Finite Group Databasebeta

← Group #13168224

Character table — Group #13168224

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111122222222222244444444444444466888888888888888812121212121212121212121212181824242424242424242424242424242424242424243636363636363636363636363654547272108
order1222333666666666333466666666612122236661212121212121212121212122444466661212121244666666121212121212121212121212121224444661212121212124412124
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111-11-1111111-1-1-1-111111111-11-1-11111-1-1-1-1-111-1-1-1-1-1-111-1-1-1-11-1-1
χ31111111111111111111111111111111111111111111111111-111-111111-1-111-1-1-1-111-1-11-1111111-1-11111-1-1-111-1-1-1-1-1-111-1-1-11-1
χ41111111111111111111111111111111111111111111111111-11-1-1-11111-1-1-1-111-1-111-1-11-1-11-1-111-1-1-1-1-1-11-1-1-1-11111-1-1-1-111-1-11
χ51111111111111111111111111111111-1-111111111111111111-1111-1-1-1-111111111-1-111-111-111-1-11111111-1-1-1-11111-1-1-1-1-1-1-1-1-1
χ61111111111111111111111111111111-1-111111111111111111-1-11-1-1-1-1-111-1-1-1-111-1-111-11-1-1-1-1-1-111-1-1-1-1-1-1-111-1-1-1-1-1-11111-111
χ71111111111111111111111111111111-1-11111111111111111-1-11-11-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11-111-1-1-1-11111-111-1-1-1-1-1-111-1-1111-11
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
χ91111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-11-1-11111-1-1-1-111111111-1-11-11-1-1-1-1-111-1-1-11-11-1-1-111-1-1-1-11111-1
χ101111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-111111-1-111-1-1111111-1-1-1-1-11-1-1-1-1-1-11111-1-1111-1-1-1-111-1-11-11
χ111111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1111111-1-1-1-1-1-111-1-1-111-11-1-1-11111-1-11-111-111-1-111-1-1-1-1-111
χ121111111111111111111-1111111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-1-11-1-1-11-1-111-1-111-1-11-11-1-111111111-1-1-1
χ131111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-11111-1-1111-1111-111-1-111-1-1-1-11-11-1-1111111-1-1-1-11
χ141111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-11-1-1-1-1-1-111-1-111-1-1111-1-11-1111-1-1-1-1111-111-111-1-111-1-111-11-1
χ151111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111-1111111-1-111-1-1111-1-1-1-111111-1-1
χ161111111111111111111-1111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11-111-1-1-1-1111111-1-1-1-1-1-111-11-111111-1-111-11-11-1-1-111-1-1-1-1-1-1111
χ17222222-1222-1-12-122-12-12-12-12-1-12-1-1-1-100-1-1-1-12222-1-1-1-1-1-1-1-12022200002222222-100-1-10-1-102-100-1-1-1-1-1-120000-1-1-1-1000000000
χ18222222-1222-1-12-122-12-12-12-12-1-12-1-1-1-100-1-1-1-12222-1-1-1-1-1-1-1-120-22-2000022-2-2-2-22-100-1-10-110-2100-1-11111-200001111000000000
χ19222222-1222-1-12-122-12-12-12-12-1-12-1-1-1-100-1-1-1-12222-1-1-1-1-1-1-1-1-202-220000-2-222-2-2-21001101-102-10011-1-1-1-1-200001111000000000
χ20222222-1222-1-12-122-12-12-12-12-1-12-1-1-1-100-1-1-1-12222-1-1-1-1-1-1-1-1-20-2-2-20000-2-2-2-222-2100110110-210011111120000-1-1-1-1000000000
χ21222222-1222-1-12-122-12-1-2-12-12-1-12-1-11100-1-1-1-1-2-2-2-211111111202-2-20000-2-2-2-2222-100-1-101-10210011-1-111-2000011-1-1000000000
χ22222222-1222-1-12-122-12-1-2-12-12-1-12-1-11100-1-1-1-1-2-2-2-21111111120-2-220000-2-222-2-22-100-1-10110-2-1001111-1-120000-1-111000000000
χ23222222-1222-1-12-122-12-1-2-12-12-1-12-1-11100-1-1-1-1-2-2-2-211111111-2022-2000022-2-2-2-2-2100110-1-102100-1-1-1-11120000-1-111000000000
