Finite Group Databasebeta

← Group #13168229

Character table — Group #13168229

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111122222222222244444444444444466888888888888888812121212121212121212121212181824242424242424242424242424242424242424243636363636363636363636363654547272108
order122233366666666633346666666661212223666121212121212121212121212244446666121212124466666612121212121212121212121212124444412121212121212124412122
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-111-1111111-1-1-1-11111111-1-11-111111-1-1-1-111-1-1-1-1-1-1-111-1-1-1-11-1-1
χ31111111111111111111111111111111111111111111111111-11-1111111-1-111-1-1-1-111-1-1111-11111-1-11111-1-1-111-1-1-1-1-1-111-1-1-11-1
χ41111111111111111111111111111111111111111111111111-1-1-11-11111-1-1-1-111-1-111-1-11-1-1-1-1111-1-1-1-1-1-1-1-11-1-11111-1-1-1-111-1-11
χ51111111111111111111111111111111-1-11111111111111111111-11-1-1-1-111111111-1-111-11111-1-1-1111111-1-11-1-11111-1-1-1-1-1-1-1-1-1
χ61111111111111111111111111111111-1-111111111111111111-11-1-1-1-1-1-111-1-1-1-111-1-111-1-1-11-1-1-1-111-1-1-1-1-1-1-111-1-1-1-1-1-11111-111
χ71111111111111111111111111111111-1-11111111111111111-11-1-11-1-1-1-1-1-111-1-1-1-1-1-1-1-1-111-11-1-1-1-1-1111111-1-1-1-1-1-1-111-1-1111-11
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
χ91111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-11111-1-1-1-111111111-111-1-1-1-1-1-1-1-1-1111-1-11-111-1-1-1-1-1-11111-1
χ101111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-111111-1-111-1-1111111-1-1-1-11-1-1-1-1-111-1-11-11-11-1-111-1-111-1-11-11
χ111111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-111-1-1-1111-1-1-1-111-1-111-1111-1-1-11111-1-1-1-1-111
χ121111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-111111111111-1-111-1-1-1-1-111-1-1-11111-1-1-11-1-1111-1-1111111-1-1-1
χ131111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-11-1-1-1-1-1-1-1-1-11111-1-111111-1-1111-1-1-1-111-11-1-1111-1-11111-1-1-1-11
χ141111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-1-1-1-1-111-1-111-1-1111-1-1-11111-1-111-1-1-1111-1-1-11111-1-111-11-1
χ151111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-111111-1-1111-11-11-1-111-1-111111-1-1
χ161111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1111111-1-1-1-1-1-11-1-1111111111-1-11-1-11-111-1-1-1-1-1-1-1-1111
χ17222222-12-1-12222-122-1-122-1-1-1-12-1-122222-1-1-1-1-12-1-1-1-122-1-1-1-12022022-1-1-1-100002-1-1-1-1-1-100202-1-1-1-10000220000000-1-10000-100
χ18222222-12-1-12222-122-1-122-1-1-1-12-1-122222-1-1-1-1-12-1-1-1-122-1-1-1-1-20-22022-1-1110000-21-1-111-100-202-1-1110000-2-20000000110000100
χ19222222-12-1-12222-122-1-122-1-1-1-12-1-1222-2-2-1-1-1-1-12-1-1-1-122-1-1-1-1202-20-2-211-1-100002-111-1-110020-211-1-10000-2-20000000110000100
