100-1-1-1-10-20-20110000001000
χ19222222-1222-1-12-1222-1-122-1-1-12-12-1-1-2-2-1-1-1-122-1-1-122-1-1-1-1-1-1-2202022000011-1-1-2-20021-10-20-1-100-1-10011110-20-20110000001000
χ20222222-1222-1-12-1222-1-122-1-1-12-12-1-1-2-2-1-1-1-122-1-1-122-1-1-1-1-1-1-2-20-20-2-200001111-2-200-2110-2011001100111102020-1-1000000-1000
χ21222222-1222-1-12-1222-1-1-22-1-1-12-12-1-122-1-1-1-1-2-2111-2-2111111-220-20220000-1-1112200-21-10-20-1-1001100-1-1110-202011000000-1000
χ22222222-1222-1-12-1222-1-1-22-1-1-12-12-1-122-1-1-1-1-2-2111-2-2111111-2-2020-2-20000-1-1-1-122002110-201100-1-100-1-111020-20-1-10000001000
χ23222222-1222-1-12-1222-1-1-22-1-1-12-12-1-1-2-2-1-1-1-1-2-2111-2-2111111220-202200001111-2-200-2-1-1020-1-100110011-1-1020-20-1-10000001000
χ24222222-1222-1-12-1222-1-1-22-1-1-12-12-1-1-2-2-1-1-1-1-2-2111-2-21111112-2020-2-2000011-1-1-2-2002-110201100-1-10011-1-10-202011000000-1000
χ2522222-122-1222-12-12-12-12-12-1-1-12-12-122-1-1-1-12-12-1-1-1-122-1-1-1-12020200-1-1222200-1-100020-1-1200-1-100-1-1-1-1-1-12000200-1-100000-100
χ2622222-122-1222-12-12-12-12-12-1-1-12-12-122-1-1-1-12-12-1-1-1-122-1-1-1-120-20-20011-2-22200-1-1000201-1-200110011-1-1-1-1-2000-2001100000100
χ2722222-122-1222-12-12-12-12-12-1-1-12-12-1-2-2-1-1-1-12-12-1-1-1-122-1-1-1-1-2020200-1-122-2-20011000-20-11200-1-100-1-11111-2000-2001100000100
χ2822222-122-1222-12-12-12-12-12-1-1-12-12-1-2-2-1-1-1-12-12-1-1-1-122-1-1-1-1-20-20-20011-2-2-2-20011000-2011-20011001111112000200-1-100000-100
χ2922222-122-1222-12-12-12-1-2-12-1-1-12-12-122-1-1-1-1-21-21111-2-21111-2020-200-1-1-2-22200-1-1000-2011200-1-10011-1-111-2000200-1-100000100
χ3022222-122-1222-12-12-12-1-2-12-1-1-12-12-122-1-1-1-1-21-21111-2-21111-20-2020011222200-1-1000-20-11-2001100-1-1-1-1112000-2001100000-100
χ3122222-122-1222-12-12-12-1-2-12-1-1-12-12-1-2-2-1-1-1-1-21-21111-2-211112020-200-1-1-2-2-2-20011000201-1200-1-1001111-1-12000-2001100000-100
χ3222222-122-1222-12-12-12-1-2-12-1-1-12-12-1-2-2-1-1-1-1-21-21111-2-2111120-202001122-2-2001100020-1-1-2001100-1-111-1-1-2000200-1-100000100
χ332222-122-12-122222-1-1-122-1-122-1-1-1-1200-1-1-1-1-12222-1-1-1-1-1-1-1-102222-1-122-1-100220022-10220-1-1-1-1-1-1-1-1-10000002000000-1-10000-10
χ342222-122-12-122222-1-1-122-1-122-1-1-1-1200-1-1-1-1-12222-1-1-1-1-1-1-1-102-22-2-1-1-2-211002200-2-2-102-201-1-111-1-111000000-200000011000010
χ352222-122-12-122222-1-1-122-1-122-1-1-1-1200-1-1-1-1-12222-1-1-1-1-1-1-1-10-22-221122-1-100-2-200-2-210-220-111-1-111-1-1000000-200000011000010
χ362222-122-12-122222-1-1-122-1-122-1-1-1-1200-1-1-1-1-12222-1-1-1-1-1-1-1-10-2-2-2-211-2-21100-2-2002210-2-201111111110000002000000-1-10000-10
χ372222-122-12-122222-1-1-12-2-1-122-1-1-1-1200-1-1-1-11-2-2-2-211111111022-2-2-1-1221100-2-200-2-2102-20-1-1-1-1-111110000002000000110000-10