χ24222222-1222-1-12-122-12-1-2-12-12-1-12-1-11100-1-1-1-1-2-2-2-211111111-20-2220000222222-2100110-110-2-100-1-111-1-1-2000011-1-1000000000
χ2522222-122-1-12222-122-1-122-1-1-1-12-1-122222-1-1-1-1-12-1-1-1-122-1-1-1-12202022-1-1-1-10000-12-1-1-1-1-120200-1-1-1-10000022000000-1-10000-100
χ2622222-122-1-12222-122-1-122-1-1-1-12-1-122222-1-1-1-1-12-1-1-1-122-1-1-1-1-220-2022-1-11100001-2-1-111-1-20200-1-11100000-2-2000000110000100
χ2722222-122-1-12222-122-1-122-1-1-1-12-1-1222-2-2-1-1-1-1-12-1-1-1-122-1-1-1-12-2020-2-211-1-10000-1211-1-1120-20011-1-100000-2-2000000110000100
χ2822222-122-1-12222-122-1-122-1-1-1-12-1-1222-2-2-1-1-1-1-12-1-1-1-122-1-1-1-1-2-20-20-2-2111100001-211111-20-20011110000022000000-1-10000-100
χ2922222-122-1-12222-122-1-1-22-1-1-1-12-1-12-2-222-1-1-1-11-21111-2-211112-20-2022-1-1110000-12-1-1-1-11-20-2001111000002-2000000110000-100
χ3022222-122-1-12222-122-1-1-22-1-1-1-12-1-12-2-222-1-1-1-11-21111-2-21111-2-202022-1-1-1-100001-2-1-111120-20011-1-100000-22000000-1-10000100
χ3122222-122-1-12222-122-1-1-22-1-1-1-12-1-12-2-2-2-2-1-1-1-11-21111-2-21111220-20-2-211110000-1211-1-1-1-20200-1-11100000-22000000-1-10000100
χ3222222-122-1-12222-122-1-1-22-1-1-1-12-1-12-2-2-2-2-1-1-1-11-21111-2-21111-22020-2-211-1-100001-21111-120200-1-1-1-1000002-2000000110000-100
χ332222-122-12222-122-1-1-122-1-12-12-1-12-12222-1-1-1-12-1-1-122-1-1-1-1-1-102202-1-12200-1-10000-1-100202-1-12-1-100-1-1-1-100022000000-1-1000-10
χ342222-122-12222-122-1-1-122-1-12-12-1-12-12222-1-1-1-12-1-1-122-1-1-1-1-1-102-20-2-1-12200110000-1-10020-2-11-2-1-1001111000-2-20000001100010
χ352222-122-12222-122-1-1-122-1-12-12-1-12-122-2-2-1-1-1-12-1-1-122-1-1-1-1-1-10-220211-2-200-1-100001100-2021-121100-1-1-1-1000-2-20000001100010
χ362222-122-12222-122-1-1-122-1-12-12-1-12-122-2-2-1-1-1-12-1-1-122-1-1-1-1-1-10-2-20-211-2-2001100001100-20-211-21100111100022000000-1-1000-10
χ372222-122-12222-122-1-1-12-2-1-12-12-1-12-1-2-222-1-1-1-1-2111-2-21111110-220-2-1-12200110000-1-100-2021-1-21100-1-1110002-200000011000-10
χ382222-122-12222-122-1-1-12-2-1-12-12-1-12-1-2-222-1-1-1-1-2111-2-21111110-2-202-1-12200-1-10000-1-100-20-2112110011-1-1000-22000000-1-100010
χ392222-122-12222-122-1-1-12-2-1-12-12-1-12-1-2-2-2-2-1-1-1-1-2111-2-21111110220-211-2-2001100001100202-1-1-2-1-100-1-111000-22000000-1-100010
χ402222-122-12222-122-1-1-12-2-1-12-12-1-12-1-2-2-2-2-1-1-1-1-2111-2-211111102-20211-2-200-1-10000110020-2-112-1-10011-1-10002-200000011000-10
χ412-22-22222-2-22-2-2-22-2222022-2-2-2-2-22-2002-222-2-2000000000000000002-22-200002i−2i002-2000000000000000000000002i−2i00002i−2i000
χ422-22-22222-2-22-2-2-22-2222022-2-2-2-2-22-2002-222-2-2000000000000000002-22-20000−2i2i002-200000000000000000000000−2i2i0000−2i2i000
χ432-22-22222-2-22-2-2-22-2222022-2-2-2-2-22-200-2222-2-200000000000000000-22-2200002i−2i00-22000000000000000000000002i−2i0000−2i2i000
χ442-22-22222-2-22-2-2-22-2222022-2-2-2-2-22-200-2222-2-200000000000000000-22-220000−2i2i00-2200000000000000000000000−2i2i00002i−2i000
χ4544444-2-24-2-2-2-24-2-24-2-214-2-21-21-2-21-2-2-2001111-24-2-211-2-21111400400000-2-20000-2-200110-2000000110000000000000000000000
χ4644444-2-24-2-2-2-24-2-24-2-214-2-21-21-2-21-2-2-2001111-24-2-211-2-21111-400-4000002200002200-1-102000000-1-10000000000000000000000
χ4744444-2-24-2-2-2-24-2-24-2-21-4-2-21-21-2-21-2220011112-422-1-122-1-1-1-1400-400000220000-2-2001102000000-1-10000000000000000000000
χ4844444-2-24-2-2-2-24-2-24-2-21-4-2-21-21-2-21-2220011112-422-1-122-1-1-1-1-400400000-2-200002200-1-10-2000000110000000000000000000000
