Finite Group Databasebeta

← Group #13168222

Character table — Group #13168222

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size1111222222222222444444444444466888888888888888881212121212121212121212121212121212181824242424242424242424242424242424242436363636363636363636365454727272108
order122233366666666633346666666662236661212121212121212121212121244444666612121212121212124466121212121212121212121212121212122444412121212121244612122
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-11111111-1-1-1-111-1-1111111-1-1111111-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11-1
χ31111111111111111111111111111111111111111111111111-111-11111-1-11111-1-1-1-11111-1-11111-1-1-1-1111111-1-1-1-1-111-1-1-1-11-1-1-1
χ41111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11-1-111-1-1-1-111-11-11
χ511111111111111111111111111111-1-111111111111111111-11111-1-1-1-11111111111-1-1-1-11111-1-111111111-1-11-1-111-1-1-1-1-1-1-11-1-1
χ611111111111111111111111111111-1-111111111111111111-11-1-11-1-1-1-111-1-1-1-111-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-1-1-1-111-1-1111-1-11
χ711111111111111111111111111111-1-111111111111111111-1-111-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-111-1-1-1-11111-1-111
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
χ91111111111111111111-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-11111-1-11-11-1-1-111-1-111-1-11-1-11-111-1-1-1-1111-11-1
χ101111111111111111111-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1111111-1-111-1-1-1-111-1-11-1-11-1-111-1-1-1-111-1111-1-1-111-1-1-1-1-1111
χ111111111111111111111-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111111-1-111-1-111-1-111-1-1-111-1-1-1-1-11111-1-11-11-11-1-1-1-111-1-111-11
χ121111111111111111111-1111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-11-11-1-1-1-111-1-111-11-1-1111111111-1-1-1-1
χ131111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-11111-1-1-1-111-1-1111-11-11111-1-111-1-1-11-1-11111111-1-1-1-1-11
χ141111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-111-11-1-1-1-1-111-1-111-1-1-1-1-1-1111-1-111111-1-1-1-1111-11-11-1-1-1-1111111-1-1
χ151111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-11-1-1-1-1-1-111-1-111-1-1-1-111-111-111-1-11111-1-1-1111-1-1-111-1-111-111-1
χ161111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-1-1-1-1-1-1-1111111-1-111-11-1111-1-111-1-1111-1-11-111-1-1-1-1-1-11-111
χ17222222-12-12-1222-122-1-122-1-1-1-12-12-122-1-1-1-1-122-1-1-1-122-1-1-1-12022022-1-10022-1-10000-1-1-1200-12-1-10000-1-1-1-12200000-1-10000-1000
χ18222222-12-12-1222-122-1-122-1-1-1-12-12-122-1-1-1-1-122-1-1-1-122-1-1-1-120-2-2022-1-100-2-2110000-1-1-12001-2-1-100001111-2-2000001100001000
χ19222222-12-12-1222-122-1-122-1-1-1-12-12-1-2-2-1-1-1-1-122-1-1-1-122-1-1-1-1-20220-2-2110022-1-10000111-200-12110000-1-1-1-1-2-2000001100001000
χ20222222-12-12-1222-122-1-122-1-1-1-12-12-1-2-2-1-1-1-1-122-1-1-1-122-1-1-1-1-20-2-20-2-21100-2-2110000111-2001-211000011112200000-1-10000-1000
χ21222222-12-12-1222-122-1-1-22-1-1-1-12-12-122-1-1-1-11-2-21111-2-21111-202-2022-1-10022110000-1-11-200-1-2110000-1-1112-200000110000-1000
χ22222222-12-12-1222-122-1-1-22-1-1-1-12-12-122-1-1-1-11-2-21111-2-21111-20-22022-1-100-2-2-1-10000-1-11-2001211000011-1-1-2200000-1-100001000
χ23222222-12-12-1222-122-1-1-22-1-1-1-12-12-1-2-2-1-1-1-11-2-21111-2-21111202-20-2-211002211000011-1200-1-2-1-10000-1-111-2200000-1-100001000
