Finite Group Databasebeta

← Group #13169396

Character table — Group #13169396

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111122222222222244444444444444466888888888888888812121212121212121212121212181824242424242424242424242424242424242424243636363636363636363636363654547272108
order12223336666666663334666666666121244366612121212121212121212121244444121212121212121244121212121212121212121212121212121212121224444661212121212124412124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111-11-1111111-1-1-1-11-1111-11-111-1-111-1-11111-11-11-1-1-111-1-1-1-1-1-11-1-1
χ311111111111111111111111111111111111111111111111111-11-111111-1-111-1-1-1111-11-11-1-111-1-1111111-1-11-11-1-1-1-111-1-1-1-1-11-1
χ411111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-111-1-1-1-11111-1-11
χ51111111111111111111111111111111-1-11111111111111111-11111-1-1-1-111111111-1-1111111111111-1-1-1-11-1-1-1-111-1-1-1-111-1-1-1-1-1
χ61111111111111111111111111111111-1-11111111111111111-11-11-1-1-1-1-111-1-1-1-11-1-1-11-11-111-1-111-1-1-1-1-1-1-1-11-11-1-1-1-111-1-111-111
χ71111111111111111111111111111111-1-11111111111111111-1-11-11-1-1-1-1-1-111-1-1-11-1-1-11-11-1-111-1-111-1-1-1-1-11-11-1-1-111-1-1-1-1111-11
χ81111111111111111111111111111111-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1-111-1
χ91111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111-1-111-1-11111-1-1-1-111-1-1-111-1-1-1-1-1-1-1-1111111-1
χ101111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111111-1-111-1-11-1-1-11-1-1111-1-1-1-11111-1-111-1-1111-1-111-1-1-1-11-11
χ111111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1111111-1-1-1-1-11-1-1-111-1-1-11111-1-111-1-11-111-11111-1-1-1-1-1-1-111
χ121111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-111-1-111111111-1-1-1
χ131111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-111-1-1-111-1-1111111-1-1-1-11
χ141111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-11-1-1-1-1-1-111-1-11-1111-1-1111-1-1-1-111-1-1111-111-11111-1-1-1-111-11-1
χ151111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-111-1-1-1-1-111-1-1-1-1-1111-111-1-1-11111-1-1-1-11111-1-1111-1-111-1-1111-1-1
χ161111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-1-1-1111111-1-111-1-111-1-1-1-11111-1-111-111-1-1-1-1-1-1-1-111-1-1111
χ17222222-1-1-1222222-12-1-122-1-12-1-1-1-12-1-100-1-1-1-12222-1-1-1-1-1-1-1-1022220000222222-1-10022-1-1-1-1-1-1-1-1-1-1000020000-1-10000-1-100000
χ18222222-1-1-1222222-12-1-122-1-12-1-1-1-12-1-100-1-1-1-12222-1-1-1-1-1-1-1-102-22-2000022-2-2-2-2-11002-2-11-1-111-1-1110000-200001100001100000
χ19222222-1-1-1222222-12-1-122-1-12-1-1-1-12-1-100-1-1-1-12222-1-1-1-1-1-1-1-10-22-220000-2-222-2-21-100-221-111-1-111-1-10000-200001100001100000
χ20222222-1-1-1222222-12-1-122-1-12-1-1-1-12-1-100-1-1-1-12222-1-1-1-1-1-1-1-10-2-2-2-20000-2-2-2-2221100-2-21111111111000020000-1-10000-1-100000