χ494444-24-2-244-2-2-2-24-21-2-241-2-2-2-21-2-21-2-20011114-2-2-2-2-211111100404000000-2-20000000000-20-2-200001111000000000000000000
χ504444-24-2-244-2-2-2-24-21-2-241-2-2-2-21-2-21-2-20011114-2-2-2-2-211111100-40-400000022000000000020220000-1-1-1-1000000000000000000
χ514444-24-2-244-2-2-2-24-21-2-2-41-2-2-2-21-2-2122001111-422222-1-1-1-1-1-10040-4000000220000000000-20-22000011-1-1000000000000000000
χ524444-24-2-244-2-2-2-24-21-2-2-41-2-2-2-21-2-2122001111-422222-1-1-1-1-1-100-404000000-2-20000000000202-20000-1-111000000000000000000
χ534444-2-24-2-2-244-24-2-2-21-24-21-21-2-21-2-244441111-2-211-2-2-2-2111104000-2-2-2-2000000001100-200-20011000000000000000000000000
χ544444-2-24-2-2-244-24-2-2-21-24-21-21-2-21-2-244-4-41111-2-211-2-2-2-211110-4000222200000000-1-100200200-1-1000000000000000000000000
χ554444-2-24-2-2-244-24-2-2-21-2-4-21-21-2-21-2-2-4-444111122-1-12222-1-1-1-10-4000-2-2-2-2000000001100200200-1-1000000000000000000000000
χ564444-2-24-2-2-244-24-2-2-21-2-4-21-21-2-21-2-2-4-4-4-4111122-1-12222-1-1-1-104000222200000000-1-100-200-20011000000000000000000000000
χ5744-4-4444-4-44-444-4-4-44440-4-44-4-444-4-400004-44-400000000000000000000000000000000000000000000000000000000000000000
χ5844-4-444-2-4-442-242-4-4-24-202-4-2-42-242223−2300-22-22000023−2323−232323−23−2300000000000000000000000000000000000000000000000000000
χ5944-4-444-2-4-442-242-4-4-24-202-4-2-42-2422−232300-22-220000−2323−2323−23−23232300000000000000000000000000000000000000000000000000000
χ6044-4-44-24-42-2-444-42-44-2-20-42-2224-22-40000-22-2200000000000000000000023−2300000000000000000023−230000000000000000000000
χ6144-4-44-24-42-2-444-42-44-2-20-42-2224-22-40000-22-22000000000000000000000−2323000000000000000000−23230000000000000000000000
χ6244-4-44-2-2-42-22-2422-4-2-2102212-1-2-2-1223−23001-11-10000−3323−23−3−33300000000023−23000000003-300000000−330000000000000000000000
χ6344-4-44-2-2-42-22-2422-4-2-2102212-1-2-2-1223−23001-11-10000−3323−23−3−333000000000−232300000000-33000000003−30000000000000000000000
χ6444-4-44-2-2-42-22-2422-4-2-2102212-1-2-2-12−2323001-11-100003−3−232333−3−300000000023−2300000000-3300000000−330000000000000000000000
χ6544-4-44-2-2-42-22-2422-4-2-2102212-1-2-2-12−2323001-11-100003−3−232333−3−3000000000−2323000000003-3000000003−30000000000000000000000
χ6644-4-4-2442-44-44-2-4-42-2-2402242-4-2-2-420000-22-220000000000000000000000023−230000000000000000000023−23000000000000000000
χ6744-4-4-2442-44-44-2-4-42-2-2402242-4-2-2-420000-22-2200000000000000000000000−232300000000000000000000−2323000000000000000000
χ6844-4-4-24-22-442-2-22-421-2-20-12-2221-22-123−23001-11-1000023−23−33−3−3330000000000023−230000000000000000003-3−33000000000000000000
χ6944-4-4-24-22-442-2-22-421-2-20-12-2221-22-123−23001-11-1000023−23−33−3−33300000000000−2323000000000000000000-333−3000000000000000000
χ7044-4-4-24-22-442-2-22-421-2-20-12-2221-22-1−2323001-11-10000−23233−333−3−30000000000023−23000000000000000000-33−33000000000000000000
χ7144-4-4-24-22-442-2-22-421-2-20-12-2221-22-1−2323001-11-10000−23233−333−3−300000000000−23230000000000000000003-33−3000000000000000000
χ724-44-444-24-4-4-22-424-4-24-20-242-422-4-220000-2-22200000000000000000000000004i−4i000000000000000000000000000−2i2i000000000
χ734-44-444-24-4-4-22-424-4-24-20-242-422-4-220000-2-2220000000000000000000000000−4i4i0000000000000000000000000002i−2i000000000
χ744-44-44-244224-4-4-4-2-44-2-204-2222-42-2-4004-4-2-222000000000000000004-4-2200000000-220000000000000000000000000000000000