χ20222222-12-1-12222-122-1-122-1-1-1-12-1-1222-2-2-1-1-1-1-12-1-1-1-122-1-1-1-1-20-2-20-2-211110000-211111100-20-211110000220000000-1-10000-100
χ21222222-12-1-12222-122-1-1-22-1-1-1-12-1-12-2-222-1-1-1-11-21111-2-2111120-2-2022-1-11100002-1-1-1-1-1100-20-2111100002-20000000110000-100
χ22222222-12-1-12222-122-1-1-22-1-1-1-12-1-12-2-222-1-1-1-11-21111-2-21111-202-2022-1-1-1-10000-21-1-11110020-211-1-10000-220000000-1-10000100
χ23222222-12-1-12222-122-1-1-22-1-1-1-12-1-12-2-2-2-2-1-1-1-11-21111-2-2111120-220-2-2111100002-111-1-1-100-202-1-1110000-220000000-1-10000100
χ24222222-12-1-12222-122-1-1-22-1-1-1-12-1-12-2-2-2-2-1-1-1-11-21111-2-21111-20220-2-211-1-10000-211111-100202-1-1-1-100002-20000000110000-100
χ2522222-122222-1-1-122-12-12-12-12-1-12-1-1-1-100-1-1-1-12222-1-1-1-1-1-1-1-1222020000222222-1200-1-102-1-1-1000-1-1-1-1-1-100200-1-1-1-1000000000
χ2622222-122222-1-1-122-12-12-12-12-1-12-1-1-1-100-1-1-1-12222-1-1-1-1-1-1-1-12-220-2000022-2-2-2-2-1200-1-10-21-11000-1-1111100-2001111000000000
χ2722222-122222-1-1-122-12-12-12-12-1-12-1-1-1-100-1-1-1-12222-1-1-1-1-1-1-1-1-22-2020000-2-222-2-21-2001102-11-100011-1-1-1-100-2001111000000000
χ2822222-122222-1-1-122-12-12-12-12-1-12-1-1-1-100-1-1-1-12222-1-1-1-1-1-1-1-1-2-2-20-20000-2-2-2-2221-200110-211100011111100200-1-1-1-1000000000
χ2922222-122222-1-1-122-12-1-2-12-12-1-12-1-11100-1-1-1-1-2-2-2-21111111122-20-20000-2-2-2-222-1200-1-102-1110001111-1-100-200-1-111000000000
χ3022222-122222-1-1-122-12-1-2-12-12-1-12-1-11100-1-1-1-1-2-2-2-2111111112-2-2020000-2-222-2-2-1200-1-10-211-100011-1-1110020011-1-1000000000
χ3122222-122222-1-1-122-12-1-2-12-12-1-12-1-11100-1-1-1-1-2-2-2-211111111-2220-2000022-2-2-2-21-2001102-1-11000-1-111-1-10020011-1-1000000000
χ3222222-122222-1-1-122-12-1-2-12-12-1-12-1-11100-1-1-1-1-2-2-2-211111111-2-220200002222221-200110-21-1-1000-1-1-1-11100-200-1-111000000000
χ332222-122-122-12222-1-1-122-1-12-12-1-12-12222-1-1-1-12-1-1-122-1-1-1-1-1-102022-1-12200-1-10000-1-1002-1202-1-1-100-1-1-1-100022000000-1-1000-10
χ342222-122-122-12222-1-1-122-1-12-12-1-12-12222-1-1-1-12-1-1-122-1-1-1-1-1-10-202-2-1-12200110000-1-10021-20-2-1-1-1001111000-2-20000001100010
χ352222-122-122-12222-1-1-122-1-12-12-1-12-122-2-2-1-1-1-12-1-1-122-1-1-1-1-1-1020-2211-2-200-1-100001100-2-120211100-1-1-1-1000-2-20000001100010
χ362222-122-122-12222-1-1-122-1-12-12-1-12-122-2-2-1-1-1-12-1-1-122-1-1-1-1-1-10-20-2-211-2-2001100001100-21-20-211100111100022000000-1-1000-10
χ372222-122-122-12222-1-1-12-2-1-12-12-1-12-1-2-222-1-1-1-1-2111-2-2111111020-2-2-1-12200110000-1-100-2-120-21110011-1-10002-200000011000-10
χ382222-122-122-12222-1-1-12-2-1-12-12-1-12-1-2-222-1-1-1-1-2111-2-21111110-20-22-1-12200-1-10000-1-100-21-20211100-1-111000-22000000-1-100010