χ21222222-1-1-1222222-12-1-1-22-1-12-1-1-1-121100-1-1-1-1-2-2-2-211111111022-2-20000-2-2-2-222-1-1002211-1-1-1-111110000-20000110000-1-100000
χ22222222-1-1-1222222-12-1-1-22-1-12-1-1-1-121100-1-1-1-1-2-2-2-21111111102-2-220000-2-222-2-2-11002-21-1-1-11111-1-1000020000-1-100001100000
χ23222222-1-1-1222222-12-1-1-22-1-12-1-1-1-121100-1-1-1-1-2-2-2-2111111110-222-2000022-2-2-2-21-100-22-1111-1-1-1-111000020000-1-100001100000
χ24222222-1-1-1222222-12-1-1-22-1-12-1-1-1-121100-1-1-1-1-2-2-2-2111111110-2-22200002222221100-2-2-1-11111-1-1-1-10000-20000110000-1-100000
χ2522222-122222-1-12-12-12-12-12-1-12-12-1-12222-1-1-1-12-1-1-122-1-1-1-1-1-12020222-1-100-1-100022-10-10200-1-100-1-1-1-1-1-1002020000-1-100000-10
χ2622222-122222-1-12-12-12-12-12-1-12-12-1-12222-1-1-1-12-1-1-122-1-1-1-1-1-120-20-222-1-10011000-22-1010-200110011-1-1-1-100-20-20000110000010
χ2722222-122222-1-12-12-12-12-12-1-12-12-1-122-2-2-1-1-1-12-1-1-122-1-1-1-1-1-1-20202-2-21100-1-10002-210-10200-1-100-1-1111100-20-20000110000010
χ2822222-122222-1-12-12-12-12-12-1-12-12-1-122-2-2-1-1-1-12-1-1-122-1-1-1-1-1-1-20-20-2-2-2110011000-2-21010-2001100111111002020000-1-100000-10
χ2922222-122222-1-12-12-12-1-2-12-1-12-12-1-1-2-222-1-1-1-1-2111-2-2111111-2020-222-1-100110002-210-10-200-1-10011-1-1110020-200001100000-10
χ3022222-122222-1-12-12-12-1-2-12-1-12-12-1-1-2-222-1-1-1-1-2111-2-2111111-20-20222-1-100-1-1000-2-210102001100-1-1-1-11100-2020000-1-10000010
χ3122222-122222-1-12-12-12-1-2-12-1-12-12-1-1-2-2-2-2-1-1-1-1-2111-2-21111112020-2-2-211001100022-10-10-200-1-1001111-1-100-2020000-1-10000010
χ3222222-122222-1-12-12-12-1-2-12-1-12-12-1-1-2-2-2-2-1-1-1-1-2111-2-211111120-202-2-21100-1-1000-22-10102001100-1-111-1-10020-200001100000-10
χ332222-12222-1-122-122-1-122-1-12-1-12-12-12222-1-1-1-1-12-1-1-1-122-1-1-1-122020-1-122-1-1000020-12-1020-1-100-1-100-1-1-1-10202000-1-1000000-100
χ342222-12222-1-122-122-1-122-1-12-1-12-12-12222-1-1-1-1-12-1-1-1-122-1-1-1-12-20-20-1-122110000-20-1210-2011001100-1-1-1-10-20-200011000000100
χ352222-12222-1-122-122-1-122-1-12-1-12-12-122-2-2-1-1-1-1-12-1-1-1-122-1-1-1-1-2202011-2-2-1-10000201-2-1020-1-100-1-10011110-20-200011000000100
χ362222-12222-1-122-122-1-122-1-12-1-12-12-122-2-2-1-1-1-1-12-1-1-1-122-1-1-1-1-2-20-2011-2-2110000-201-210-201100110011110202000-1-1000000-100
χ372222-12222-1-122-122-1-12-2-1-12-1-12-12-1-2-222-1-1-1-11-21111-2-21111-220-20-1-122110000201-2-10-20-1-1001100-1-111020-200011000000-100
χ382222-12222-1-122-122-1-12-2-1-12-1-12-12-1-2-222-1-1-1-11-21111-2-21111-2-2020-1-122-1-10000-201-210201100-1-100-1-1110-202000-1-1000000100
χ392222-12222-1-122-122-1-12-2-1-12-1-12-12-1-2-2-2-2-1-1-1-11-21111-2-21111220-2011-2-211000020-12-10-20-1-100110011-1-10-202000-1-1000000100
