Finite Group Databasebeta

← Group #13168525

Character table — Group #13168525

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size1111222222222222444444444444466888888888888888881212121212121212121212121212121212181824242424242424242424242424242424242436363636363636363636365454727272108
order12223336666666663334666666666443666121212121212121212121212122244466661212121212121212446666661212121212121212121212122444412121212121244612124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-11-1111111-1-111-1-1-1-1111111-111-111-1-111-1-11-1-11-111-1-1-1-1-1-11-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1111-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-111-1-1-1-1-1-111-1-1-1-11-1
χ4111111111111111111111111111111111111111111111111-1-1-11-1-1-1-1-111-1-111-1-111-1-1-1-1-1-1-111-111-1-111-1-1-1-1-1-11-1-111-1-111-11-11
χ511111111111111111111111111111-1-111111111111111111111-111111-1-111-1-111111111111-1-11-1-111-1-111-1-1-1-11-1-111-1-1-1-1-11-1-1
χ611111111111111111111111111111-1-11111111111111111111-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-111
χ711111111111111111111111111111-1-111111111111111111-1-11-11-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-11-1-11-1-111-1-1111-1-11-111-1-1-1-1111-1-11
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
χ91111111111111111111-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111-1-1111111-1-1-1-1-1111-1-11-1-1-11111-1-1-1-111-1-11-1-1-1-111-1-111-11
χ101111111111111111111-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1111-1-111-1-1111111-1111-1-1-1-1-1111-1-1-1-1111-11-1-1-1-111-1-1111-11-1
χ111111111111111111111-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1111-1-1-1111-1-1-11111-1-1-1-1-11-11-111111111-1-1-1-1
χ121111111111111111111-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-11111-1-11111-1-11-1-1-111-1-1-1111-1-1-1-111-1-111111-1-1-1-1-1-1-1111
χ131111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-111-111-1-1-1-111-1-1-1-1-1-1-1111-1-1111-1-1-11111-1-1-1-111111-1-1-1-111-111-1
χ141111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11111-1-1-1-1-1-1-1-11111-1111-1-1-1111-1-1-1-11111-11-11-1111111-1-1-1-1-11
χ151111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-111-1-111-1-1-1-1111-1-1-111111-1-1-11111-1-11-11-1-1-1-111-1-1-1-11-111
χ161111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-111-1-1-1-1-1-111-1-11-1-1-111-1111-1-1-1-1111111-1-11-1-1-1-1111111-1-1
χ17222222-1-1222-12-1222-1-122-1-1-1-12-12-122-1-1-1-1-122-1-122-1-1-1-1-1-12202022-1-12200-1-100002-1-1-1-1-10-120-1-100-1-10020020-1-1000000-1000
χ18222222-1-1222-12-1222-1-122-1-1-1-12-12-122-1-1-1-1-122-1-122-1-1-1-1-1-1-2-2020-2-2112200-1-10000-2111110-120-1-100-1-100-200-20110000001000
