Finite Group Databasebeta

← Group #13168673

Character table — Group #13168673

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111122222222222244444444444444488888888888888881212121212121212121212121212181818181818242424242424242424242424242424242424242436363636363636363636367272108108
order122233366666666633346666666661212366612121212121212121212121224444412121212121212124444446666121212121212121212121212121212124441212121212121212121244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-11111111-1-1-1-111-1-11111-111-11-111-1-1-1-11111-11-1-1-111-1-1-1-11-1-1-1
χ3111111111111111111111111111111111111111111111111-1-1111-1-1-1-1111111-1-1-1-111111-1-1111111111-1-1-1-1-1-11-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111111111111111111111-1-1-1-11-1-1-1-111-1-1-1-1-1-1111111-1-1-1-11-111-1-1-1-1-1-1-1-11-1-111-1-1-1-1-1-1-1111
χ511111111111111111111111111111111111111111111111-11111-11111-1-111-1-1-1-111-1-1-1-11111-11-1-1111111111-1-111-1-1-1-1-1-1-11-1-1
χ611111111111111111111111111111111111111111111111-111-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-11111-1-11-1-1-1-11111-1-111
χ711111111111111111111111111111111111111111111111-1-1-111-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11-1-11-11-1-11111-1-1-1-1-11-1-1-111-1-1-1-11-111
χ811111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-1
χ91111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-11-1-111-1-1-1-1-1-1-1-1-1-1111111-1-111-11-1-111-1-111-1-1-11111-1-111-1-11-11-1
χ101111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-11-111-1-1-1-11111-1-1-1-111111-11-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-11111-11
χ111111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-111-1-1-1-111-1-1-1-1-1-111-1-11111-11-11-11-1-111-1-1-1-1111-11-1-11111-1-1-11-11
χ121111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-11-11-1-1-111-1-111111111111111-1-1-1-1-1-1-1-111-1-111-1-1-11111-1-111-1-11-1
χ131111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-11-1111-1-111-1-1111111-1-1-1-1-1-111111111-1-111-1-1-1-1-11111-1-111-1-1-11
χ141111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11111-1-11111-1-111-1-1-1-1-1-11-11-11-111-1-11111-1-11-11-1-11111-1-1-111-1
χ151111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-11-1-11111-1-111-1-1-1-1-1-1-1-1-11-11111111-1-1-1-11111-1-1-1-1-1-1-111111-1
χ161111111111111111111-1111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-1111111-1-1-1-111-1-1-1-111-1-11-111-1-111-1-111-11111-1-111-1-11-1-11
χ17222222-12-122-122-122-1-122-1-1-1-12-12-122-1-1-1-1-12-1-1-1-122-1-1-1-1222002-1-122-1-1000022002-1-1-10-12020-1-10000-1-1-1-102000-1-10000-1000
χ18222222-12-122-122-122-1-122-1-1-1-12-12-122-1-1-1-1-12-1-1-1-122-1-1-1-12-2-200211-2-2-1-10000-2-2002-1-1-101-2020-1-1000011110-20001100001000
