Finite Group Databasebeta

← Group #13169165

Character table — Group #13169165

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size1111222222222222444444444444466888888888888888881212121212121212121212121212121212181824242424242424242424242424242424242436363636363636363636365454727272108
order12223336666666663334666666666443666121212121212121212121212124444412121212121212121212121244121212121212121212121212121212121212222446666121244612124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-11-1-111-1-1111111-1-11-1111-111-1-111-1-111111-1-1-1111-1-1-1-1-1-1-11-1-1
χ3111111111111111111111111111111111111111111111111-1-111111111111-1-1-1-1-1-111-11-1111111111-1-1-1-1-111-1-1-1-111-1-1-1-11-1-1-1
χ4111111111111111111111111111111111111111111111111-1-1-1-11-1-111-1-111-1-1-1-1111-1-11-1-111-1-111-1-1-1-1-1-1-1-1-11-1-1-1-1-11111-1-111
χ511111111111111111111111111111-1-1111111111111111111111-111-1-111-1-1111111-111-111-1-111-1-1111111-1-1-11-1-1-1-1-111-1-1-1-11-1
χ611111111111111111111111111111-1-11111111111111111111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-11-1-1-1-1-1-1-1-1-11111-111-1-1-1-111-1-1111-1-11
χ711111111111111111111111111111-1-111111111111111111-1-111-111-1-111-1-1-1-1-1-1-1-1-11-1-1-11-1-111-1-111-1-1-1-11-1-1-1111-1-1-1-111-11-11
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
χ91111111111111111111-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-1-1-111111111-1-111-1-1-1-111-1-1-1-1111111-1-111-1-1-111111111-1-1-1-1
χ101111111111111111111-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-11111-1-11111-1-1-1-1-11-1-11-1-1-11111-1-111-1-11-111-111-1-1-1-1-1-11-111
χ111111111111111111111-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-111-1-1-1-11-1-11-1-1-1-11111-1-111-11-111-1-111-1-1-1-1-1111
χ121111111111111111111-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-11111-1-111-1-11111-111-1-1-1-1-11111-1-1-1-111-1-11-11-1-1-1-1111111-1-1
χ131111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-11-1-1-1-111-1-111-1-1111-1-111111-1-1-1-11111-1-1-1-11-11-1-1-1-111-1-111-11
χ141111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11111-1-1-1-1-1-111-1-1-1-111-111-11111-1-1-1-111-1-1-11-111-1-111-1-111-111-1
χ151111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11-1-1-1-111-1-1-1-111-1-11-111-1111-1-1-1-111-1-1111-111-111-1-1-1-1111-11-1
χ161111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-11111-1-1-1111111-1-1-1-1-11
χ17222222-122-1-1-122222-1-1222-1-1-1-1-1-1222-1-1-1-1-122-1-1-1-122-1-1-1-10022222-1-1-1-122000000-1-10202-1-1-1-1-1-1-1-100000220000-1-10000-1000
χ18222222-122-1-1-122222-1-1222-1-1-1-1-1-1222-1-1-1-1-122-1-1-1-122-1-1-1-100-2-22-2-2-1-11122000000-11020-2-1-111-1-11100000-2-200001100001000