χ392222-122-122-12222-1-1-12-2-1-12-12-1-12-1-2-2-2-2-1-1-1-1-2111-2-21111110202-211-2-20011000011002-120-2-1-1-10011-1-1000-22000000-1-100010
χ402222-122-122-12222-1-1-12-2-1-12-12-1-12-1-2-2-2-2-1-1-1-1-2111-2-21111110-202211-2-200-1-10000110021-202-1-1-100-1-1110002-200000011000-10
χ412-22-22222-2-2-2-22-22-2222022-2-2-2-2-22-2002-222-2-2000000000000000002-22-200002i−2i002-20000000000000000000002i−2i0000002i−2i000
χ422-22-22222-2-2-2-22-22-2222022-2-2-2-2-22-2002-222-2-2000000000000000002-22-20000−2i2i002-2000000000000000000000−2i2i000000−2i2i000
χ432-22-22222-2-2-2-22-22-2222022-2-2-2-2-22-200-2222-2-200000000000000000-22-2200002i−2i00-220000000000000000000002i−2i000000−2i2i000
χ442-22-22222-2-2-2-22-22-2222022-2-2-2-2-22-200-2222-2-200000000000000000-22-220000−2i2i00-22000000000000000000000−2i2i0000002i−2i000
χ4544444-2-24-2-24-2-2-2-24-2-214-2-21-21-2-21-2-2-2001111-24-2-211-2-21111404000000-2-20000-2-20011000-20000110000000000000000000000
χ4644444-2-24-2-24-2-2-2-24-2-214-2-21-21-2-21-2-2-2001111-24-2-211-2-21111-40-40000002200002200-1-100020000-1-10000000000000000000000
χ4744444-2-24-2-24-2-2-2-24-2-21-4-2-21-21-2-21-2220011112-422-1-122-1-1-1-140-4000000220000-2-2001100020000-1-10000000000000000000000
χ4844444-2-24-2-24-2-2-2-24-2-21-4-2-21-21-2-21-2220011112-422-1-122-1-1-1-1-404000000-2-200002200-1-1000-20000110000000000000000000000
χ494444-24-2-2-2-2-2444-2-2-21-24-21-21-2-21-2-244441111-2-211-2-2-2-2111100040-2-2-2-2000000001100-20000-211000000000000000000000000
χ504444-24-2-2-2-2-2444-2-2-21-24-21-21-2-21-2-244-4-41111-2-211-2-2-2-21111000-40222200000000-1-100200002-1-1000000000000000000000000
χ514444-24-2-2-2-2-2444-2-2-21-2-4-21-21-2-21-2-2-4-444111122-1-12222-1-1-1-1000-40-2-2-2-2000000001100200002-1-1000000000000000000000000
χ524444-24-2-2-2-2-2444-2-2-21-2-4-21-21-2-21-2-2-4-4-4-4111122-1-12222-1-1-1-100040222200000000-1-100-20000-211000000000000000000000000
χ534444-2-24-244-2-2-2-24-21-2-241-2-2-2-21-2-21-2-20011114-2-2-2-2-211111104004000000-2-2000000000-2-20-2000001111000000000000000000
χ544444-2-24-244-2-2-2-24-21-2-241-2-2-2-21-2-21-2-20011114-2-2-2-2-21111110-400-400000022000000000220200000-1-1-1-1000000000000000000
χ554444-2-24-244-2-2-2-24-21-2-2-41-2-2-2-21-2-2122001111-422222-1-1-1-1-1-10400-400000022000000000-2-20200000-1-111000000000000000000
χ564444-2-24-244-2-2-2-24-21-2-2-41-2-2-2-21-2-2122001111-422222-1-1-1-1-1-10-4004000000-2-2000000000220-20000011-1-1000000000000000000
χ5744-4-4444-44-444-4-4-4-44440-4-4-444-4-4-4400004-4-4400000000000000000000000000000000000000000000000000000000000000000
χ5844-4-444-2-4-2244-4-42-44-2-20-422-2-2-42240000-222-20000000000000000000000000000000000000000000000000000000023−230000000
χ5944-4-444-2-4-2244-4-42-44-2-20-422-2-2-42240000-222-200000000000000000000000000000000000000000000000000000000−23230000000