χ19222222-12-122-122-122-1-122-1-1-1-12-12-122-1-1-1-1-12-1-1-1-122-1-1-1-1-22200-2-1-122110000-2-200-21110-120-20110000-1-1-1-10-20001100001000
χ20222222-12-122-122-122-1-122-1-1-1-12-12-122-1-1-1-1-12-1-1-1-122-1-1-1-1-2-2-200-211-2-21100002200-211101-20-20110000111102000-1-10000-1000
χ21222222-12-122-122-122-1-1-22-1-1-1-12-12-1-2-2-1-1-1-11-21111-2-2111122-200-2-1-1-2-2110000-2-2002-1-1-10120-20110000-1-11102000110000-1000
χ22222222-12-122-122-122-1-1-22-1-1-1-12-12-1-2-2-1-1-1-11-21111-2-211112-2200-2112211000022002-1-1-10-1-20-2011000011-1-10-2000-1-100001000
χ23222222-12-122-122-122-1-1-22-1-1-1-12-12-1-2-2-1-1-1-11-21111-2-21111-22-2002-1-1-2-2-1-100002200-2111012020-1-10000-1-1110-2000-1-100001000
χ24222222-12-122-122-122-1-1-22-1-1-1-12-12-1-2-2-1-1-1-11-21111-2-21111-2-220021122-1-10000-2-200-21110-1-2020-1-1000011-1-102000110000-1000
χ2522222-12-12222-1-122-12-12-12-12-1-1-1-12-1-1-1-1-1-12222-1-1-1-1-1-1-1-120022200002222220000-12-1-1-1002-1-1-1-1-1-1-1-100000020000-1-1-1-10000
χ2622222-12-12222-1-122-12-12-12-12-1-1-1-12-1-1-1-1-1-12222-1-1-1-1-1-1-1-1200-2-22000022-2-2-2-20000-12-1-1100-2-11-1-11111000000-2000011110000
χ2722222-12-12222-1-122-12-12-12-12-1-1-1-12-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-20022-20000-2-222-2-200001-211-10021-111-1-1-1-1000000-2000011110000
χ2822222-12-12222-1-122-12-12-12-12-1-1-1-12-1-1-1-1-1-12222-1-1-1-1-1-1-1-1-200-2-2-20000-2-2-2-22200001-211100-21111111100000020000-1-1-1-10000
χ2922222-12-12222-1-122-12-1-2-12-12-1-1-1-1211-1-1-1-1-2-2-2-2111111112002-2-20000-2-2-2-2-2-20000-12-1-110021-111-1-11100000020000-1-1110000
χ3022222-12-12222-1-122-12-1-2-12-12-1-1-1-1211-1-1-1-1-2-2-2-211111111200-22-20000-2-222220000-12-1-1-100-2111111-1-1000000-2000011-1-10000
χ3122222-12-12222-1-122-12-1-2-12-12-1-1-1-1211-1-1-1-1-2-2-2-211111111-2002-22000022-2-22200001-2111002-1-1-1-1-1-111000000-2000011-1-10000
χ3222222-12-12222-1-122-12-1-2-12-12-1-1-1-1211-1-1-1-1-2-2-2-211111111-200-22200002222-2-200001-211-100-2-11-1-111-1-100000020000-1-1110000
χ332222-12222-1-12222-1-1-122-1-12-12-12-1-122-1-1-1-12-1-1-122-1-1-1-1-1-102222022-1-100-1-1000022000022-1-10200-1-1-1-1-1-1-1-1200-1-10000000-100
χ342222-12222-1-12222-1-1-122-1-12-12-12-1-122-1-1-1-12-1-1-122-1-1-1-1-1-1022-2-2022-1-100110000-2-20000-22-110-2001111-1-1-1-1-200110000000100
χ352222-12222-1-12222-1-1-122-1-12-12-12-1-122-1-1-1-12-1-1-122-1-1-1-1-1-10-2-2220-2-21100-1-10000-2-200002-21-10200-1-1-1-11111-200110000000100
χ362222-12222-1-12222-1-1-122-1-12-12-12-1-122-1-1-1-12-1-1-122-1-1-1-1-1-10-2-2-2-20-2-21100110000220000-2-2110-20011111111200-1-10000000-100
χ372222-12222-1-12222-1-1-12-2-1-12-12-12-1-1-2-2-1-1-1-1-2111-2-211111102-22-20221100110000220000-2-2-1-10200-1-111-1-111-200-1-10000000100
χ382222-12222-1-12222-1-1-12-2-1-12-12-12-1-1-2-2-1-1-1-1-2111-2-211111102-2-220221100-1-10000-2-200002-2-110-20011-1-1-1-111200110000000-100