χ19222222-122-1-1-122222-1-1222-1-1-1-1-1-12-2-2-1-1-1-1-122-1-1-1-122-1-1-1-10022-22211-1-1-2-20000001-10-20211-1-111-1-100000-2-200001100001000
χ20222222-122-1-1-122222-1-1222-1-1-1-1-1-12-2-2-1-1-1-1-122-1-1-1-122-1-1-1-100-2-2-2-2-21111-2-2000000110-20-21111111100000220000-1-10000-1000
χ21222222-122-1-1-122222-1-1-222-1-1-1-1-1-1222-1-1-1-11-2-21111-2-21111002-2-2-2-2-1-1-1-122000000110-2021111-1-1-1-1000002-20000-1-100001000
χ22222222-122-1-1-122222-1-1-222-1-1-1-1-1-1222-1-1-1-11-2-21111-2-2111100-22-222-1-111220000001-10-20-211-1-1-1-11100000-220000110000-1000
χ23222222-122-1-1-122222-1-1-222-1-1-1-1-1-12-2-2-1-1-1-11-2-21111-2-21111002-22-2-211-1-1-2-2000000-110202-1-11111-1-100000-220000110000-1000
χ24222222-122-1-1-122222-1-1-222-1-1-1-1-1-12-2-2-1-1-1-11-2-21111-2-2111100-222221111-2-2000000-1-1020-2-1-1-1-11111000002-20000-1-100001000
χ2522222-12-122222-1-12-12-12-1-12-12-12-1-122-1-1-1-12-1222-1-1-1-1-1-1-1-122002002200-1-1-1-1220020-1-120-1-100-1-100-1-1-1-120002-1-10000000-100
χ2622222-12-122222-1-12-12-12-1-12-12-12-1-122-1-1-1-12-1222-1-1-1-1-1-1-1-1-2-2002002200-1-111-2-200201-1-20-1-100-1-1001111-2000-2110000000100
χ2722222-12-122222-1-12-12-12-1-12-12-12-1-1-2-2-1-1-1-12-1222-1-1-1-1-1-1-1-12200-200-2-20011-1-12200-20-112011001100-1-1-1-1-2000-2110000000100
χ2822222-12-122222-1-12-12-12-1-12-12-12-1-1-2-2-1-1-1-12-1222-1-1-1-1-1-1-1-1-2-200-200-2-2001111-2-200-2011-2011001100111120002-1-10000000-100
χ2922222-12-122222-1-12-12-1-2-1-12-12-12-1-122-1-1-1-1-21-2-2-2111111112-200-2002200-1-1-1-1-2-200-2011201100-1-100-1-1112000-2-1-10000000100
χ3022222-12-122222-1-12-12-1-2-1-12-12-12-1-122-1-1-1-1-21-2-2-211111111-2200-2002200-1-1112200-20-11-201100-1-10011-1-1-20002110000000-100
χ3122222-12-122222-1-12-12-1-2-1-12-12-12-1-1-2-2-1-1-1-1-21-2-2-2111111112-200200-2-20011-1-1-2-200201-120-1-1001100-1-111-20002110000000-100
χ3222222-12-122222-1-12-12-1-2-1-12-12-12-1-1-2-2-1-1-1-1-21-2-2-211111111-2200200-2-2001111220020-1-1-20-1-100110011-1-12000-2-1-10000000100
χ332222-1222-1222-122-1-1-122-1-1-12-12-12-100-1-1-1-122-1-1-122-1-1-1-1-1-122220-1-100220022-1-1220220-1-100-1-100-1-1-1-1-1-1000200000-1-10000-10
χ342222-1222-1222-122-1-1-122-1-1-12-12-12-100-1-1-1-122-1-1-122-1-1-1-1-1-122-2-201100-2-20022-1-1-2-20-220-1100110011-1-1-1-1000-20000011000010
χ352222-1222-1222-122-1-1-122-1-1-12-12-12-100-1-1-1-122-1-1-122-1-1-1-1-1-1-2-2220-1-1002200-2-211-2-202-201-100-1-100-1-11111000-20000011000010
χ362222-1222-1222-122-1-1-122-1-1-12-12-12-100-1-1-1-122-1-1-122-1-1-1-1-1-1-2-2-2-201100-2-200-2-211220-2-2011001100111111000200000-1-10000-10
χ372222-1222-1222-122-1-1-12-2-1-1-12-12-12-100-1-1-1-1-2-2111-2-21111112-22-20110022002211220-2-20-1-1001100-1-1-1-111000-200000-1-1000010
χ382222-1222-1222-122-1-1-12-2-1-1-12-12-12-100-1-1-1-1-2-2111-2-21111112-2-220-1-100-2-2002211-2-202-20-1100-1-10011-1-111000200000110000-10