χ19222222-1-1222-12-1222-1-122-1-1-1-12-12-1-2-2-1-1-1-1-122-1-122-1-1-1-1-1-1220-2022-1-1-2-2001100002-1-1-1-1-101-2011001100-200-20110000001000
χ20222222-1-1222-12-1222-1-122-1-1-1-12-12-1-2-2-1-1-1-1-122-1-122-1-1-1-1-1-1-2-20-20-2-211-2-200110000-21111101-201100110020020-1-1000000-1000
χ21222222-1-1222-12-1222-1-1-22-1-1-1-12-12-122-1-1-1-11-2-211-2-21111112-20-2022112200-1-10000-2-1-1-11101-20-1-1001100200-2011000000-1000
χ22222222-1-1222-12-1222-1-1-22-1-1-1-12-12-122-1-1-1-11-2-211-2-2111111-220-20-2-2-1-12200-1-100002111-1-101-20-1-1001100-20020-1-10000001000
χ23222222-1-1222-12-1222-1-1-22-1-1-1-12-12-1-2-2-1-1-1-11-2-211-2-21111112-20202211-2-200110000-2-1-1-1110-1201100-1-100-20020-1-10000001000
χ24222222-1-1222-12-1222-1-1-22-1-1-1-12-12-1-2-2-1-1-1-11-2-211-2-2111111-22020-2-2-1-1-2-2001100002111-1-10-1201100-1-100200-2011000000-1000
χ2522222-12222-12-12-12-12-12-12-1-1-1-12-1200-1-1-1-12-12-1-1-1-122-1-1-1-122202-1-122002200-1-122-12-1-1-1-1-100200-1-100-1-10000200-1-100000-100
χ2622222-12222-12-12-12-12-12-12-1-1-1-12-1200-1-1-1-12-12-1-1-1-122-1-1-1-122-20-2-1-12200-2-20011-2-2-12-1-1-1-1100-2001100110000-2001100000100
χ2722222-12222-12-12-12-12-12-12-1-1-1-12-1200-1-1-1-12-12-1-1-1-122-1-1-1-1-2-220211-2-2002200-1-1-2-21-21111-100200-1-100-1-10000-2001100000100
χ2822222-12222-12-12-12-12-12-12-1-1-1-12-1200-1-1-1-12-12-1-1-1-122-1-1-1-1-2-2-20-211-2-200-2-20011221-21111100-2001100110000200-1-100000-100
χ2922222-12222-12-12-12-12-1-2-12-1-1-1-12-1200-1-1-1-1-21-21111-2-211112-220-2-1-1-2-200220011-2-212-1-111-100-200-1-1001100002001100000-100
χ3022222-12222-12-12-12-12-1-2-12-1-1-1-12-1200-1-1-1-1-21-21111-2-211112-2-202-1-1-2-200-2-200-1-12212-1-1111002001100-1-10000-200-1-100000100
χ3122222-12222-12-12-12-12-1-2-12-1-1-1-12-1200-1-1-1-1-21-21111-2-21111-2220-211220022001122-1-211-1-1-100-200-1-100110000-200-1-100000100
χ3222222-12222-12-12-12-12-1-2-12-1-1-1-12-1200-1-1-1-1-21-21111-2-21111-22-202112200-2-200-1-1-2-2-1-211-1-11002001100-1-100002001100000-100
χ332222-1222-1-122222-1-1-122-1-1222-1-1-1-122-1-1-1-122-122-1-1-1-1-1-1-1-1002220000-1-1-1-122220000000022-1-1-1-1-1-1-1-1-1-1022000000-1-10000-10
χ342222-1222-1-122222-1-1-122-1-1222-1-1-1-122-1-1-1-122-122-1-1-1-1-1-1-1-100-22-20000-1-11122-2-200000000-22-11-1-111-1-1110-2-200000011000010
χ352222-1222-1-122222-1-1-122-1-1222-1-1-1-1-2-2-1-1-1-122-122-1-1-1-1-1-1-1-1002-22000011-1-1-2-222000000002-21-111-1-111-1-10-2-200000011000010
χ362222-1222-1-122222-1-1-122-1-1222-1-1-1-1-2-2-1-1-1-122-122-1-1-1-1-1-1-1-100-2-2-200001111-2-2-2-200000000-2-21111111111022000000-1-10000-10
χ372222-1222-1-122222-1-1-12-2-1-1222-1-1-1-122-1-1-1-1-2-21-2-211111111002-2-20000-1-1-1-122-2-2000000002-211-1-1-1-1111102-2000000-1-1000010
χ382222-1222-1-122222-1-1-12-2-1-1222-1-1-1-122-1-1-1-1-2-21-2-21111111100-2-220000-1-111222200000000-2-21-1-1-11111-1-10-22000000110000-10