χ382222-122-12-122222-1-1-12-2-1-122-1-1-1-1200-1-1-1-11-2-2-2-21111111102-2-22-1-1-2-2-1-100-2-20022102201-1-11111-1-1000000-2000000-1-1000010
χ392222-122-12-122222-1-1-12-2-1-122-1-1-1-1200-1-1-1-11-2-2-2-2111111110-222-211221100220022-10-2-20-111-1-1-1-111000000-2000000-1-1000010
χ402222-122-12-122222-1-1-12-2-1-122-1-1-1-1200-1-1-1-11-2-2-2-2111111110-2-22211-2-2-1-1002200-2-2-10-22011111-1-1-1-10000002000000110000-10
χ412-2-22222-2-22-2-222-2-22220-2-2-22-2-222-22i−2i2-2-220000000000000000000000002i−2i002i−2i2i−2i000000000000002i−2i000000000002i−2i2-20000
χ422-2-22222-2-22-2-222-2-22220-2-2-22-2-222-22i−2i2-2-220000000000000000000000002i−2i002i−2i−2i2i000000000000002i−2i00000000000−2i2i-220000
χ432-2-22222-2-22-2-222-2-22220-2-2-22-2-222-2−2i2i2-2-22000000000000000000000000−2i2i00−2i2i2i−2i00000000000000−2i2i000000000002i−2i-220000
χ442-2-22222-2-22-2-222-2-22220-2-2-22-2-222-2−2i2i2-2-22000000000000000000000000−2i2i00−2i2i−2i2i00000000000000−2i2i00000000000−2i2i2-20000
χ4544444-2-24-24-2-2-2-2-24-2-214-2-211-2-2-2-214411114-2-211-2-2-2-2111140000000000-2-200-2-2000-200-2000000000111100000000000000000
χ4644444-2-24-24-2-2-2-2-24-2-214-2-211-2-2-2-21-4-411114-2-211-2-2-2-21111-400000000002200220002002000000000-1-1-1-100000000000000000
χ4744444-2-24-24-2-2-2-2-24-2-21-4-2-211-2-2-2-21441111-422-1-12222-1-1-1-1-40000000000-2-200-2-2000200200000000011-1-100000000000000000
χ4844444-2-24-24-2-2-2-2-24-2-21-4-2-211-2-2-2-21-4-41111-422-1-12222-1-1-1-140000000000220022000-200-2000000000-1-11100000000000000000
χ494444-24-2-24-2-2-24-24-2-21-24-21-2-2-21-21-2001111-24-2-2-2-2-211111104040-2-2000000-2-20000-20-200011001100000000000000000000000
χ504444-24-2-24-2-2-24-24-2-21-24-21-2-2-21-21-2001111-24-2-2-2-2-21111110-40-4022000000220000202000-1-100-1-100000000000000000000000
χ514444-24-2-24-2-2-24-24-2-21-2-4-21-2-2-21-21-20011112-422222-1-1-1-1-1-1040-40-2-200000022000020-20001100-1-100000000000000000000000
χ524444-24-2-24-2-2-24-24-2-21-2-4-21-2-2-21-21-20011112-422222-1-1-1-1-1-10-404022000000-2-20000-202000-1-1001100000000000000000000000
χ534444-2-24-2-2-244-24-2-21-2-241-2-2-21-21-2-2001111-2-24-2-211-2-211110040400-2-2-2-200000000000-20-200110011000000000000000000000
χ544444-2-24-2-2-244-24-2-21-2-241-2-2-21-21-2-2001111-2-24-2-211-2-2111100-40-40022220000000000020200-1-100-1-1000000000000000000000
χ554444-2-24-2-2-244-24-2-21-2-2-41-2-2-21-21-2-200111122-422-1-122-1-1-1-10040-400-2-2220000000000020-2001100-1-1000000000000000000000
χ564444-2-24-2-2-244-24-2-21-2-2-41-2-2-21-21-2-200111122-422-1-122-1-1-1-100-4040022-2-200000000000-20200-1-10011000000000000000000000
χ5744-4-44444-4-44-4-4-44-444404-4-4-4-44-4-440044-4-40000000000000000000000000000000000000000000000000000000000000000000
χ5844-4-444-24-4-4-22-424-44-2-204222-4-2-42-200-2-2220000000000000000000000000023−230000000000000023−2300000000000000000000000