χ24222222-12-12-1222-122-1-1-22-1-1-1-12-12-1-2-2-1-1-1-11-2-21111-2-2111120-220-2-21100-2-2-1-1000011-120012-1-1000011-1-12-200000110000-1000
χ2522222-12-1222-1222-1-12-12-12-12-1-1-1-1222-1-1-1-122-122-1-1-1-1-1-1-1-122002-1-122220000-1-100-1-12-1-1200-1-1-1-1-1-10000000220000-1-10000-10
χ2622222-12-1222-1222-1-12-12-12-12-1-1-1-1222-1-1-1-122-122-1-1-1-1-1-1-1-12-200-2-1-122-2-200001100-1-12-11-200-1-111110000000-2-2000011000010
χ2722222-12-1222-1222-1-12-12-12-12-1-1-1-12-2-2-1-1-1-122-122-1-1-1-1-1-1-1-1-2200211-2-2220000-1-10011-21-120011-1-1-1-10000000-2-2000011000010
χ2822222-12-1222-1222-1-12-12-12-12-1-1-1-12-2-2-1-1-1-122-122-1-1-1-1-1-1-1-1-2-200-211-2-2-2-20000110011-211-2001111110000000220000-1-10000-10
χ2922222-12-1222-1222-1-12-1-2-12-12-1-1-1-1222-1-1-1-1-2-21-2-211111111-2200-2-1-1222200001100-1-1-21-1-20011-1-11100000002-20000110000-10
χ3022222-12-1222-1222-1-12-1-2-12-12-1-1-1-1222-1-1-1-1-2-21-2-211111111-2-2002-1-122-2-20000-1-100-1-1-2112001111-1-10000000-220000-1-1000010
χ3122222-12-1222-1222-1-12-1-2-12-12-1-1-1-12-2-2-1-1-1-1-2-21-2-2111111112200-211-2-22200001100112-1-1-200-1-1-1-1110000000-220000-1-1000010
χ3222222-12-1222-1222-1-12-1-2-12-12-1-1-1-12-2-2-1-1-1-1-2-21-2-2111111112-200211-2-2-2-20000-1-100112-11200-1-111-1-100000002-20000110000-10
χ332222-12222-122-1-122-1-122-1-12-12-12-1-100-1-1-1-12-12-1-122-1-1-1-1-1-1022220000-1-1-1-122222200002-12-100-1-1-1-1-1-1-1-100200-1-10000000-100
χ342222-12222-122-1-122-1-122-1-12-12-12-1-100-1-1-1-12-12-1-122-1-1-1-1-1-102-2-220000-1-111-2-222-2-200002-1-2100-1-1-1-1111100-200110000000100
χ352222-12222-122-1-122-1-122-1-12-12-12-1-100-1-1-1-12-12-1-122-1-1-1-1-1-10-222-2000011-1-122-2-2-2-20000-212-1001111-1-1-1-100-200110000000100
χ362222-12222-122-1-122-1-122-1-12-12-12-1-100-1-1-1-12-12-1-122-1-1-1-1-1-10-2-2-2-200001111-2-2-2-2220000-21-21001111111100200-1-10000000-100
χ372222-12222-122-1-122-1-12-2-1-12-12-12-1-100-1-1-1-1-21-211-2-2111111022-2-20000-1-1-1-1-2-2-2-2220000212100-1-111-1-11100-200-1-10000000100
χ382222-12222-122-1-122-1-12-2-1-12-12-12-1-100-1-1-1-1-21-211-2-211111102-22-20000-1-11122-2-2-2-2000021-2-100-1-11111-1-100200110000000-100
χ392222-12222-122-1-122-1-12-2-1-12-12-12-1-100-1-1-1-1-21-211-2-21111110-22-22000011-1-1-2-222-2-20000-2-1210011-1-1-1-11100200110000000-100
χ402222-12222-122-1-122-1-12-2-1-12-12-12-1-100-1-1-1-1-21-211-2-21111110-2-222000011112222220000-2-1-2-10011-1-111-1-100-200-1-10000000100
χ412-22-22222-2-2-2-2-222-222202-22-2-2-2-2-222-222-2-20000000000000000002-22-2000000002i−2i2-20000000000000000000002i−2i00002i−2i0000
χ422-22-22222-2-2-2-2-222-222202-22-2-2-2-2-222-222-2-20000000000000000002-22-200000000−2i2i2-2000000000000000000000−2i2i0000−2i2i0000
χ432-22-22222-2-2-2-2-222-222202-22-2-2-2-2-22-2222-2-2000000000000000000-22-22000000002i−2i-220000000000000000000002i−2i0000−2i2i0000
χ442-22-22222-2-2-2-2-222-222202-22-2-2-2-2-22-2222-2-2000000000000000000-22-2200000000−2i2i-22000000000000000000000−2i2i00002i−2i0000
χ4544444-2-2-2-24-2-244-2-2-2-214-2-21-21-21-2-2441111-24-2-2-211-2-2111140000-2-2-2-2000000000011-2-20000110000000000000000000000000
χ4644444-2-2-2-24-2-244-2-2-2-214-2-21-21-21-2-2-4-41111-24-2-2-211-2-21111-4000022220000000000-1-1220000-1-10000000000000000000000000
χ4744444-2-2-2-24-2-244-2-2-2-21-4-2-21-21-21-2-24411112-4222-1-122-1-1-1-1-40000-2-2-2-2000000000011220000-1-10000000000000000000000000
χ4844444-2-2-2-24-2-244-2-2-2-21-4-2-21-21-21-2-2-4-411112-4222-1-122-1-1-1-14000022220000000000-1-1-2-20000110000000000000000000000000