χ392222-1222-1222-122-1-1-12-2-1-1-12-12-12-100-1-1-1-1-2-2111-2-2111111-222-2011002200-2-2-1-1-2-20-2201-1001100-1-111-1-1000200000110000-10
χ402222-1222-1222-122-1-1-12-2-1-1-12-12-12-100-1-1-1-1-2-2111-2-2111111-22-220-1-100-2-200-2-2-1-12202201100-1-1001111-1-1000-200000-1-1000010
χ412-2-22222-2-22-2-22-22-222202-22-2-22-2-2-22i−2i22-2-2000000000000000000002i−2i002i−2i00002-200000000002i−2i0000000000000002-22i−2i0000
χ422-2-22222-2-22-2-22-22-222202-22-2-22-2-2-22i−2i22-2-2000000000000000000002i−2i002i−2i0000-2200000000002i−2i000000000000000-22−2i2i0000
χ432-2-22222-2-22-2-22-22-222202-22-2-22-2-2-2−2i2i22-2-200000000000000000000−2i2i00−2i2i00002-20000000000−2i2i0000000000000002-2−2i2i0000
χ442-2-22222-2-22-2-22-22-222202-22-2-22-2-2-2−2i2i22-2-200000000000000000000−2i2i00−2i2i0000-220000000000−2i2i000000000000000-222i−2i0000
χ4544444-2-2-24-2-2-24-2-24-2-214-2-2-21-21-21-2441111-2-24-2-211-2-211110000400-2-200-2-2000000-200-20011001100000000000000000000000
χ4644444-2-2-24-2-2-24-2-24-2-214-2-2-21-21-21-2-4-41111-2-24-2-211-2-211110000-400220022000000200200-1-100-1-100000000000000000000000
χ4744444-2-2-24-2-2-24-2-24-2-21-4-2-2-21-21-21-244111122-422-1-122-1-1-1-10000-400-2-200-2-2000000200200-1-1001100000000000000000000000
χ4844444-2-2-24-2-2-24-2-24-2-21-4-2-2-21-21-21-2-4-4111122-422-1-122-1-1-1-10000400220022000000-200-2001100-1-100000000000000000000000
χ494444-24-24-2-2-2-2-244-2-21-24-2-21-21-21-2-2001111-24-211-2-2-2-2111100440-2-200-2-2000000000-2000-200110011000000000000000000000
χ504444-24-24-2-2-2-2-244-2-21-24-2-21-21-21-2-2001111-24-211-2-2-2-2111100-4-402200220000000002000200-1-100-1-1000000000000000000000
χ514444-24-24-2-2-2-2-244-2-21-2-4-2-21-21-21-2-20011112-42-1-12222-1-1-1-1004-402200-2-20000000002000-200-1-10011000000000000000000000
χ524444-24-24-2-2-2-2-244-2-21-2-4-2-21-21-21-2-20011112-42-1-12222-1-1-1-100-440-2-20022000000000-20002001100-1-1000000000000000000000
χ534444-2-24-2-2444-2-2-2-21-2-2411-2-2-2-2-2-210011114-2-2-2-2-2-21111114400000000000-2-2-2-20000-20-2000000000111100000000000000000
χ544444-2-24-2-2444-2-2-2-21-2-2411-2-2-2-2-2-210011114-2-2-2-2-2-2111111-4-40000000000022220000202000000000-1-1-1-100000000000000000
χ554444-2-24-2-2444-2-2-2-21-2-2-411-2-2-2-2-2-21001111-4222222-1-1-1-1-1-14-400000000000-2-222000020-200000000011-1-100000000000000000
χ564444-2-24-2-2444-2-2-2-21-2-2-411-2-2-2-2-2-21001111-4222222-1-1-1-1-1-1-440000000000022-2-20000-202000000000-1-11100000000000000000
χ5744-4-4444-4-4-4-44-44-444440-4-4-4-4-4-4444004-4-440000000000000000000000000000000000000000000000000000000000000000000
χ5844-4-444-2-4-422-2-44-444-2-20-4-42222-2-2400-222-2000000000000000000000000000000000000000000000000000000000−2i32i300000000
χ5944-4-444-2-4-422-2-44-444-2-20-4-42222-2-2400-222-20000000000000000000000000000000000000000000000000000000002i3−2i300000000
