Finite Group Databasebeta

← Group #13168518

Character table — Group #13168518

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size1111222222222222444444444444466888888888888888881212121212121212121212121212121212181824242424242424242424242424242424242436363636363636363636365454727272108
order1222333666666666333466666666644366612121212121212121212121212224446666121212121212121244666666121212121212121212121212224441212121212124466122
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-11-1111111-1-111-1-1-1-11111111-11-111-1-111-1-11-11-1-111-1-1-1-1-1-11-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1111-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-111-1-1-1-111-1-1-1-11-1
χ4111111111111111111111111111111111111111111111111-1-1-11-1-1-1-1-111-1-111-1-111-1-1-1-1-1-11-11-111-1-111-1-1-11-1-1-1-1-111-1-111-11-11
χ511111111111111111111111111111-1-111111111111111111111-111111-1-111-1-11111111111-11-11-1-111-1-111-11-1-1-1-1-111-1-1-1-1-11-1-1
χ611111111111111111111111111111-1-11111111111111111111-1-1-11111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111
χ711111111111111111111111111111-1-111111111111111111-1-11-11-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-11-11-1-111-1-1111-11-1-111-1-1-1-1111-1-11
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
χ91111111111111111111-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1-111-1-111-1-11111111-111-1-1-1-1-111111-1-1-1-11-1-11-1-1-111-1-1111-11-1
χ101111111111111111111-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1111-1-1111111-1-1-1-11-111-1-1-11-1-111-1-1-1-11111-1-11-1-1-1-111-1-111-11
χ111111111111111111111-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-11111-1-1-11-1-111-1-1-111111-1-1-1-1-1111-111-1-1-1-1-1-1-1111
χ121111111111111111111-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-111111111-1-111-11-1-111-11-1-111-1-1-1-111-1-11-1111111111-1-1-1-1
χ131111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-111-111-1-1-1-1-1-1-1-111111-111-1-11-111-1-11111-1-1-1-11-11111111-1-1-1-1-11
χ141111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11111-1-1-1-111-1-1-1-1-1-11-111-1-1111-1-1-1-1-11111-1111-111-1-1-1-111-111-1
χ151111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-111-1-1-1-1-1-111-1-1-11-1-1111-111-1-11111-1-111-1-11-1-1-1-1111111-1-1
χ161111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-111-1-111-1-1-1-111-11-1-111111-1-1-1-1-111111-1-11-1-1-111-1-1-1-11-111
χ17222222-12-122-122-122-1-122-1-1-1-12-12-100-1-1-1-12-12-1-122-1-1-1-1-1-122202-1-122002200-1-1222-1-1-1-1-10-10200-1-100-1-10200000-1-100000-100
χ18222222-12-122-122-122-1-122-1-1-1-12-12-100-1-1-1-12-12-1-122-1-1-1-1-1-122-20-2-1-12200-2-20011-2-22-1-1-1-1-1010-2001100110-2000001100000100