χ392222-1222-1-122222-1-1-12-2-1-1222-1-1-1-1-2-2-1-1-1-1-2-21-2-2111111110022-2000011-1-1-2-2-2-20000000022-1111-1-1-1-1110-22000000110000-10
χ402222-1222-1-122222-1-1-12-2-1-1222-1-1-1-1-2-2-1-1-1-1-2-21-2-21111111100-22200001111-2-22200000000-22-1-11111-1-1-1-102-2000000-1-1000010
χ412-2-22222-22-2-2-222-2-222202-22-2-2-22-2-22-222-2-200000000000000000000002-2002-2002i−2i00000000002-200000000000002i−2i002i−2i0000
χ422-2-22222-22-2-2-222-2-222202-22-2-2-22-2-22-222-2-200000000000000000000002-2002-200−2i2i00000000002-20000000000000−2i2i00−2i2i0000
χ432-2-22222-22-2-2-222-2-222202-22-2-2-22-2-2-2222-2-20000000000000000000000-2200-22002i−2i0000000000-2200000000000002i−2i00−2i2i0000
χ442-2-22222-22-2-2-222-2-222202-22-2-2-22-2-2-2222-2-20000000000000000000000-2200-2200−2i2i0000000000-220000000000000−2i2i002i−2i0000
χ4544444-2-2-244-2-2-2-2-24-2-214-2-2111-2-2-2-2001111-2-2411-2-2-2-2111144000-2-2-2-20000000000-2-2111100000000000000000000000000000
χ4644444-2-2-244-2-2-2-2-24-2-214-2-2111-2-2-2-2001111-2-2411-2-2-2-21111-4-40002222000000000022-1-1-1-100000000000000000000000000000
χ4744444-2-2-244-2-2-2-2-24-2-21-4-2-2111-2-2-2-200111122-4-1-12222-1-1-1-14-4000-2-22200000000002-211-1-100000000000000000000000000000
χ4844444-2-2-244-2-2-2-2-24-2-21-4-2-2111-2-2-2-200111122-4-1-12222-1-1-1-1-4400022-2-20000000000-22-1-11100000000000000000000000000000
χ494444-24-2-2-2-24-24-24-2-21-24-21-2-2-2-21-21441111-24-2-2-2-2-2111111000400000-2-200-2-200000000000-2-201100110000000000000000000
χ504444-24-2-2-2-24-24-24-2-21-24-21-2-2-2-21-21-4-41111-24-2-2-2-2-2111111000-40000022002200000000000220-1-100-1-10000000000000000000
χ514444-24-2-2-2-24-24-24-2-21-2-4-21-2-2-2-21-214411112-422222-1-1-1-1-1-1000-400000-2-200-2-2000000000002201100-1-10000000000000000000
χ524444-24-2-2-2-24-24-24-2-21-2-4-21-2-2-2-21-21-4-411112-422222-1-1-1-1-1-100040000022002200000000000-2-20-1-100110000000000000000000
χ534444-2-244-2-2-24-24-2-21-2-241-2-2-2-21-21-20011114-2-2-2-211-2-2111100404000000-2-200-2-200000000-200-20011001100000000000000000
χ544444-2-244-2-2-24-24-2-21-2-241-2-2-2-21-21-20011114-2-2-2-211-2-2111100-40-400000022002200000000200200-1-100-1-100000000000000000
χ554444-2-244-2-2-24-24-2-21-2-2-41-2-2-2-21-21-2001111-42222-1-122-1-1-1-10040-4000000-2-2002200000000-2002001100-1-100000000000000000
χ564444-2-244-2-2-24-24-2-21-2-2-41-2-2-2-21-21-2001111-42222-1-122-1-1-1-100-4040000002200-2-200000000200-200-1-1001100000000000000000
χ5744-4-44444-444-4-4-4-4-44440-44-44-44-4-4-4004-44-40000000000000000000000000000000000000000000000000000000000000000000
χ5844-4-444-2-2-4442-42-4-44-2-20-4-22-2242-4200-22-22000000000000000000000000000000000000000000000000000000023−230000000000