χ6044-4-44-242-4-4-44-4-224-24-2022-42-424-2-200-222-200000000000000000000000000−2i32i3000000000000000000−2i32i30000000000000000000
χ6144-4-44-242-4-4-44-4-224-24-2022-42-424-2-200-222-2000000000000000000000000002i3−2i30000000000000000002i3−2i30000000000000000000
χ6244-4-4-244-42-4-4424-4-2-2-240222-42-4-24-200-222-20000000000000000000000000000−2i32i3000000000000000000−2i32i300000000000000000
χ6344-4-4-244-42-4-4424-4-2-2-240222-42-4-24-200-222-200000000000000000000000000002i3−2i30000000000000000002i3−2i300000000000000000
χ6444-4-4-2-2422-4-442-22-21-2-20-1-12222-2-21001-1-1100000003-333-3-30000000000000−2i32i3−2i32i30000000000000000i3−i3i3−i300000000000000000
χ6544-4-4-2-2422-4-442-22-21-2-20-1-12222-2-21001-1-1100000003-333-3-300000000000002i3−2i32i3−2i30000000000000000−i3i3−i3i300000000000000000
χ6644-4-4-2-2422-4-442-22-21-2-20-1-12222-2-21001-1-110000000-33-3-3330000000000000−2i32i32i3−2i30000000000000000i3−i3−i3i300000000000000000
χ6744-4-4-2-2422-4-442-22-21-2-20-1-12222-2-21001-1-110000000-33-3-33300000000000002i3−2i3−2i32i30000000000000000−i3i3i3−i300000000000000000
χ684-44-444444-44-4-4-4-4-44440-44-444-4-4-4-4004-44-40000000000000000000000000000000000000000000000000000000000000000000
χ694-44-444-2442-22-4-4-4-44-2-20-442-2-2222-400-22-22000000000000000000000023−230000000000000000000023−23000000000000000000000
χ704-44-444-2442-22-4-4-4-44-2-20-442-2-2222-400-22-220000000000000000000000−232300000000000000000000−2323000000000000000000000
χ714-44-44-24-24-44-4-422-4-24-202-2-4-242-42200-22-220000000000000000000000000000000000000000000000000000000−2i32i30000000000
χ724-44-44-24-24-44-4-422-4-24-202-2-4-242-42200-22-2200000000000000000000000000000000000000000000000000000002i3−2i30000000000
χ734-44-4-2444-2-44-42-4-42-2-2402-224-2-42-4200-22-22000000000000000000−2i32i300000000000000000000−2i32i30000000000000000000000000
χ744-44-4-2444-2-44-42-4-42-2-2402-224-2-42-4200-22-220000000000000000002i3−2i3000000000000000000002i3−2i30000000000000000000000000
χ754-44-4-24-24-22-222-4-42-21-202-2-1-212-122001-11-10003i−3i00003i−3i3i−3i00000−2i32i30023−230000000000000000i3−i300−33000000000000000000000
χ764-44-4-24-24-22-222-4-42-21-202-2-1-212-122001-11-10003i−3i00003i−3i3i−3i000002i3−2i300−23230000000000000000−i3i3003−3000000000000000000000
χ774-44-4-24-24-22-222-4-42-21-202-2-1-212-122001-11-1000−3i3i0000−3i3i−3i3i00000−2i32i300−23230000000000000000i3−i3003−3000000000000000000000
χ784-44-4-24-24-22-222-4-42-21-202-2-1-212-122001-11-1000−3i3i0000−3i3i−3i3i000002i3−2i30023−230000000000000000−i3i300−33000000000000000000000
χ794-4-4444-2-4-4-2224-44-44-2-204-4-222-222-44i−4i-2-22200000000000000000000−2i2i004i−4i0000000000000000−2i2i00000000000000000000000