χ5944-4-444-24-4-4-22-424-44-2-204222-4-2-42-200-2-22200000000000000000000000000−232300000000000000−232300000000000000000000000
χ6044-4-44-2442-44-42-4-2-4-24-20-2-422242-4-200-2-22200000000000000000000000000000000000000000000000000000000023−2300000000
χ6144-4-44-2442-44-42-4-2-4-24-20-2-422242-4-200-2-222000000000000000000000000000000000000000000000000000000000−232300000000
χ6244-4-4-244-2-424-4-4-442-2-240-22-4-42-222400-2-222000000000000000000−2i32i3000000000000000000−2i32i3000000000000000000000000000
χ6344-4-4-244-2-424-4-4-442-2-240-22-4-42-222400-2-2220000000000000000002i3−2i30000000000000000002i3−2i3000000000000000000000000000
χ6444-4-4-24-2-2-42-22-4242-21-20-2-122212-1-20011-1-100000003i−3i3i3i−3i−3i00000−2i32i300000023−230000000000i3−i300−3300000000000000000000000
χ6544-4-4-24-2-2-42-22-4242-21-20-2-122212-1-20011-1-100000003i−3i3i3i−3i−3i000002i3−2i3000000−23230000000000−i3i3003−300000000000000000000000
χ6644-4-4-24-2-2-42-22-4242-21-20-2-122212-1-20011-1-10000000−3i3i−3i−3i3i3i00000−2i32i3000000−23230000000000i3−i3003−300000000000000000000000
χ6744-4-4-24-2-2-42-22-4242-21-20-2-122212-1-20011-1-10000000−3i3i−3i−3i3i3i000002i3−2i300000023−230000000000−i3i300−3300000000000000000000000
χ684-44-4444-44-4-44-4-4-444440-444-44-4-4-4-4004-44-40000000000000000000000000000000000000000000000000000000000000000000
χ694-44-444-2-44-42-2-42-444-2-20-4-2-2242-42200-22-220000000000000000000000000000000000000000000000000000000−2i32i30000000000
χ704-44-444-2-44-42-2-42-444-2-20-4-2-2242-42200-22-2200000000000000000000000000000000000000000000000000000002i3−2i30000000000
χ714-44-44-24-4-2-4-442-424-24-2024-22-2-42-4200-22-2200000000000000000000−2i32i3000000000000000000−2i32i30000000000000000000000000
χ724-44-44-24-4-2-4-442-424-24-2024-22-2-42-4200-22-22000000000000000000002i3−2i30000000000000000002i3−2i30000000000000000000000000
χ734-44-4-244242-44-4-4-4-2-2-2402-24-4-2222-400-22-22000000000000000000000023−230000000000000000000023−23000000000000000000000
χ744-44-4-244242-44-4-4-4-2-2-2402-24-4-2222-400-22-220000000000000000000000−232300000000000000000000−2323000000000000000000000
χ754-44-4-2-242-22-442-42-21-2-20-1-2-2212-122001-11-1000003i−3i003i−3i3i−3i0000000−2i32i323−230000000000000000i3−i300−33000000000000000000000
χ764-44-4-2-242-22-442-42-21-2-20-1-2-2212-122001-11-1000003i−3i003i−3i3i−3i00000002i3−2i3−23230000000000000000−i3i3003−3000000000000000000000
χ774-44-4-2-242-22-442-42-21-2-20-1-2-2212-122001-11-100000−3i3i00−3i3i−3i3i0000000−2i32i3−23230000000000000000i3−i3003−3000000000000000000000
χ784-44-4-2-242-22-442-42-21-2-20-1-2-2212-122001-11-100000−3i3i00−3i3i−3i3i00000002i3−2i323−230000000000000000−i3i300−33000000000000000000000
χ794-4-4444-2-4-44224-2-4-44-2-20-422-2-424-224i−4i-222-2000000000000000000000000−2i2i004i−4i0000000000000000−2i2i0000000000000000000