χ5944-4-444-2-2-4442-42-4-44-2-20-4-22-2242-4200-22-220000000000000000000000000000000000000000000000000000000−23230000000000
χ6044-4-44-244-44-2-42-42-4-24-20242-22-2-42-400-22-22000000000000000000000000000023−2300000000000000000023−2300000000000000000
χ6144-4-44-244-44-2-42-42-4-24-20242-22-2-42-400-22-220000000000000000000000000000−2323000000000000000000−232300000000000000000
χ6244-4-4-24442-24-4-4-4-42-2-2402-2-44-4-222200-22-22000000000000000000000000−2i32i3000000000000000000−2i32i3000000000000000000000
χ6344-4-4-24442-24-4-4-4-42-2-2402-2-44-4-222200-22-220000000000000000000000002i3−2i30000000000000000002i3−2i3000000000000000000000
χ6444-4-4-2-2442-2-2-42-4221-2-20-1-22-2212-12001-11-1000003i−3i003i3i−3i−3i00000000000−2i32i30023−2300000000000000i3−i300−3300000000000000000
χ6544-4-4-2-2442-2-2-42-4221-2-20-1-22-2212-12001-11-1000003i−3i003i3i−3i−3i000000000002i3−2i300−232300000000000000−i3i3003−300000000000000000
χ6644-4-4-2-2442-2-2-42-4221-2-20-1-22-2212-12001-11-100000−3i3i00−3i−3i3i3i00000000000−2i32i300−232300000000000000i3−i3003−300000000000000000
χ6744-4-4-2-2442-2-2-42-4221-2-20-1-22-2212-12001-11-100000−3i3i00−3i−3i3i3i000000000002i3−2i30023−2300000000000000−i3i300−3300000000000000000
χ684-44-4444-4-4-4-44-4-4444440-4-4-4-44-4-444004-4-440000000000000000000000000000000000000000000000000000000000000000000
χ694-44-444-22-4-4-4-2-42444-2-20-4222-2-424-200-222-200000000000000000000−2i32i300000000000000−2i32i300000000000000000000000000000
χ704-44-444-22-4-4-4-2-42444-2-20-4222-2-424-200-222-2000000000000000000002i3−2i3000000000000002i3−2i300000000000000000000000000000
χ714-44-44-24-4-4-4242-4-24-24-202-422-22-4-2400-222-2000000000000000000−2i32i300000000000000−2i32i30000000000000000000000000000000
χ724-44-44-24-4-4-4242-4-24-24-202-422-22-4-2400-222-20000000000000000002i3−2i3000000000000002i3−2i30000000000000000000000000000000
χ734-44-44-2-22-4-42-222-24-2-21022-1-1122-2-2001-1-110003-300003-33-300000−2i32i3−2i32i3000000000000i3−i3i3−i300000000000000000000000000000
χ744-44-44-2-22-4-42-222-24-2-21022-1-1122-2-2001-1-110003-300003-33-3000002i3−2i32i3−2i3000000000000−i3i3−i3i300000000000000000000000000000
χ754-44-44-2-22-4-42-222-24-2-21022-1-1122-2-2001-1-11000-330000-33-3300000−2i32i32i3−2i3000000000000i3−i3−i3i300000000000000000000000000000
χ764-44-44-2-22-4-42-222-24-2-21022-1-1122-2-2001-1-11000-330000-33-33000002i3−2i3−2i32i3000000000000−i3i3i3−i300000000000000000000000000000
χ774-44-4-244-422-44-4-44-2-2-24022-4-4422-2-200-222-200000000000000000000000000000000000000000000000000000000000−2i32i3000000
χ784-44-4-244-422-44-4-44-2-2-24022-4-4422-2-200-222-2000000000000000000000000000000000000000000000000000000000002i3−2i3000000
χ794-4-4444-224-4-424-2-4-44-2-2042-222-4-2-424-4-2-22200000000000000000000004-400-2200000000000000-2200000000000000000000000