χ19222222-12-122-122-122-1-122-1-1-1-12-12-100-1-1-1-12-12-1-122-1-1-1-1-1-1-2-220211-2-2002200-1-1-2-2-2111110-10200-1-100-1-10-2000001100000100
χ20222222-12-122-122-122-1-122-1-1-1-12-12-100-1-1-1-12-12-1-122-1-1-1-1-1-1-2-2-20-211-2-200-2-2001122-211111010-2001100110200000-1-100000-100
χ21222222-12-122-122-122-1-1-22-1-1-1-12-12-100-1-1-1-1-21-211-2-21111112-220-2-1-1-2-200-2-200-1-12221-1-111010200-1-100110-200000-1-100000100
χ22222222-12-122-122-122-1-1-22-1-1-1-12-12-100-1-1-1-1-21-211-2-21111112-2-202-1-1-2-200220011-2-221-1-1110-10-2001100-1-102000001100000-100
χ23222222-12-122-122-122-1-1-22-1-1-1-12-12-100-1-1-1-1-21-211-2-2111111-2220-2112200-2-200-1-1-2-2-2-111-1-1010200-1-1001102000001100000-100
χ24222222-12-122-122-122-1-1-22-1-1-1-12-12-100-1-1-1-1-21-211-2-2111111-22-20211220022001122-2-111-1-10-10-2001100-1-10-200000-1-100000100
χ2522222-12-122-122-122-12-12-12-1-1-1-12-1222-1-1-1-1-122-1-1-1-122-1-1-1-12202022-1-12200-1-10000-12-1-1-1-1-1020-1-100-1-10020200-1-1000000-1000
χ2622222-12-122-122-122-12-12-12-1-1-1-12-1222-1-1-1-1-122-1-1-1-122-1-1-1-1-2-2020-2-2112200-1-100001-21111-1020-1-100-1-100-20-200110000001000
χ2722222-12-122-122-122-12-12-12-1-1-1-12-12-2-2-1-1-1-1-122-1-1-1-122-1-1-1-1220-2022-1-1-2-200110000-12-1-1-1-110-2011001100-20-200110000001000
χ2822222-12-122-122-122-12-12-12-1-1-1-12-12-2-2-1-1-1-1-122-1-1-1-122-1-1-1-1-2-20-20-2-211-2-2001100001-2111110-201100110020200-1-1000000-1000
χ2922222-12-122-122-122-12-1-2-12-1-1-1-12-1222-1-1-1-11-2-21111-2-211112-20-2022112200-1-10000-1-2-1-11110-20-1-100110020-20011000000-1000
χ3022222-12-122-122-122-12-1-2-12-1-1-1-12-1222-1-1-1-11-2-21111-2-21111-220-20-2-2-1-12200-1-100001211-1-110-20-1-1001100-20200-1-10000001000
χ3122222-12-122-122-122-12-1-2-12-1-1-1-12-12-2-2-1-1-1-11-2-21111-2-211112-20202211-2-200110000-1-2-1-111-10201100-1-100-20200-1-10000001000
χ3222222-12-122-122-122-12-1-2-12-1-1-1-12-12-2-2-1-1-1-11-2-21111-2-21111-22020-2-2-1-1-2-2001100001211-1-1-10201100-1-10020-20011000000-1000
χ332222-12222-122-122-1-1-122-1-1222-1-1-1-122-1-1-1-122-122-1-1-1-1-1-1-1-1002220000-1-1-1-122220000000022-1-1-1-1-1-1-1-1-1-1000220000-1-10000-10
χ342222-12222-122-122-1-1-122-1-1222-1-1-1-122-1-1-1-122-122-1-1-1-1-1-1-1-100-22-20000-1-11122-2-2000000002-2-11-1-111-1-111000-2-2000011000010
χ352222-12222-122-122-1-1-122-1-1222-1-1-1-1-2-2-1-1-1-122-122-1-1-1-1-1-1-1-1002-22000011-1-1-2-22200000000-221-111-1-111-1-1000-2-2000011000010
χ362222-12222-122-122-1-1-122-1-1222-1-1-1-1-2-2-1-1-1-122-122-1-1-1-1-1-1-1-100-2-2-200001111-2-2-2-200000000-2-21111111111000220000-1-10000-10
χ372222-12222-122-122-1-1-12-2-1-1222-1-1-1-122-1-1-1-1-2-21-2-211111111002-2-20000-1-111222200000000-2-21-1-1-1-1-111110002-20000110000-10
χ382222-12222-122-122-1-1-12-2-1-1222-1-1-1-122-1-1-1-1-2-21-2-21111111100-2-220000-1-1-1-122-2-200000000-2211-1-11111-1-1000-220000-1-1000010