χ804-4-4444-2-4-44224-2-4-44-2-20-422-2-424-22−4i4i-222-20000000000000000000000002i−2i00−4i4i00000000000000002i−2i0000000000000000000
χ814-4-444-24-424-4-4-242-4-24-202-42-22-4-2424i−4i-222-20000000000000000000000004i−4i00−2i2i0000000000000000−2i2i0000000000000000000
χ824-4-444-24-424-4-4-242-4-24-202-42-22-4-242−4i4i-222-2000000000000000000000000−4i4i002i−2i00000000000000002i−2i0000000000000000000
χ834-4-444-2-2-42422-2-22-4-2-21022-1122-2-2-14i−4i1-1-110003-300003-3-3300000000000−2i2i00−2i2i0000000000000000i−i3i−3i00000000000000000
χ844-4-444-2-2-42422-2-22-4-2-21022-1122-2-2-14i−4i1-1-11000-330000-333-300000000000−2i2i00−2i2i0000000000000000i−i−3i3i00000000000000000
χ854-4-444-2-2-42422-2-22-4-2-21022-1122-2-2-1−4i4i1-1-110003-300003-3-33000000000002i−2i002i−2i0000000000000000−ii−3i3i00000000000000000
χ864-4-444-2-2-42422-2-22-4-2-21022-1122-2-2-1−4i4i1-1-11000-330000-333-3000000000002i−2i002i−2i0000000000000000−ii3i−3i00000000000000000
χ874-4-44-2442-4-2-4-444-42-2-24022-4422-2-2-400-222-20000000000000000000000000000004i−4i000000000000000000000000000−2i2i000000
χ884-4-44-2442-4-2-4-444-42-2-24022-4422-2-2-400-222-2000000000000000000000000000000−4i4i0000000000000000000000000002i−2i000000
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
χ9188-8-88-4-484-8-4444-4-8-4-420-44-2-24-44420022-2-20000000000000000000000000000000000000000000000000000000000000000000
χ9288-8-8-4-48-4448-84-8-442-4-402444-2-4-24-40022-2-20000000000000000000000000000000000000000000000000000000000000000000
χ9388-8-8-4-4-4-444-4444-4422202-2-2-2-22-2-2200-1-11100000006i−6i−3i−3i3i3i000000000000000000000000000000000000000000000000000000
χ9488-8-8-4-4-4-444-4444-4422202-2-2-2-22-2-2200-1-1110000000−6i6i3i3i−3i−3i000000000000000000000000000000000000000000000000000000
χ958-88-88-4-4-8-4-84-44448-4-4204-42-2-4444-2002-22-20000000000000000000000000000000000000000000000000000000000000000000
χ968-88-8-48-44844-4-84-8-4-42-4042-44-4-24-24002-22-20000000000000000000000000000000000000000000000000000000000000000000
χ978-88-8-4-4-44-444-4444-42220-222-22-2-2-2-200-11-11000006i−6i00−3i3i−3i3i000000000000000000000000000000000000000000000000000000
χ988-88-8-4-4-44-444-4444-42220-222-22-2-2-2-200-11-1100000−6i6i003i−3i3i−3i000000000000000000000000000000000000000000000000000000
χ998-8-88-48-44-8-4448-4-84-42-404-24-44-2-424002-2-220000000000000000000000000000000000000000000000000000000000000000000
χ1008-8-88-4-4844-4-8-8-48442-4-40-244-4-242-44002-2-220000000000000000000000000000000000000000000000000000000000000000000
χ1018-8-88-4-4-444-444-4-4442220-2-2-22-2-222-200-111-10006-60000-333-3000000000000000000000000000000000000000000000000000000
χ1028-8-88-4-4-444-444-4-4442220-2-2-22-2-222-200-111-1000-6600003-3-33000000000000000000000000000000000000000000000000000000

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