χ6044-4-44-24-44-44-222-4-4-24-202-424-22-42-20000-222-200000000000000000000000000000000000000000000000000000023−23000000000
χ6144-4-44-24-44-44-222-4-4-24-202-424-22-42-20000-222-2000000000000000000000000000000000000000000000000000000−2323000000000
χ6244-4-4-24424-4-24-4-4-42-2-24022-4-2422-4-20000-222-2000000000000000000000000000000000000000000000000000000000023−2300000
χ6344-4-4-24424-4-24-4-4-42-2-24022-4-2422-4-20000-222-20000000000000000000000000000000000000000000000000000000000−232300000
χ644-44-444-2422-4-44-4-2-44-2-204-2222-42-2-4004-4-2-222000000000000000004-4-2200000000-220000000000000000000000000000000000
χ654-44-444-2422-4-44-4-2-44-2-204-2222-42-2-400-44-2-22200000000000000000-442-2000000002-20000000000000000000000000000000000
χ664-44-44-244-4-4-42-224-4-24-20-242-422-4-220000-2-22200000000000000000000000004i−4i0000000000000000000000000−2i2i00000000000
χ674-44-44-244-4-4-42-224-4-24-20-242-422-4-220000-2-2220000000000000000000000000−4i4i00000000000000000000000002i−2i00000000000
χ684-44-4-244-2-4-42-44-442-2-240-2-2-42-42242004-4-2-22200000000000000000-224-400000000-220000000000000000000000000000000000
χ694-44-4-244-2-4-42-44-442-2-240-2-2-42-4224200-44-2-222000000000000000002-2-44000000002-20000000000000000000000000000000000
χ704-44-4-24-2-2222-44-4-22-21-20-212-122-1-22004-411-1-1003i−3i00003i3i−3i−3i00000-22-22000000001-1000000003i−3i000000000000000000000000
χ714-44-4-24-2-2222-44-4-22-21-20-212-122-1-22004-411-1-100−3i3i0000−3i−3i3i3i00000-22-22000000001-100000000−3i3i000000000000000000000000
χ724-44-4-24-2-2222-44-4-22-21-20-212-122-1-2200-4411-1-1003i−3i00003i3i−3i−3i000002-22-200000000-1100000000−3i3i000000000000000000000000
χ734-44-4-24-2-2222-44-4-22-21-20-212-122-1-2200-4411-1-100−3i3i0000−3i−3i3i3i000002-22-200000000-11000000003i−3i000000000000000000000000
χ744-4-44444-4-44-4-4-44-444440-4-44-4-444-4-400004-44-400000000000000000000000000000000000000000000000000000000000000000
χ754-4-4444-2-42-2-4-4-44244-2-20-42-2224-22-40000-22-2200000000000000000000023−2300000000000000000023−230000000000000000000000
χ764-4-4444-2-42-2-4-4-44244-2-20-42-2224-22-40000-22-22000000000000000000000−2323000000000000000000−23230000000000000000000000
χ774-4-444-24-4-44-422-2-44-24-202-4-2-42-242223−2300-22-22000023−2323−2323−2323−2300000000000000000000000000000000000000000000000000000
χ784-4-444-24-4-44-422-2-44-24-202-4-2-42-2422−232300-22-220000−2323−2323−2323−232300000000000000000000000000000000000000000000000000000
χ794-4-444-2-2-42-2-422-224-2-2102212-1-2-2-1223−23001-11-10000−3323−23−33−3300000000023−23000000003-300000000−330000000000000000000000
χ804-4-444-2-2-42-2-422-224-2-2102212-1-2-2-1223−23001-11-10000−3323−23−33−33000000000−232300000000-33000000003−30000000000000000000000