χ392222-12222-122-122-1-1-12-2-1-1222-1-1-1-1-2-2-1-1-1-1-2-21-2-2111111110022-200001111-2-222000000002-2-1-111-1-1-1-111000-220000-1-1000010
χ402222-12222-122-122-1-1-12-2-1-1222-1-1-1-1-2-2-1-1-1-1-2-21-2-21111111100-222000011-1-1-2-2-2-20000000022-111111-1-1-1-10002-20000110000-10
χ4122-2-2222-222-2-2-22-2-22220-222-2-22-2-2-22-222-2-200000000000000000000002-2002-2002i−2i00000000002-200000000000002i−2i002i−2i0000
χ4222-2-2222-222-2-2-22-2-22220-222-2-22-2-2-22-222-2-200000000000000000000002-2002-200−2i2i00000000002-20000000000000−2i2i00−2i2i0000
χ4322-2-2222-222-2-2-22-2-22220-222-2-22-2-2-2-2222-2-20000000000000000000000-2200-22002i−2i0000000000-2200000000000002i−2i00−2i2i0000
χ4422-2-2222-222-2-2-22-2-22220-222-2-22-2-2-2-2222-2-20000000000000000000000-2200-2200−2i2i0000000000-220000000000000−2i2i002i−2i0000
χ4544444-2-2-2-24-2-24-2-24-2-214-2-2111-2-2-2-2001111-2-2411-2-2-2-2111144000-2-2-2-20000000000-2-2111100000000000000000000000000000
χ4644444-2-2-2-24-2-24-2-24-2-214-2-2111-2-2-2-2001111-2-2411-2-2-2-21111-4-40002222000000000022-1-1-1-100000000000000000000000000000
χ4744444-2-2-2-24-2-24-2-24-2-21-4-2-2111-2-2-2-200111122-4-1-12222-1-1-1-14-4000-2-2220000000000-2211-1-100000000000000000000000000000
χ4844444-2-2-2-24-2-24-2-24-2-21-4-2-2111-2-2-2-200111122-4-1-12222-1-1-1-1-4400022-2-200000000002-2-1-11100000000000000000000000000000
χ494444-24-24-2-24-2-24-2-2-21-24-21-2-2-2-21-210011114-2-2-2-2-2-211111100404000000-2-200-2-2000000000-20-20011001100000000000000000
χ504444-24-24-2-24-2-24-2-2-21-24-21-2-2-2-21-210011114-2-2-2-2-2-211111100-40-400000022002200000000020200-1-100-1-100000000000000000
χ514444-24-24-2-24-2-24-2-2-21-2-4-21-2-2-2-21-21001111-4222222-1-1-1-1-1-10040-40000002200-2-200000000020-2001100-1-100000000000000000
χ524444-24-24-2-24-2-24-2-2-21-2-4-21-2-2-2-21-21001111-4222222-1-1-1-1-1-100-404000000-2-20022000000000-20200-1-1001100000000000000000
χ534444-2-24-24-2-24-2-24-21-2-241-2-2-2-21-21-2441111-24-2-2-211-2-21111000400000-2-200-2-20000000000-20-201100110000000000000000000
χ544444-2-24-24-2-24-2-24-21-2-241-2-2-2-21-21-2-4-41111-24-2-2-211-2-21111000-40000022002200000000002020-1-100-1-10000000000000000000
χ554444-2-24-24-2-24-2-24-21-2-2-41-2-2-2-21-21-24411112-4222-1-122-1-1-1-1000-400000-2-200-2-2000000000020201100-1-10000000000000000000
χ564444-2-24-24-2-24-2-24-21-2-2-41-2-2-2-21-21-2-4-411112-4222-1-122-1-1-1-10004000002200220000000000-20-20-1-100110000000000000000000
χ5744-4-444-2-4-24-42-442-44-2-20-4-2-22242-4200-2-2220000000000000000000000000000004i−4i0000000000000000000000000−2i2i00000000
χ5844-4-444-2-4-24-42-442-44-2-20-4-2-22242-4200-2-222000000000000000000000000000000−4i4i00000000000000000000000002i−2i00000000