χ392222-12222-1-12222-1-1-12-2-1-12-12-12-1-1-2-2-1-1-1-1-2111-2-21111110-222-20-2-2-1-100110000-2-20000-221-10200-1-11111-1-1200110000000-100
χ402222-12222-1-12222-1-1-12-2-1-12-12-12-1-1-2-2-1-1-1-1-2111-2-21111110-22-220-2-2-1-100-1-1000022000022110-20011-1-111-1-1-200-1-10000000100
χ412-2-22222-2-22-2-22-22-2222022-2-2-2-22-2-20022-2-2000000000000000000000000002i−2i2i−2i2-2000000000000000000000002-22i−2i002i−2i0000
χ422-2-22222-2-22-2-22-22-2222022-2-2-2-22-2-20022-2-2000000000000000000000000002i−2i−2i2i-2200000000000000000000000-22−2i2i002i−2i0000
χ432-2-22222-2-22-2-22-22-2222022-2-2-2-22-2-20022-2-200000000000000000000000000−2i2i2i−2i-2200000000000000000000000-222i−2i00−2i2i0000
χ442-2-22222-2-22-2-22-22-2222022-2-2-2-22-2-20022-2-200000000000000000000000000−2i2i−2i2i2-2000000000000000000000002-2−2i2i00−2i2i0000
χ4544444-2-2-2-244-2-2-2-24-2-214-2-21-21-21-2-2-2-21111-24-2-211-2-211114000040000-2-200000000-2-2110000-201100000000000000000000000
χ4644444-2-2-2-244-2-2-2-24-2-214-2-21-21-21-2-2-2-21111-24-2-211-2-21111-40000-40000220000000022-1-1000020-1-100000000000000000000000
χ4744444-2-2-2-244-2-2-2-24-2-21-4-2-21-21-21-2-22211112-422-1-122-1-1-1-140000-400002200000000-2-211000020-1-100000000000000000000000
χ4844444-2-2-2-244-2-2-2-24-2-21-4-2-21-21-21-2-22211112-422-1-122-1-1-1-1-4000040000-2-20000000022-1-10000-201100000000000000000000000
χ494444-24-24-2-2-2-244-2-2-21-24-21-21-2-2-2-21441111-2-211-2-2-2-21111044000-2-2-2-2000000000000000-2-20000000001111000000000000000
χ504444-24-24-2-2-2-244-2-2-21-24-21-21-2-2-2-21441111-2-211-2-2-2-211110-4-4000222200000000000000022000000000-1-1-1-1000000000000000
χ514444-24-24-2-2-2-244-2-2-21-2-4-21-21-2-2-2-21-4-4111122-1-12222-1-1-1-104-4000-2-2220000000000000002-200000000011-1-1000000000000000
χ524444-24-24-2-2-2-244-2-2-21-2-4-21-21-2-2-2-21-4-4111122-1-12222-1-1-1-10-4400022-2-2000000000000000-22000000000-1-111000000000000000
χ534444-2-24-24-2-24-2-24-21-2-241-2-2-2-21-21-2-2-211114-2-2-2-2-2111111000440000000-2-20000000000-200-20-20011110000000000000000000
χ544444-2-24-24-2-24-2-24-21-2-241-2-2-2-21-21-2-2-211114-2-2-2-2-2111111000-4-4000000022000000000020020200-1-1-1-10000000000000000000
χ554444-2-24-24-2-24-2-24-21-2-2-41-2-2-2-21-21-2221111-422222-1-1-1-1-1-10004-40000000220000000000200-20-20011-1-10000000000000000000
χ564444-2-24-24-2-24-2-24-21-2-2-41-2-2-2-21-21-2221111-422222-1-1-1-1-1-1000-440000000-2-20000000000-20020200-1-1110000000000000000000
χ5744-4-4444-44-44-4-44-4-44440-4-44-4-44-4-44004-44-40000000000000000000000000000000000000000000000000000000000000000000
χ5844-4-444-2-4-2-442-442-44-2-20-42-22242-4-200-22-22000000000000000000000023−2300000000000000000023−2300000000000000000000000
χ5944-4-444-2-4-2-442-442-44-2-20-42-22242-4-200-22-220000000000000000000000−2323000000000000000000−232300000000000000000000000