χ814-4-444-2-2-42-2-422-224-2-2102212-1-2-2-12−2323001-11-100003−3−23233−33−300000000023−2300000000-3300000000−330000000000000000000000
χ824-4-444-2-2-42-2-422-224-2-2102212-1-2-2-12−2323001-11-100003−3−23233−33−3000000000−2323000000003-3000000003−30000000000000000000000
χ834-4-44-2442-442-4-44-4-2-2-2402242-4-2-2-420000-22-2200000000000000000000000−2i32i3000000000000000000−2i32i300000000000000000000
χ844-4-44-2442-442-4-44-4-2-2-2402242-4-2-2-420000-22-22000000000000000000000002i3−2i30000000000000000002i3−2i300000000000000000000
χ854-4-44-2-242-44222-2-4-21-2-20-12-2221-22-123−23001-11-1000023−23−33−33−3300000000000−2i32i3000000000000000000i3−i33i−3i000000000000000000
χ864-4-44-2-242-44222-2-4-21-2-20-12-2221-22-123−23001-11-1000023−23−33−33−33000000000002i3−2i3000000000000000000−i3i3−3i3i000000000000000000
χ874-4-44-2-242-44222-2-4-21-2-20-12-2221-22-1−2323001-11-10000−23233−33−33−300000000000−2i32i3000000000000000000i3−i3−3i3i000000000000000000
χ884-4-44-2-242-44222-2-4-21-2-20-12-2221-22-1−2323001-11-10000−23233−33−33−3000000000002i3−2i3000000000000000000−i3i33i−3i000000000000000000
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
χ9188-8-88-4-4-8-448-4444-8-4-42044-2-4244-2-400002-2-2200000000000000000000000000000000000000000000000000000000000000000
χ9288-8-8-48-44-44-48-8-844-42-404-242-44-24-400002-2-2200000000000000000000000000000000000000000000000000000000000000000
χ9388-8-8-4-4848-8-4-444-842-4-40-244-4-4-244200002-2-2200000000000000000000000000000000000000000000000000000000000000000
χ9488-8-8-4-4-44-44-4-444442220-2-2-222-2-2-220000-111-100000000−3i33i33i3−3i300000000000000000000000000000000000000000000000000000
χ9588-8-8-4-4-44-44-4-444442220-2-2-222-2-2-220000-111-1000000003i3−3i3−3i33i300000000000000000000000000000000000000000000000000000
χ968-88-88-4-4844-84-44-4-8-4-420-4-4-24-24424000022-2-200000000000000000000000000000000000000000000000000000000000000000
χ978-88-8-4-48-4-8-844-44842-4-402-4444-24-4-2000022-2-200000000000000000000000000000000000000000000000000000000000000000
χ988-88-8-4-4-4-44444-44-44222022-2-2-2-2-22-20000-1-111006i−6i0000−3i−3i3i3i00000000000000000000000000000000000000000000000000000
χ998-88-8-4-4-4-44444-44-44222022-2-2-2-2-22-20000-1-11100−6i6i00003i3i−3i−3i00000000000000000000000000000000000000000000000000000
χ1008-8-88-48-444-44-8-884-4-42-404-2-4-24-424400002-22-200000000000000000000000000000000000000000000000000000000000000000
χ1018-8-88-4-4-444-4444-44-42220-2-22-2-222-2-243−4300-11-110000−2323−23233−33−300000000000000000000000000000000000000000000000000000
χ1028-8-88-4-4-444-4444-44-42220-2-22-2-222-2-2−434300-11-11000023−2323−23−33−3300000000000000000000000000000000000000000000000000000

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