Finite Group Databasebeta

← Group #13156257

Character table — Group #13156257

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11222222222224444444444444444444488888888888888121212121212121212121212181818181818242424242424242424242424242424242424242424363636727272727272216
order12233344666121233366666612121212121212121212123666666121212121212122466881212242424248824242424666812121224242424242424242424242424248242444121212128
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111-1111111111-1-1-1-1-1-1-1-1111-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-11111111-1-1-1-1-1-111111111-1-1-11-1-1-111-1
χ4111111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1111-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-11
χ511111111111111111111111111111111111111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-11-1-1-111111111111111-1-1-1-1111-1-1-1
χ611111111111111111111111111111111111111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-11-1-1-1111
χ711111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-11-1-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-11
χ811111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1
χ9222222-2-2222-2-2222222222-2-2-2-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-200002i−2i002i2i−2i−2i00000000000002i2i2i−2i−2i−2i000000000000000000
χ10222222-2-2222-2-2222222222-2-2-2-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-20000−2i2i00−2i−2i2i2i0000000000000−2i−2i−2i2i2i2i000000000000000000
χ1122222-12222-1222-1-122-12-1-12-1-1-122-122-1-1-12-1-1-1-1-12-1-1-1-1-1-1222200220000000000-1-1-12-1-1-100000022-1-1-1-1-1-10002000-1-10
χ1222222-12222-1222-1-122-12-1-12-1-1-122-122-1-1-12-1-1-1-1-12-1-1-1-1-1-1222200220000000000-1-1-1-2-1-1-1000000-2-2111111000-2000110
χ1322222-12222-1222-1-122-12-1-12-1-1-122-122-1-1-12-1-1-1-1-12-1-1-1-1-1-1-2-2-2-200-2-20000000000111211100000022-1-1-1-1-1-1000-2000110
χ1422222-12222-1222-1-122-12-1-12-1-1-122-122-1-1-12-1-1-1-1-12-1-1-1-1-1-1-2-2-2-200-2-20000000000111-2111000000-2-21111110002000-1-10
χ152222-1222-122-1-1-12-12-12-12-1-12-1-1222-1-122-1-12-1-1-1-1-12-1-1-1-1-122-1-122-1-1-1-1-1-122-1-1-1-12-1-102-1-12-1-12-1-1000000002-1-10000000
χ162222-1222-122-1-1-12-12-12-12-1-12-1-1222-1-122-1-12-1-1-1-1-12-1-1-1-1-122-1-1-2-2-1-11111-2-211112-1-102-1-1-211-21100000000-2110000000
χ172222-1222-122-1-1-12-12-12-12-1-12-1-1222-1-122-1-12-1-1-1-1-12-1-1-1-1-1-2-2112211-1-1-1-1-2-21111-2110-2112-1-12-1-100000000-2110000000
χ182222-1222-122-1-1-12-12-12-12-1-12-1-1222-1-122-1-12-1-1-1-1-12-1-1-1-1-1-2-211-2-211111122-1-1-1-1-2110-211-211-211000000002-1-10000000
χ192222-12-2-2-12211-12-12-12-12-11-211-2-2-211-2-2-1-12-1-1-1-11-21111100−i3i32i−2i−i3i3−i−iii0033−3−30−i3i300−i3i32i−i−i−2iii0000000003−30000000
χ202222-12-2-2-12211-12-12-12-12-11-211-2-2-211-2-2-1-12-1-1-1-11-21111100−i3i3−2i2i−i3i3ii−i−i00−3−3330−i3i300−i3i3−2iii2i−i−i000000000−330000000
χ212222-12-2-2-12211-12-12-12-12-11-211-2-2-211-2-2-1-12-1-1-1-11-21111100i3−i32i−2ii3−i3−i−iii00−3−3330i3−i300i3−i32i−i−i−2iii000000000−330000000
χ222222-12-2-2-12211-12-12-12-12-11-211-2-2-211-2-2-1-12-1-1-1-11-21111100i3−i3−2i2ii3−i3ii−i−i0033−3−30i3−i300i3−i3−2iii2i−i−i0000000003−30000000