χ6044-4-44-2424-44-42-2-4-4-24-202-4-2-42-222423−23-22-22000023−2323−232323−23−230000000000000000000000000000000000000000000000000000000
χ6144-4-44-2424-44-42-2-4-4-24-202-4-2-42-2224−2323-22-220000−2323−2323−23−2323230000000000000000000000000000000000000000000000000000000
χ6244-4-44-2-22-2-4422-22-4-2-2102212-1-2-12-223−231-11-10000−3323−23−3−333000000000023−2300000000003-3000000−3300000000000000000000000
χ6344-4-44-2-22-2-4422-22-4-2-2102212-1-2-12-223−231-11-10000−3323−23−3−3330000000000−23230000000000-330000003−300000000000000000000000
χ6444-4-44-2-22-2-4422-22-4-2-2102212-1-2-12-2−23231-11-100003−3−232333−3−3000000000023−230000000000-33000000−3300000000000000000000000
χ6544-4-44-2-22-2-4422-22-4-2-2102212-1-2-12-2−23231-11-100003−3−232333−3−30000000000−232300000000003-30000003−300000000000000000000000
χ6644-4-4-244-442-2-4-44-42-2-2402242-4-2-42-200-22-2200000000000000000000000023−230000000000000000000023−230000000000000000000
χ6744-4-4-244-442-2-4-44-42-2-2402242-4-2-42-200-22-22000000000000000000000000−232300000000000000000000−23230000000000000000000
χ6844-4-4-2-24242-2-42-2-421-2-20-12-22212-1-223−231-11-1000023−23−33−3−33300000000000023−230000000000000000003-3−330000000000000000000
χ6944-4-4-2-24242-2-42-2-421-2-20-12-22212-1-223−231-11-1000023−23−33−3−333000000000000−2323000000000000000000-333−30000000000000000000
χ7044-4-4-2-24242-2-42-2-421-2-20-12-22212-1-2−23231-11-10000−23233−333−3−300000000000023−23000000000000000000-33−330000000000000000000
χ7144-4-4-2-24242-2-42-2-421-2-20-12-22212-1-2−23231-11-10000−23233−333−3−3000000000000−23230000000000000000003-33−30000000000000000000
χ724-44-44444-4-4-44-4-4-444440-4-4-444-4-44-4004-4-440000000000000000000000000000000000000000000000000000000000000000000
χ734-44-444-242-4-4-2-4-4244-2-20-422-2-2-424200-222-200000000000000000023−23000000000000000000000000000023−2300000000000000000
χ744-44-444-242-4-4-2-4-4244-2-20-422-2-2-424200-222-2000000000000000000−23230000000000000000000000000000−232300000000000000000
χ754-44-44-24-2-4-4-4422-44-24-202-424-222-2-400-222-20000000000000000000000000000000000000000000000000000000000023−23000000
χ764-44-44-24-2-4-4-4422-44-24-202-424-222-2-400-222-200000000000000000000000000000000000000000000000000000000000−2323000000
χ774-44-4-2444-4224-4-4-4-2-2-24022-4-242-4-2200-222-20000000000000000000023−23000000000000000000000000000023−23000000000000000
χ784-44-4-2444-4224-4-4-4-2-2-24022-4-242-4-2200-222-200000000000000000000−23230000000000000000000000000000−2323000000000000000
χ794-44-4-24-24222-2-4-42-2-21-202-121-222-2-1001-1-11003-300003-33-300000023−2323−2300000000000000000000000000−33−33000000000000000
χ804-44-4-24-24222-2-4-42-2-21-202-121-222-2-1001-1-11003-300003-33-3000000−2323−2323000000000000000000000000003−33−3000000000000000