χ754-44-44-244224-4-4-4-2-44-2-204-2222-42-2-400-44-2-22200000000000000000-442-2000000002-20000000000000000000000000000000000
χ764-44-4-244-2-4-44-42-442-2-240-2-2-42-42242004-4-2-22200000000000000000-224-400000000-220000000000000000000000000000000000
χ774-44-4-244-2-4-44-42-442-2-240-2-2-42-4224200-44-2-222000000000000000002-2-44000000002-20000000000000000000000000000000000
χ784-44-4-2-24-2224-42-4-22-21-20-212-122-1-22004-411-1-1003i−3i00003i−3i3i−3i00000-22-22000000001-1000000003i−3i000000000000000000000000
χ794-44-4-2-24-2224-42-4-22-21-20-212-122-1-22004-411-1-100−3i3i0000−3i3i−3i3i00000-22-22000000001-100000000−3i3i000000000000000000000000
χ804-44-4-2-24-2224-42-4-22-21-20-212-122-1-2200-4411-1-1003i−3i00003i−3i3i−3i000002-22-200000000-1100000000−3i3i000000000000000000000000
χ814-44-4-2-24-2224-42-4-22-21-20-212-122-1-2200-4411-1-100−3i3i0000−3i3i−3i3i000002-22-200000000-11000000003i−3i000000000000000000000000
χ824-4-44444-44-4-4-4-44-444440-4-4-444-4-4-4400004-4-4400000000000000000000000000000000000000000000000000000000000000000
χ834-4-4444-2-44-422-4-2-44-24-202-424-22-42-20000-222-20000000000000000000000000000000000000000000000000000−2i32i300000000000
χ844-4-4444-2-44-422-4-2-44-24-202-424-22-42-20000-222-200000000000000000000000000000000000000000000000000002i3−2i300000000000
χ854-4-444-24-4-22-4-4-44244-2-20-422-2-2-42240000-222-20000000000000000000000000000000000000000000000000000000023−230000000
χ864-4-444-24-4-22-4-4-44244-2-20-422-2-2-42240000-222-200000000000000000000000000000000000000000000000000000000−23230000000
χ874-4-44-24424-4-4-424-4-2-2-24022-4-2422-4-20000-222-20000000000000000000000000000000000000000000000000000000000−2i32i300000
χ884-4-44-24424-4-4-424-4-2-2-24022-4-2422-4-20000-222-200000000000000000000000000000000000000000000000000000000002i3−2i300000
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
χ9188-8-8-4-4844-4-88-4-844-42-404-2-4-24-424400002-22-200000000000000000000000000000000000000000000000000000000000000000
χ9288-8-8-4-4-444-44-4-44442220-2-22-2-222-2-243−4300-11-110000−2323−232333−3−300000000000000000000000000000000000000000000000000000
χ9388-8-8-4-4-444-44-4-44442220-2-22-2-222-2-2−434300-11-11000023−2323−23−3−33300000000000000000000000000000000000000000000000000000
χ948-88-88-4-4844-44-84-4-8-4-420-4-4-24-24424000022-2-200000000000000000000000000000000000000000000000000000000000000000
χ958-88-8-48-4-4-8-8-4444842-4-402-4444-24-4-2000022-2-200000000000000000000000000000000000000000000000000000000000000000
χ968-88-8-4-4-4-444-4444-44222022-2-2-2-2-22-20000-1-111006i−6i0000−3i3i−3i3i00000000000000000000000000000000000000000000000000000
χ978-88-8-4-4-4-444-4444-44222022-2-2-2-2-22-20000-1-11100−6i6i00003i−3i3i−3i00000000000000000000000000000000000000000000000000000
χ988-8-888-4-4-8-4444-8-448-4-42044-2-4244-2-400002-2-2200000000000000000000000000000000000000000000000000000000000000000
χ998-8-88-48-448-8444-4-8-42-4-40-244-4-4-244200002-2-2200000000000000000000000000000000000000000000000000000000000000000
χ1008-8-88-4-484-44-8-8484-4-42-404-242-44-24-400002-2-2200000000000000000000000000000000000000000000000000000000000000000
χ1018-8-88-4-4-44-44444-44-42220-2-2-222-2-2-220000-111-100000000−3i33i33i3−3i300000000000000000000000000000000000000000000000000000
χ1028-8-88-4-4-44-44444-44-42220-2-2-222-2-2-220000-111-1000000003i3−3i3−3i33i300000000000000000000000000000000000000000000000000000

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