χ494444-24-24-2-2-24-2-2-24-21-24-21-21-2-2-2-21001111-2-2411-2-2-2-2111100440000000-2-2-2-20000000000-2-2000000111100000000000000000
χ504444-24-24-2-2-24-2-2-24-21-24-21-21-2-2-2-21001111-2-2411-2-2-2-2111100-4-400000002222000000000022000000-1-1-1-100000000000000000
χ514444-24-24-2-2-24-2-2-24-21-2-4-21-21-2-2-2-2100111122-4-1-12222-1-1-1-1004-40000000-2-2220000000000-2200000011-1-100000000000000000
χ524444-24-24-2-2-24-2-2-24-21-2-4-21-21-2-2-2-2100111122-4-1-12222-1-1-1-100-44000000022-2-200000000002-2000000-1-11100000000000000000
χ534444-2-24-24-24-2-2-24-21-2-241-2-2-2-21-21-20011114-2-2-2-2-2-2111111040040000-2-20000-2-2000000-2-200001111000000000000000000000
χ544444-2-24-24-24-2-2-24-21-2-241-2-2-2-21-21-20011114-2-2-2-2-2-21111110-400-4000022000022000000220000-1-1-1-1000000000000000000000
χ554444-2-24-24-24-2-2-24-21-2-2-41-2-2-2-21-21-2001111-4222222-1-1-1-1-1-10400-40000-2-2000022000000-22000011-1-1000000000000000000000
χ564444-2-24-24-24-2-2-24-21-2-2-41-2-2-2-21-21-2001111-4222222-1-1-1-1-1-10-40040000220000-2-20000002-20000-1-111000000000000000000000
χ5744-4-4444-4-4444-4-4-4-44440-44-4-4-444-4-4004-44-40000000000000000000000000000000000000000000000000000000000000000000
χ5844-4-444-2-424-24-4-42-44-2-20-4-22224-2-4200-22-2200000000000000000000000000000000000000000000000000000000023−2300000000
χ5944-4-444-2-424-24-4-42-44-2-20-4-22224-2-4200-22-22000000000000000000000000000000000000000000000000000000000−232300000000
χ6044-4-44-242-444-2-4-4-42-24-20242-42-2-22-400-22-22000000000000000000000000000023−230000000000000023−23000000000000000000000
χ6144-4-44-242-444-2-4-4-42-24-20242-42-2-22-400-22-220000000000000000000000000000−232300000000000000−2323000000000000000000000
χ6244-4-4-244-4-4-24422-4-4-2-2402-2-42-4-242200-22-220000000000000000000000−2i32i3000000000000000000−2i32i300000000000000000000000
χ6344-4-4-244-4-4-24422-4-4-2-2402-2-42-4-242200-22-2200000000000000000000002i3−2i30000000000000000002i3−2i300000000000000000000000
χ6444-4-4-2-242-4-24-222-421-2-20-1-22221-2-12001-11-100000003i−3i3i3i−3i−3i000000000−2i32i3000023−23000000000000i3−i3−33000000000000000000000
χ6544-4-4-2-242-4-24-222-421-2-20-1-22221-2-12001-11-100000003i−3i3i3i−3i−3i0000000002i3−2i30000−2323000000000000−i3i33−3000000000000000000000
χ6644-4-4-2-242-4-24-222-421-2-20-1-22221-2-12001-11-10000000−3i3i−3i−3i3i3i000000000−2i32i30000−2323000000000000i3−i33−3000000000000000000000
χ6744-4-4-2-242-4-24-222-421-2-20-1-22221-2-12001-11-10000000−3i3i−3i−3i3i3i0000000002i3−2i3000023−23000000000000−i3i3−33000000000000000000000
χ684-44-444-242-42-4-44-2-44-2-2042-222-42-4-24-4-2-2220000000000000000004-4-220000000000-22000000000000000000000000000000000
χ694-44-444-242-42-4-44-2-44-2-2042-222-42-4-2-44-2-222000000000000000000-442-200000000002-2000000000000000000000000000000000
χ704-44-44-24-2-4-4-42-4442-24-20-2-4-2-4222244-4-2-222000000000000000000-224-40000000000-22000000000000000000000000000000000
χ714-44-44-24-2-4-4-42-4442-24-20-2-4-2-422224-44-2-2220000000000000000002-2-4400000000002-2000000000000000000000000000000000
χ724-44-44-2-2-22-422-44-22-2-210-2212-12-12-24-411-1-1000003i−3i003i−3i3i−3i00000-22-2200000000001-10000003i−3i0000000000000000000000000
χ734-44-44-2-2-22-422-44-22-2-210-2212-12-12-24-411-1-100000−3i3i00−3i3i−3i3i00000-22-2200000000001-1000000−3i3i0000000000000000000000000
χ744-44-44-2-2-22-422-44-22-2-210-2212-12-12-2-4411-1-1000003i−3i003i−3i3i−3i000002-22-20000000000-11000000−3i3i0000000000000000000000000