χ402222-12222-1-122-122-1-12-2-1-12-1-12-12-1-2-2-2-2-1-1-1-11-21111-2-211112-202011-2-2-1-10000-20-1210201100-1-10011-1-1020-200011000000-100
χ412-22-2222-2-2-2-2-2-22222220-2-2-22-2-222-2002i−2i2-2-22000000000000000002i−2i2i−2i00002-200000000000000002i−2i00000000000002-22i−2i000
χ422-22-2222-2-2-2-2-2-22222220-2-2-22-2-222-2002i−2i2-2-22000000000000000002i−2i2i−2i0000-2200000000000000002i−2i0000000000000-22−2i2i000
χ432-22-2222-2-2-2-2-2-22222220-2-2-22-2-222-200−2i2i2-2-2200000000000000000−2i2i−2i2i00002-20000000000000000−2i2i00000000000002-2−2i2i000
χ442-22-2222-2-2-2-2-2-22222220-2-2-22-2-222-200−2i2i2-2-2200000000000000000−2i2i−2i2i0000-220000000000000000−2i2i0000000000000-222i−2i000
χ4544444-2-2-2-244-2-24-2-2-2-214-2-21-2-21-21-2-2-20011114-2-2-2-2-211111100404000000-2-2000-2000-20-2001100110000000000000000000000
χ4644444-2-2-2-244-2-24-2-2-2-214-2-21-2-21-21-2-2-20011114-2-2-2-2-211111100-40-400000022000200020200-1-100-1-10000000000000000000000
χ4744444-2-2-2-244-2-24-2-2-2-21-4-2-21-2-21-21-222001111-422222-1-1-1-1-1-10040-400000022000-2000-202001100-1-10000000000000000000000
χ4844444-2-2-2-244-2-24-2-2-2-21-4-2-21-2-21-21-222001111-422222-1-1-1-1-1-100-404000000-2-2000200020-200-1-100110000000000000000000000
χ494444-24-2-2-2-2-244-24-2-21-24-21-2-21-21-2-2-2-2001111-24-2-211-2-21111040400000-2-20000-2000-20-20110011000000000000000000000000
χ504444-24-2-2-2-2-244-24-2-21-24-21-2-21-21-2-2-2-2001111-24-2-211-2-211110-40-40000022000020002020-1-100-1-1000000000000000000000000
χ514444-24-2-2-2-2-244-24-2-21-2-4-21-2-21-21-2-2220011112-422-1-122-1-1-1-1040-400000220000-2000-20201100-1-1000000000000000000000000
χ524444-24-2-2-2-2-244-24-2-21-2-4-21-2-21-21-2-2220011112-422-1-122-1-1-1-10-40400000-2-20000200020-20-1-10011000000000000000000000000
χ534444-2-2444-2-2-2-2-2-241-2-241-2-21-2-2-2-2144441111-2-211-2-2-2-2111140000-2-2-2-200000000-2-20000000000001111000000000000000000
χ544444-2-2444-2-2-2-2-2-241-2-241-2-21-2-2-2-2144-4-41111-2-211-2-2-2-21111-4000022220000000022000000000000-1-1-1-1000000000000000000
χ554444-2-2444-2-2-2-2-2-241-2-2-41-2-21-2-2-2-21-4-444111122-1-12222-1-1-1-1-40000-2-2-2-2000000002200000000000011-1-1000000000000000000
χ564444-2-2444-2-2-2-2-2-241-2-2-41-2-21-2-2-2-21-4-4-4-4111122-1-12222-1-1-1-140000222200000000-2-2000000000000-1-111000000000000000000
χ5744-4-4444-444-44-4-4-4-44440-4-4-4-444-4-44000044-4-400000000000000000000000000000000000000000000000000000000000000000
χ5844-4-444-22-24-44-4-4-424-2-20-422-4-2-222423−2300-2-222000023−2323−232323−23−2300000000000000000000000000000000000000000000000000000
χ5944-4-444-22-24-44-4-4-424-2-20-422-4-2-2224−232300-2-2220000−2323−2323−23−23232300000000000000000000000000000000000000000000000000000