χ814-44-4-24-24222-2-4-42-2-21-202-121-222-2-1001-1-1100-330000-33-3300000023−23−232300000000000000000000000000−333−3000000000000000
χ824-44-4-24-24222-2-4-42-2-21-202-121-222-2-1001-1-1100-330000-33-33000000−232323−23000000000000000000000000003−3−33000000000000000
χ834-4-4444-2-424-424-4-2-44-2-204-2222-4-2-4200-2-22200000000000000000000000000004i−4i000000000000000000000000000−2i2i00000000
χ844-4-4444-2-424-424-4-2-44-2-204-2222-4-2-4200-2-2220000000000000000000000000000−4i4i0000000000000000000000000002i−2i00000000
χ854-4-444-242-44-4-4-224-4-24-20-242-422-22-400-2-222000000000000000000000000004i−4i000000000000000000000000000000000−2i2i0000
χ864-4-444-242-44-4-4-224-4-24-20-242-422-22-400-2-22200000000000000000000000000−4i4i0000000000000000000000000000000002i−2i0000
χ874-4-44-244-4-4-22-44-442-2-240-2-2-42-4242200-2-2220000000000000000000000000000004-400000000000000000000000-220000000000
χ884-4-44-244-4-4-22-44-442-2-240-2-2-42-4242200-2-222000000000000000000000000000000-44000000000000000000000002-20000000000
χ898888-4-4-4-4-4-4-4-4-4-4-4-42228222222222-4-4-1-1-1-1-4-4222222-1-1-1-10000000000000000000000000000000000000000000000000000000
χ908888-4-4-4-4-4-4-4-4-4-4-4-4222-822222222244-1-1-1-144-2-2-2-2-2-211110000000000000000000000000000000000000000000000000000000
χ9188-8-8-48-4-8-44-44-8844-42-404-2-4-24-4442002-22-20000000000000000000000000000000000000000000000000000000000000000000
χ9288-8-8-4-4-44-44-444-4442220-2-22-2-22-2-2243−43-11-110000−2323−232333−3−30000000000000000000000000000000000000000000000000000000
χ9388-8-8-4-4-44-44-444-4442220-2-22-2-22-2-22−4343-11-11000023−2323−23−3−3330000000000000000000000000000000000000000000000000000000
χ948-88-88-4-4-44-8-8-44448-4-42044-2-424-2-44002-2-220000000000000000000000000000000000000000000000000000000000000000000
χ958-88-8-4-48-4-844844-8-42-4-40-244-4-4-2424002-2-220000000000000000000000000000000000000000000000000000000000000000000
χ968-88-8-4-4-4-4444-4444-42220-2-2-222-2-22-200-111-1006-60000-33-330000000000000000000000000000000000000000000000000000000
χ978-88-8-4-4-4-4444-4444-42220-2-2-222-2-22-200-111-100-6600003-33-30000000000000000000000000000000000000000000000000000000
χ988-8-888-4-4448-84-44-4-8-4-420-4-4-24-242440022-2-20000000000000000000000000000000000000000000000000000000000000000000
χ998-8-88-48-4-84-4448-8-44-42-40-424-244-44-20022-2-20000000000000000000000000000000000000000000000000000000000000000000
χ1008-8-88-4-484-8-44-8-44842-4-402-4444-2-4-240022-2-20000000000000000000000000000000000000000000000000000000000000000000
χ1018-8-88-4-4-444-444-44-44222022-2-2-2-22-2-200-1-1110000000033−33−33330000000000000000000000000000000000000000000000000000000
χ1028-8-88-4-4-444-444-44-44222022-2-2-2-22-2-200-1-11100000000−333333−330000000000000000000000000000000000000000000000000000000

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