χ804-4-4444-224-4-424-2-4-44-2-2042-222-4-2-42-44-2-2220000000000000000000000-44002-2000000000000002-200000000000000000000000
χ814-4-444-24-44-42-4-242-4-24-20-2-4-222242-400-2-2220000000000000000000000000000004i−4i0000000000000000000000000−2i2i00000000
χ824-4-444-24-44-42-4-242-4-24-20-2-4-222242-400-2-222000000000000000000000000000000−4i4i00000000000000000000000002i−2i00000000
χ834-4-44-244-4-22-4-444-42-2-240-224-4-42-2224-4-2-2220000000000000000000000-22004-400000000000000-2200000000000000000000000
χ844-4-44-244-4-22-4-444-42-2-240-224-4-42-222-44-2-22200000000000000000000002-200-44000000000000002-200000000000000000000000
χ854-4-44-24-22-22-424-2-42-21-20-2-1-222212-14-411-1-100000003i−3i3i−3i−3i3i000000000-2200-22000000000000001-1003i−3i0000000000000000000
χ864-4-44-24-22-22-424-2-42-21-20-2-1-222212-14-411-1-10000000−3i3i−3i3i3i−3i000000000-2200-22000000000000001-100−3i3i0000000000000000000
χ874-4-44-24-22-22-424-2-42-21-20-2-1-222212-1-4411-1-100000003i−3i3i−3i−3i3i0000000002-2002-200000000000000-1100−3i3i0000000000000000000
χ884-4-44-24-22-22-424-2-42-21-20-2-1-222212-1-4411-1-10000000−3i3i−3i3i3i−3i0000000002-2002-200000000000000-11003i−3i0000000000000000000
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
χ9188-8-88-4-4-4-88-44444-8-4-4204-4-22-2-4444002-22-20000000000000000000000000000000000000000000000000000000000000000000
χ9288-8-8-48-4-44-484-84-84-42-40424-44-4-24-2002-22-20000000000000000000000000000000000000000000000000000000000000000000
χ9388-8-8-4-4-4-44-4-4444442220-22-22-22-2-2-200-11-11000006i−6i00−3i−3i3i3i000000000000000000000000000000000000000000000000000000
χ9488-8-8-4-4-4-44-4-4444442220-22-22-22-2-2-200-11-1100000−6i6i003i3i−3i−3i000000000000000000000000000000000000000000000000000000
χ958-88-8-48-4444-8-4-848-4-42-404-244-44-2-42002-2-220000000000000000000000000000000000000000000000000000000000000000000
χ968-88-8-4-48-844484-8-4-42-4-40-2444-4-242-4002-2-220000000000000000000000000000000000000000000000000000000000000000000
χ978-88-8-4-4-44444-444-4-42220-2-2-2-22-2-22200-111-10006-60000-33-33000000000000000000000000000000000000000000000000000000
χ988-88-8-4-4-44444-444-4-42220-2-2-2-22-2-22200-111-1000-6600003-33-3000000000000000000000000000000000000000000000000000000
χ998-8-888-4-448-844-4-44-8-4-420-442-2-24-4440022-2-20000000000000000000000000000000000000000000000000000000000000000000
χ1008-8-88-4-48-8-444-8-48442-4-4024-444-2-4-240022-2-20000000000000000000000000000000000000000000000000000000000000000000
χ1018-8-88-4-4-44-4444-4-44422202-22-2-2-22-2-200-1-11100000006i−6i−3i3i3i−3i000000000000000000000000000000000000000000000000000000
χ1028-8-88-4-4-44-4444-4-44422202-22-2-2-22-2-200-1-1110000000−6i6i3i−3i−3i3i000000000000000000000000000000000000000000000000000000

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