χ23222-122222-1222-1-12-122-1-122222-1-12-1-1-1-1-1-1-12-1-1-1-1-12-1-1-1-10000220022220000000002000-1-1-1-1-1-1-1-122-1-1-1-100002-1-1000
χ24222-122222-1222-1-12-122-1-122222-1-12-1-1-1-1-1-1-12-1-1-1-1-12-1-1-1-1000022002222000000000-2000-1-1-1-1-1-111-2-211110000-211000
χ25222-122222-1222-1-12-122-1-122222-1-12-1-1-1-1-1-1-12-1-1-1-1-12-1-1-1-10000-2-200-2-2-2-20000000002000111111-1-122-1-1-1-10000-211000
χ26222-122222-1222-1-12-122-1-122222-1-12-1-1-1-1-1-1-12-1-1-1-1-12-1-1-1-10000-2-200-2-2-2-2000000000-200011111111-2-2111100002-1-1000
χ27222-122-2-22-12-2-2-1-12-122-1-12-2-2-2-211-21111-1-1-12-1-1-111-2111100002i−2i002i2i−2i−2i0000000000000−i−i−iiii3−30033−3−300000−i3i3000
χ28222-122-2-22-12-2-2-1-12-122-1-12-2-2-2-211-21111-1-1-12-1-1-111-2111100002i−2i002i2i−2i−2i0000000000000−i−i−iiii−3300−3−33300000i3−i3000
χ29222-122-2-22-12-2-2-1-12-122-1-12-2-2-2-211-21111-1-1-12-1-1-111-211110000−2i2i00−2i−2i2i2i0000000000000iii−i−i−i3−30033−3−300000i3−i3000
χ30222-122-2-22-12-2-2-1-12-122-1-12-2-2-2-211-21111-1-1-12-1-1-111-211110000−2i2i00−2i−2i2i2i0000000000000iii−i−i−i−3300−3−33300000−i3i3000
χ3122-22222-222222222-2-2-2222-22222-2-222-2-22-2-2-2-2-22-22-222-2-2000000000000222222000000000000000000000-2-2-20000000
χ3222-22222-222222222-2-2-2222-22222-2-222-2-22-2-2-2-2-22-22-222-2-2000000000000-2-2-2-2-2-20000000000000000000002220000000
χ3322-2222-22222-2-2222-2-2-22222-2-2-2-222-2-2222-2-2-2-2-222-22-2-2222-22200-2-200000000002220-2-2-2000000000000000000000000
χ3422-2222-22222-2-2222-2-2-22222-2-2-2-222-2-2222-2-2-2-2-222-22-2-222-22-2-200220000000000-2-2-20222000000000000000000000000
χ3522-222-1-2222-1-2-22-1-1-2-212-1-12111-22-1-2-2-1-1-1-21111-121-111-1-12-22200-2-20000000000-1-1-1011100000000−i3i3−i3i3−i3i30000000−i3i30
χ3622-222-1-2222-1-2-22-1-1-2-212-1-12111-22-1-2-2-1-1-1-21111-121-111-1-12-22200-2-20000000000-1-1-1011100000000i3−i3i3−i3i3−i30000000i3−i30
χ3722-222-1-2222-1-2-22-1-1-2-212-1-12111-22-1-2-2-1-1-1-21111-121-111-1-1-22-2-2002200000000001110-1-1-100000000−i3i3−i3i3−i3i30000000i3−i30
χ3822-222-1-2222-1-2-22-1-1-2-212-1-12111-22-1-2-2-1-1-1-21111-121-111-1-1-22-2-2002200000000001110-1-1-100000000i3−i3i3−i3i3−i30000000−i3i30
χ3922-22-122-2-122-1-1-12-1-21-2-12-112-1-12-2-2-1-1-2-2-11-2111-1121-1-11100−i3i300i3−i3−i3i3−i3i322-1-1-1-10−i3i300i3−i30−i3i30−i3i300000000-2110000000
χ4022-22-122-2-122-1-1-12-1-21-2-12-112-1-12-2-2-1-1-2-2-11-2111-1121-1-11100−i3i300i3−i3i3−i3i3−i3-2-211110−i3i300i3−i30i3−i30i3−i3000000002-1-10000000
χ4122-22-122-2-122-1-1-12-1-21-2-12-112-1-12-2-2-1-1-2-2-11-2111-1121-1-11100i3−i300−i3i3−i3i3−i3i3-2-211110i3−i300−i3i30−i3i30−i3i3000000002-1-10000000
χ4222-22-122-2-122-1-1-12-1-21-2-12-112-1-12-2-2-1-1-2-2-11-2111-1121-1-11100i3−i300−i3i3i3−i3i3−i322-1-1-1-10i3−i300−i3i30i3−i30i3−i300000000-2110000000
χ4322-22-12-22-12211-12-1-21-2-12-1-1-211-2221122-11-2111-1-1-2-111-1-12-2-1-100113−3−330033−3−32-1-10-21103−30−33000000000−330000000
χ4422-22-12-22-12211-12-1-21-2-12-1-1-211-2221122-11-2111-1-1-2-111-1-12-2-1-10011−333−300−3−3332-1-10-2110−3303−30000000003−30000000
χ4522-22-12-22-12211-12-1-21-2-12-1-1-211-2221122-11-2111-1-1-2-111-1-1-221100-1-13−3−3300−3−333-21102-1-103−30−330000000003−30000000
χ4622-22-12-22-12211-12-1-21-2-12-1-1-211-2221122-11-2111-1-1-2-111-1-1-221100-1-1−333−30033−3−3-21102-1-10−3303−3000000000−330000000