χ754-44-44-2-2-22-422-44-22-2-210-2212-12-12-2-4411-1-100000−3i3i00−3i3i−3i3i000002-22-20000000000-110000003i−3i0000000000000000000000000
χ764-44-4-2444-42-4-42-24-4-2-240-2242-42-42-200-2-2220000000000000000000000000000004i−4i00000000000000000000000−2i2i0000000000
χ774-44-4-2444-42-4-42-24-4-2-240-2242-42-42-200-2-222000000000000000000000000000000−4i4i000000000000000000000002i−2i0000000000
χ784-4-44444-44-4-4-44-4-444440-4-4-444-4-44-4004-4-440000000000000000000000000000000000000000000000000000000000000000000
χ794-4-4444-2-4-2-42-44-4244-2-20-422-2-2-424200-222-20000000000000000000000000023−230000000000000000000023−2300000000000000000
χ804-4-4444-2-4-2-42-44-4244-2-20-422-2-2-424200-222-200000000000000000000000000−232300000000000000000000−232300000000000000000
χ814-4-444-2424-4-424-4-4-2-24-202-424-222-2-400-222-200000000000000000000000000000000000000000000000000000000000−2i32i3000000
χ824-4-444-2424-4-424-4-4-2-24-202-424-222-2-400-222-2000000000000000000000000000000000000000000000000000000000002i3−2i3000000
χ834-4-44-244-442-4-4-22-44-2-24022-4-242-4-2200-222-200000000000000000000000023−230000000000000000000023−230000000000000000000
χ844-4-44-244-442-4-4-22-44-2-24022-4-242-4-2200-222-2000000000000000000000000−232300000000000000000000−23230000000000000000000
χ854-4-44-24-2-4-222-4-2224-21-202-121-222-2-1001-1-110003-300003-3-330000000000023−2323−23000000000000000000−33−3300000000000000000
χ864-4-44-24-2-4-222-4-2224-21-202-121-222-2-1001-1-110003-300003-3-3300000000000−2323−23230000000000000000003−33−300000000000000000
χ874-4-44-24-2-4-222-4-2224-21-202-121-222-2-1001-1-11000-330000-333-30000000000023−23−2323000000000000000000−333−300000000000000000
χ884-4-44-24-2-4-222-4-2224-21-202-121-222-2-1001-1-11000-330000-333-300000000000−232323−230000000000000000003−3−3300000000000000000
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
χ9188-8-88-4-4448-4-4-8-844-4-4204-4-24-2-4244002-22-20000000000000000000000000000000000000000000000000000000000000000000
χ9288-8-8-48-4-84-4-48444-8-42-40424-24-4-44-2002-22-20000000000000000000000000000000000000000000000000000000000000000000
χ9388-8-8-4-4-444-4-4-444442220-22-2-2-222-2-200-11-1100000006i−6i−3i−3i3i3i000000000000000000000000000000000000000000000000000000
χ9488-8-8-4-4-444-4-4-444442220-22-2-2-222-2-200-11-110000000−6i6i3i3i−3i−3i000000000000000000000000000000000000000000000000000000
χ958-88-8-48-48444-84-4-4-8-42-40-4-2-4-2444420022-2-20000000000000000000000000000000000000000000000000000000000000000000
χ968-88-8-4-48-4-84-844-4842-4-4024-444-24-2-40022-2-20000000000000000000000000000000000000000000000000000000000000000000
χ978-88-8-4-4-4-444444-4-4422202-22-2-2-2-2-2200-1-111000006i−6i00−3i3i−3i3i000000000000000000000000000000000000000000000000000000
χ988-88-8-4-4-4-444444-4-4422202-22-2-2-2-2-2200-1-11100000−6i6i003i−3i3i−3i000000000000000000000000000000000000000000000000000000
χ998-8-888-4-44-4-8448-84-4-4-42044-2-424-2-44002-2-220000000000000000000000000000000000000000000000000000000000000000000
χ1008-8-88-4-48484-84-44-8-42-4-40-244-4-4-2424002-2-220000000000000000000000000000000000000000000000000000000000000000000
χ1018-8-88-4-4-44-4444-444-42220-2-2-222-2-22-200-111-10006-60000-333-3000000000000000000000000000000000000000000000000000000
χ1028-8-88-4-4-44-4444-444-42220-2-2-222-2-22-200-111-1000-6600003-3-33000000000000000000000000000000000000000000000000000000

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