χ5944-4-44-242442-4-4-2-4-4-24-2024-222-2-42-44-4-2-22200000000000000000000004-400-2200000000000000-2200000000000000000000000
χ6044-4-44-242442-4-4-2-4-4-24-2024-222-2-42-4-44-2-2220000000000000000000000-44002-2000000000000002-200000000000000000000000
χ6144-4-4-244-44-2-4-424-42-2-2402-24-4-4-22224-4-2-2220000000000000000000000-22004-400000000000000-2200000000000000000000000
χ6244-4-4-244-44-2-4-424-42-2-2402-24-4-4-2222-44-2-22200000000000000000000002-200-44000000000000002-200000000000000000000000
χ6344-4-4-2-2424-22-42-2-421-2-20-1-2-22212-124-411-1-1000003i−3i003i3i−3i−3i000000000-2200-22000000000000001-1003i−3i0000000000000000000
χ6444-4-4-2-2424-22-42-2-421-2-20-1-2-22212-124-411-1-100000−3i3i00−3i−3i3i3i000000000-2200-22000000000000001-100−3i3i0000000000000000000
χ6544-4-4-2-2424-22-42-2-421-2-20-1-2-22212-12-4411-1-1000003i−3i003i3i−3i−3i0000000002-2002-200000000000000-1100−3i3i0000000000000000000
χ6644-4-4-2-2424-22-42-2-421-2-20-1-2-22212-12-4411-1-100000−3i3i00−3i−3i3i3i0000000002-2002-200000000000000-11003i−3i0000000000000000000
χ674-44-44444-4-4-4-4-4-44444404-4-44-4-44-4-4004-44-40000000000000000000000000000000000000000000000000000000000000000000
χ684-44-444-242-4-42-4-4-244-2-20422-22-4-2-4200-22-220000000000000000000000000000−2i32i300000000000000−2i32i3000000000000000000000
χ694-44-444-242-4-42-4-4-244-2-20422-22-4-2-4200-22-2200000000000000000000000000002i3−2i3000000000000002i3−2i3000000000000000000000
χ704-44-44-24-2-4-42-4-4244-24-20-2-42-22242-400-22-22000000000000000000000000000000000000000000000000000000023−230000000000
χ714-44-44-24-2-4-42-4-4244-24-20-2-42-22242-400-22-220000000000000000000000000000000000000000000000000000000−23230000000000
χ724-44-4-2444-42-4-42-44-2-2-240-22-44-42-22200-22-2200000000000000000000000023−23000000000000000000000023−2300000000000000000
χ734-44-4-2444-42-4-42-44-2-2-240-22-44-42-22200-22-22000000000000000000000000−23230000000000000000000000−232300000000000000000
χ744-44-4-24-2422-422-4-2-2-21-20-2-12-22212-1001-11-100000003i−3i3i−3i3i−3i0000000000023−2300−2i32i300000000000000i3−i300−3300000000000000000
χ754-44-4-24-2422-422-4-2-2-21-20-2-12-22212-1001-11-100000003i−3i3i−3i3i−3i00000000000−2323002i3−2i300000000000000−i3i3003−300000000000000000
χ764-44-4-24-2422-422-4-2-2-21-20-2-12-22212-1001-11-10000000−3i3i−3i3i−3i3i0000000000023−23002i3−2i300000000000000−i3i300−3300000000000000000
χ774-44-4-24-2422-422-4-2-2-21-20-2-12-22212-1001-11-10000000−3i3i−3i3i−3i3i00000000000−232300−2i32i300000000000000i3−i3003−300000000000000000
χ784-4-44444-4-4-4444-4-4-44440-4-4-4-44-4-444004-4-440000000000000000000000000000000000000000000000000000000000000000000
χ794-4-4444-2-42-44-24-42-44-2-20-4222-2-424-200-222-2000000000000000000−2i32i300000000000000−2i32i30000000000000000000000000000000