χ804-4-4444-2-4-4-2224-44-44-2-204-4-222-222-4−4i4i-2-222000000000000000000002i−2i00−4i4i00000000000000002i−2i00000000000000000000000
χ814-4-444-242-44-4-442-2-4-24-20-2242-4-2-4224i−4i-2-222000000000000000000004i−4i00−2i2i0000000000000000−2i2i00000000000000000000000
χ824-4-444-242-44-4-442-2-4-24-20-2242-4-2-422−4i4i-2-22200000000000000000000−4i4i002i−2i00000000000000002i−2i00000000000000000000000
χ834-4-444-2-22-4-22242-2-4-2-210-22-2-1212-124i−4i11-1-1000003i−3i003i−3i−3i3i0000000−2i2i00−2i2i0000000000003-300i−i00000000000000000000000
χ844-4-444-2-22-4-22242-2-4-2-210-22-2-1212-124i−4i11-1-100000−3i3i00−3i3i3i−3i0000000−2i2i00−2i2i000000000000-3300i−i00000000000000000000000
χ854-4-444-2-22-4-22242-2-4-2-210-22-2-1212-12−4i4i11-1-1000003i−3i003i−3i−3i3i00000002i−2i002i−2i000000000000-3300−ii00000000000000000000000
χ864-4-444-2-22-4-22242-2-4-2-210-22-2-1212-12−4i4i11-1-100000−3i3i00−3i3i3i−3i00000002i−2i002i−2i0000000000003-300−ii00000000000000000000000
χ874-4-44-244-424-4-4-2-442-2-240-22-2-4242-4200-2-2220000000000000000000000000000004-4000000000000000000000000000-22000000
χ884-4-44-244-424-4-4-2-442-2-240-22-2-4242-4200-2-222000000000000000000000000000000-440000000000000000000000000002-2000000
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
χ9188-8-88-4-44-844-4-8-448-4-420444-24-2-42-4002-2-220000000000000000000000000000000000000000000000000000000000000000000
χ9288-8-8-48-4-8444-448-8-4-42-4044-24-242-4-4002-2-220000000000000000000000000000000000000000000000000000000000000000000
χ9388-8-8-4-4-44444-44-44-42220-2-2-2-2-2-222200-111-100000006-6-3-333000000000000000000000000000000000000000000000000000000
χ9488-8-8-4-4-44444-44-44-42220-2-2-2-2-2-222200-111-10000000-6633-3-3000000000000000000000000000000000000000000000000000000
χ958-88-88-4-4-484-44-844-8-4-4204-442-4-24-24002-22-20000000000000000000000000000000000000000000000000000000000000000000
χ968-88-8-4-48-4-4-88-844442-4-40-224-4-4444-2002-22-20000000000000000000000000000000000000000000000000000000000000000000
χ978-88-8-4-4-4-4-44-4444442220-22-222-2-2-2-200-11-110006i−6i0000−3i3i−3i3i000000000000000000000000000000000000000000000000000000
χ988-88-8-4-4-4-4-44-4444442220-22-222-2-2-2-200-11-11000−6i6i00003i−3i3i−3i000000000000000000000000000000000000000000000000000000
χ998-8-88-48-4-84-444-4-884-42-40-4424-2-4-2440022-2-20000000000000000000000000000000000000000000000000000000000000000000
χ1008-8-88-4-48448-8-8-44-442-4-402-2-444-444-20022-2-20000000000000000000000000000000000000000000000000000000000000000000
χ1018-8-88-4-4-444-444-44-4422202-22-2-22-2-2-200-1-111000006i−6i00−3i3i3i−3i000000000000000000000000000000000000000000000000000000
χ1028-8-88-4-4-444-444-44-4422202-22-2-22-2-2-200-1-11100000−6i6i003i−3i−3i3i000000000000000000000000000000000000000000000000000000

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