χ4744444-2-4-444-2-4-44-2-244-24-2-2-4222-4-42-4-422-24-2-2-2-2-2-42222220000000000000000000000000000000000000000000000000
χ484444-2-244-24-2-2-2-2-214-2-2-2-21-2-21144-2-2-2-2-21-2-21111-2-21111144-2-200-2-20000000000-2110-211000000000000000000000000
χ494444-2-244-24-2-2-2-2-214-2-2-2-21-2-21144-2-2-2-2-21-2-21111-2-211111-4-422002200000000002-1-102-1-1000000000000000000000000
χ504444-2-2-4-4-24-222-2-214-2-2-2-2122-1-1-4-4222221-2-2111122-1-1-1-1-100−2i32i300−2i32i300000000000i3−i300i3−i3000000000000000000000000
χ514444-2-2-4-4-24-222-2-214-2-2-2-2122-1-1-4-4222221-2-2111122-1-1-1-1-1002i3−2i3002i3−2i300000000000−i3i300−i3i3000000000000000000000000
χ52444-24-2444-2-244-21-2-24-2-21-24-2-2-2-2-2-2-2-2111-21-2111-21-211110000000000000000000004000000000-2-2-2-211110000000000
χ53444-24-2444-2-244-21-2-24-2-21-24-2-2-2-2-2-2-2-2111-21-2111-21-21111000000000000000000000-40000000002222-1-1-1-10000000000
χ54444-24-2-4-44-2-2-4-4-21-2-24-2-21-2-422222222-1-11-21-21112-12-1-1-1-1000000000000000000000000000000023−2300−3−3330000000000
χ55444-24-2-4-44-2-2-4-4-21-2-24-2-21-2-422222222-1-11-21-21112-12-1-1-1-10000000000000000000000000000000−23230033−3−30000000000
χ56444-2-2444-2-24-2-21-2-2-2-241-2-2-24-2-2-2-2411-2-211-2-21111-2-2111100004400-2-2-2-20000000000000-211-211000000000000000000
χ57444-2-2444-2-24-2-21-2-2-2-241-2-2-24-2-2-2-2411-2-211-2-21111-2-211110000-4-400222200000000000002-1-12-1-1000000000000000000
χ58444-2-24-4-4-2-24221-2-2-2-241-2-22-42222-4-1-12211-2-2111-122-1-1-1-100004i−4i00−2i−2i2i2i0000000000000−2iii2i−i−i000000000000000000
χ59444-2-24-4-4-2-24221-2-2-2-241-2-22-42222-4-1-12211-2-2111-122-1-1-1-10000−4i4i002i2i−2i−2i00000000000002i−i−i−2iii000000000000000000
χ6044-444-24-444-2444-2-2-4-424-2-2-4-2-2-24-424422-2-42222-2-4-22-2-2220000000000000000000000000000000000000000000000000
χ6144-44-2-24-4-24-2-2-2-2-21-422-2-212-2114-42-2-222122-1-1-112-2-111-1-100−2i32i3002i3−2i300000000000i3−i300−i3i3000000000000000000000000
χ6244-44-2-24-4-24-2-2-2-2-21-422-2-212-2114-42-2-222122-1-1-112-2-111-1-1002i3−2i300−2i32i300000000000−i3i300i3−i3000000000000000000000000
χ6344-44-2-2-44-24-222-2-21-422-2-21-22-1-1-44-222-2-2122-1-1-11-221-1-1114-4-2-200220000000000-21102-1-1000000000000000000000000
χ6444-44-2-2-44-24-222-2-21-422-2-21-22-1-1-44-222-2-2122-1-1-11-221-1-111-442200-2-200000000002-1-10-211000000000000000000000000
χ6544-4-2444-44-2444-2-242-4-4-2-24-4444-22-4-2-222-222-422-22-2-4-2-2220000000000000000000000000000000000000000000000000
χ6644-4-244-444-24-4-4-2-242-4-4-2-244-4-4-42-2422-2-2-222-422-2-22422-2-20000000000000000000000000000000000000000000000000
χ6744-4-24-24-44-2-244-21-22-42-21-2-4-2-2-2-222-2-2-1-112-12-1-1121211-1-1000000000000000000000000000000000003i−3i−3i3i0000000000
χ6844-4-24-24-44-2-244-21-22-42-21-2-4-2-2-2-222-2-2-1-112-12-1-1121211-1-100000000000000000000000000000000000−3i3i3i−3i0000000000
χ6944-4-24-2-444-2-2-4-4-21-22-42-21-242222-2-2221112-12-1-11-2-1-2-1-111000000000000000000000000000000000−2i32i3i3−i3i3−i30000000000
χ7044-4-24-2-444-2-2-4-4-21-22-42-21-242222-2-2221112-12-1-11-2-1-2-1-1110000000000000000000000000000000002i3−2i3−i3i3−i3i30000000000
χ7144-4-2-244-4-2-24-2-21-2-222-41-2-224-2-2-22-411221-122-1-11-1-2211-1-100000000−2i32i3−2i32i300000000000000i3−i30i3−i3000000000000000000