χ6044-4-44-24-444-4-22-42-4-24-202-4224-2-42-20000-2-2220000000000000000000000023−23000000000000000023−230000000000000000000000
χ6144-4-44-24-444-4-22-42-4-24-202-4224-2-42-20000-2-22200000000000000000000000−23230000000000000000−23230000000000000000000000
χ6244-4-44-2-22-24-4-22-422-2-21022-12-212-1-223−230011-1-1000023−23−33−3−3330000000000023−230000000000003-300−330000000000000000000000
χ6344-4-44-2-22-24-4-22-422-2-21022-12-212-1-223−230011-1-1000023−23−33−3−33300000000000−2323000000000000-33003−30000000000000000000000
χ6444-4-44-2-22-24-4-22-422-2-21022-12-212-1-2−23230011-1-10000−23233−333−3−30000000000023−23000000000000-3300−330000000000000000000000
χ6544-4-44-2-22-24-4-22-422-2-21022-12-212-1-2−23230011-1-10000−23233−333−3−300000000000−23230000000000003-3003−30000000000000000000000
χ6644-4-4-244-44-224-42-4-4-2-24022-42-242-4-20000-2-22200000000000000000000023−23000000000000000023−23000000000000000000000000
χ6744-4-4-244-44-224-42-4-4-2-24022-42-242-4-20000-2-222000000000000000000000−23230000000000000000−2323000000000000000000000000
χ6844-4-4-24-22-2-224-42-42-21-202-1221-2-12-223−230011-1-10000−3323−23−3−33300000000023−230000000000003-300−33000000000000000000000000
χ6944-4-4-24-22-2-224-42-42-21-202-1221-2-12-223−230011-1-10000−3323−23−3−333000000000−2323000000000000-33003−3000000000000000000000000
χ7044-4-4-24-22-2-224-42-42-21-202-1221-2-12-2−23230011-1-100003−3−232333−3−300000000023−23000000000000-3300−33000000000000000000000000
χ7144-4-4-24-22-2-224-42-42-21-202-1221-2-12-2−23230011-1-100003−3−232333−3−3000000000−23230000000000003-3003−3000000000000000000000000
χ724-44-444-222-4-4-4-444-24-2-20-422422-2-2-40000-222-200000000000000000000000004-40000000000000000000000000000000-2200000
χ734-44-444-222-4-4-4-444-24-2-20-422422-2-2-40000-222-20000000000000000000000000-4400000000000000000000000000000002-200000
χ744-44-44-24-4-4-4-4224-24-24-202-42-2-424-22004i−4i-222-2000000000000000004i−4i−2i2i0000000000000000000000−2i2i00000000000000000000
χ754-44-44-24-4-4-4-4224-24-24-202-42-2-424-2200−4i4i-222-200000000000000000−4i4i2i−2i00000000000000000000002i−2i00000000000000000000
χ764-44-4-244-4-422-4-4-244-2-24022-4-22-4-242004i−4i-222-200000000000000000−2i2i4i−4i0000000000000000000000−2i2i00000000000000000000
χ774-44-4-244-4-422-4-4-244-2-24022-4-22-4-24200−4i4i-222-2000000000000000002i−2i−4i4i00000000000000000000002i−2i00000000000000000000
χ784-44-4-2-24-4-42222-2-241-2-20-122122-2-2-1004i−4i1-1-11003-300003-33-300000−2i2i−2i2i0000000000000000000000i−i3i−3i000000000000000000
χ794-44-4-2-24-4-42222-2-241-2-20-122122-2-2-1004i−4i1-1-1100-330000-33-3300000−2i2i−2i2i0000000000000000000000i−i−3i3i000000000000000000
χ804-44-4-2-24-4-42222-2-241-2-20-122122-2-2-100−4i4i1-1-11003-300003-33-3000002i−2i2i−2i0000000000000000000000−ii−3i3i000000000000000000