χ804-4-4444-2-42-44-24-42-44-2-20-4222-2-424-200-222-20000000000000000002i3−2i3000000000000002i3−2i30000000000000000000000000000000
χ814-4-444-242-4-4-2442-4-4-24-202-422-22-4-2400-222-200000000000000000000−2i32i300000000000000−2i32i300000000000000000000000000000
χ824-4-444-242-4-4-2442-4-4-24-202-422-22-4-2400-222-2000000000000000000002i3−2i3000000000000002i3−2i300000000000000000000000000000
χ834-4-444-2-222-4-2-2422-4-2-21022-1-1122-2-2001-1-110003-300003-3-3300000−2i32i3−2i32i3000000000000i3−i3i3−i300000000000000000000000000000
χ844-4-444-2-222-4-2-2422-4-2-21022-1-1122-2-2001-1-110003-300003-3-33000002i3−2i32i3−2i3000000000000−i3i3−i3i300000000000000000000000000000
χ854-4-444-2-222-4-2-2422-4-2-21022-1-1122-2-2001-1-11000-330000-333-300000−2i32i32i3−2i3000000000000i3−i3−i3i300000000000000000000000000000
χ864-4-444-2-222-4-2-2422-4-2-21022-1-1122-2-2001-1-11000-330000-333-3000002i3−2i3−2i32i3000000000000−i3i3i3−i300000000000000000000000000000
χ874-4-44-244-4-4244-2-4-42-2-24022-4-4422-2-200-222-20000000000000000000000000000000000000000000000000000000000023−23000000
χ884-4-44-244-4-4244-2-4-42-2-24022-4-4422-2-200-222-200000000000000000000000000000000000000000000000000000000000−2323000000
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
χ9188-8-88-4-44-4844-8-44-8-4-4204-42-2-2-44440022-2-20000000000000000000000000000000000000000000000000000000000000000000
χ9288-8-8-48-4-8-4-4-844844-42-4042-444-4-24-20022-2-20000000000000000000000000000000000000000000000000000000000000000000
χ9388-8-8-4-4-44-4-4444-4442220-222-2-22-2-2-200-1-111000006i−6i00−3i−3i3i3i000000000000000000000000000000000000000000000000000000
χ9488-8-8-4-4-44-4-4444-4442220-222-2-22-2-2-200-1-11100000−6i6i003i3i−3i−3i000000000000000000000000000000000000000000000000000000
χ958-88-88-4-4-44-844-84-48-4-420-44-22-24-444002-22-20000000000000000000000000000000000000000000000000000000000000000000
χ968-88-8-4-48-4-844-8448-42-4-40244-44-2-4-24002-22-20000000000000000000000000000000000000000000000000000000000000000000
χ978-88-8-4-4-4-4444444-4-422202-2-22-2-22-2-200-11-1100000006i−6i−3i3i−3i3i000000000000000000000000000000000000000000000000000000
χ988-88-8-4-4-4-4444444-4-422202-2-22-2-22-2-200-11-110000000−6i6i3i−3i3i−3i000000000000000000000000000000000000000000000000000000
χ998-8-88-48-4-8448-4-4-844-42-404-244-44-2-42002-2-220000000000000000000000000000000000000000000000000000000000000000000
χ1008-8-88-4-484-84-48-44-842-4-40-2444-4-242-4002-2-220000000000000000000000000000000000000000000000000000000000000000000
χ1018-8-88-4-4-4444-4-4-44442220-2-2-2-22-2-22200-111-10006-60000-333-3000000000000000000000000000000000000000000000000000000
χ1028-8-88-4-4-4444-4-4-44442220-2-2-2-22-2-22200-111-1000-6600003-3-33000000000000000000000000000000000000000000000000000000

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