χ7244-4-2-244-4-2-24-2-21-2-222-41-2-224-2-2-22-411221-122-1-11-1-2211-1-1000000002i3−2i32i3−2i300000000000000−i3i30−i3i3000000000000000000
χ7344-4-2-24-44-2-24221-2-222-41-2-2-2-4222-24-1-1-2-21-122-1-1112-2-1-1110000000023−23−232300000000000000−3303−3000000000000000000
χ7444-4-2-24-44-2-24221-2-222-41-2-2-2-4222-24-1-1-2-21-122-1-1112-2-1-11100000000−232323−23000000000000003−30−33000000000000000000
χ754-4044400-4-4-400444000-4-4-400000000000400000-4000000000000000000022−2222−2222−220000000000000000000000000000000
χ764-4044400-4-4-400444000-4-4-400000000000400000-40000000000000000000−2222−2222−22220000000000000000000000000000000
χ774-404-24002-4-423−23-24-20002-420023−2300023−2300-200000200023−230000000000000022−222ζ13−2ζ23−2ζ13+2ζ232ζ5−2ζ7−2ζ5+2ζ70000000000000000000000000000000
χ784-404-24002-4-423−23-24-20002-420023−2300023−2300-200000200023−2300000000000000−2222−2ζ13+2ζ232ζ13−2ζ23−2ζ5+2ζ72ζ5−2ζ70000000000000000000000000000000
χ794-404-24002-4-4−2323-24-20002-4200−2323000−232300-2000002000−23230000000000000022−222ζ5−2ζ7−2ζ5+2ζ72ζ13−2ζ23−2ζ13+2ζ230000000000000000000000000000000
χ804-404-24002-4-4−2323-24-20002-4200−2323000−232300-2000002000−232300000000000000−2222−2ζ5+2ζ72ζ5−2ζ7−2ζ13+2ζ232ζ13−2ζ230000000000000000000000000000000
χ81888-4-4-488-4-4-4-4-4222-4-4-4222-4-422-4-4-42222-1222-1-1-1222-1-1-1-10000000000000000000000000000000000000000000000000
χ82888-4-4-4-8-8-4-4-444222-4-4-422244-2-2444-2-2-2-2-1222-1-1-1-2-2-211110000000000000000000000000000000000000000000000000
χ8388-8-4-4-48-8-4-4-4-4-42224442224-422-44422-2-2-1-2-2-211-1-22-2-1-1110000000000000000000000000000000000000000000000000
χ8488-8-4-4-4-88-4-4-444222444222-44-2-24-4-4-2-222-1-2-2-211-12-2211-1-10000000000000000000000000000000000000000000000000
χ858-8088-400-8-84008-4-4000-84400000000000-400000400000000000000000000000000000000000000000000000000000000
χ868-808-4-4004-8443−43-4-4200044-200−232300043−4300200000-2000−2323000000000000000000000000000000000000000000000000000
χ878-808-4-4004-84−4343-4-4200044-20023−23000−434300200000-200023−23000000000000000000000000000000000000000000000000000
χ888-80-48800-84-800-4-4800044-800000000000-400000400000000000000000000000000000000000000000000000000000000
χ898-80-48-400-84400-42-40004-240000000006i−6i200000-2000006i−6i0000000000000000000000000000000000000000000000000
χ908-80-48-400-84400-42-40004-24000000000−6i6i200000-200000−6i6i0000000000000000000000000000000000000000000000000
χ918-80-4-480044-843−432-4-4000-2440043−43000−232300200000-2000−2323000000000000000000000000000000000000000000000000000
χ928-80-4-480044-8−43432-4-4000-24400−434300023−2300200000-200023−23000000000000000000000000000000000000000000000000000
χ938-80-4-4-40044443−43222000-2-2-200−2323000−23236i−6i-1000−3i33i310003−3−3i3i0000000000000000000000000000000000000000000000000
χ948-80-4-4-40044443−43222000-2-2-200−2323000−2323−6i6i-10003i3−3i310003−33i−3i0000000000000000000000000000000000000000000000000
χ958-80-4-4-400444−4343222000-2-2-20023−2300023−236i−6i-10003i3−3i31000−33−3i3i0000000000000000000000000000000000000000000000000
χ968-80-4-4-400444−4343222000-2-2-20023−2300023−23−6i6i-1000−3i33i31000−333i−3i0000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.