χ814-44-4-2-24-4-42222-2-241-2-20-122122-2-2-100−4i4i1-1-1100-330000-33-33000002i−2i2i−2i0000000000000000000000−ii3i−3i000000000000000000
χ824-4-444444-4-44-44-4-4-44440444-4-4-4-4-4-400004-44-400000000000000000000000000000000000000000000000000000000000000000
χ834-4-4444-2-22-44-44-4-424-2-204-2-2-42222-40000-22-220000000000000000000000000000000000000000000000000000−2i32i300000000000
χ844-4-4444-2-22-44-44-4-424-2-204-2-2-42222-40000-22-2200000000000000000000000000000000000000000000000000002i3−2i300000000000
χ854-4-444-244-4-442-2-42-4-24-20-24-22-42-4220000-22-2200000000000000000000000000000000000000000000000000000000−2i32i30000000
χ864-4-444-244-4-442-2-42-4-24-20-24-22-42-4220000-22-22000000000000000000000000000000000000000000000000000000002i3−2i30000000
χ874-4-44-2444-42-2-442-4-4-2-240-2-2422-42-420000-22-22000000000000000000000000000000000000000000000000000000−2i32i3000000000
χ884-4-44-2444-42-2-442-4-4-2-240-2-2422-42-420000-22-220000000000000000000000000000000000000000000000000000002i3−2i3000000000
χ898888-4-4-4-4-4-4-4-4-4-4-4-42228222222222-4-400-1-1-1-1-4-4222222-1-1-1-100000000000000000000000000000000000000000000000000000
χ908888-4-4-4-4-4-4-4-4-4-4-4-4222-82222222224400-1-1-1-144-2-2-2-2-2-2111100000000000000000000000000000000000000000000000000000
χ9188-8-8-4-48-88-44-4444-82-4-40-244-2-4-4442000022-2-200000000000000000000000000000000000000000000000000000000000000000
χ9288-8-8-4-4-44-4-44-444442220-2-2-2-222-2-2243−4300-1-1110000−2323−232333−3−300000000000000000000000000000000000000000000000000000
χ9388-8-8-4-4-44-4-44-444442220-2-2-2-222-2-22−434300-1-111000023−2323−23−3−33300000000000000000000000000000000000000000000000000000
χ948-88-88-4-444-8-8448-4-4-4-42044-2-44-2-42400002-2-2200000000000000000000000000000000000000000000000000000000000000000
χ958-88-8-48-44444-8-8-48-4-42-404-24-4-242-4400002-2-2200000000000000000000000000000000000000000000000000000000000000000
χ968-88-8-4-4-4444444-4-4-42220-2-2-22-2-222-20000-111-1006-60000-33-3300000000000000000000000000000000000000000000000000000
χ978-88-8-4-4-4444444-4-4-42220-2-2-22-2-222-20000-111-100-6600003-33-300000000000000000000000000000000000000000000000000000
χ988-8-888-4-4-44-884-4-844-4-420-4-4244-24-2400002-22-200000000000000000000000000000000000000000000000000000000000000000
χ998-8-88-48-4-444-4-884-84-42-40-42-44-24-24400002-22-200000000000000000000000000000000000000000000000000000000000000000
χ1008-8-88-4-488-84-44-444-82-4-402-4-4-24444-200002-22-200000000000000000000000000000000000000000000000000000000000000000
χ1018-8-88-4-4-4-444-44-44442220222-2-2-2-2-2-20000-11-110000000033−33−333300000000000000000000000000000000000000000000000000000
χ1028-8-88-4-4-4-444-44-44442220222-2-2-2-2-2-20000-11-1100000000−333333−3300000000000000000000000000000000000000000000000000000

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