Finite Group Databasebeta

← Group #13156239

Character table — Group #13156239

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11222222222224444444444444444444488888888888888121212121212121212121212181818181818242424242424242424242424242424242424242424363636727272727272216
order12233344666121233366666666121212121212121212366666121212121212121224668812122424242488242424242666666666661212122424242424248242488242424242
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111-1-1-11-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-11-111-1-1-1
χ4111111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111-1-1-1-1111-1-1-1-1-1-1-1-1-1-11-1-1111
χ511111111111111111111111111111111111111111111111-1-1-1-111-1-11111-1-1-1-1-1-1111-111-1-11111-1-1-1111111-1-1-1-11-1-111-1
χ611111111111111111111111111111111111111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-11-111-1-11
χ711111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1111111111-111-1-11111-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-11
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
χ9222222-2-2222-2-222222222222-2-2-2-2-2-2-2-2-2222222-2-2-2-2-2-2-2-200002i−2i002i2i−2i−2i0000000000000000000002i2i2i−2i−2i−2i0000000000
χ10222222-2-2222-2-222222222222-2-2-2-2-2-2-2-2-2222222-2-2-2-2-2-2-2-20000−2i2i00−2i−2i2i2i000000000000000000000−2i−2i−2i2i2i2i0000000000
χ1122222-12222-1222-1-122-1-1-12-1-12-1-1-12222-1-12-1-1-1-12-1-1-1-1-1-1-1222200220000000000222-1-1-1-1-1-1-1-1-1-1-1-100000000020-1-1000
χ1222222-12222-1222-1-122-1-1-12-1-12-1-1-12222-1-12-1-1-1-12-1-1-1-1-1-1-1222200220000000000-2-2-2-111-1-11111-1-1-1000000000-2011000
χ1322222-12222-1222-1-122-1-1-12-1-12-1-1-12222-1-12-1-1-1-12-1-1-1-1-1-1-1-2-2-2-200-2-200000000002221-1-111-1-1-1-1111000000000-2011000
χ1422222-12222-1222-1-122-1-1-12-1-12-1-1-12222-1-12-1-1-1-12-1-1-1-1-1-1-1-2-2-2-200-2-20000000000-2-2-211111111111100000000020-1-1000
χ152222-1222-12222-12-12-12-1-1-1-122222-1-1-1-12-1-12-1-1-1-1-1-12-1-1-1-10000220022220000002-1-102200-1-1-1-1000-1-1-1-1-1-10000200-1-10
χ162222-1222-12222-12-12-12-1-1-1-122222-1-1-1-12-1-12-1-1-1-1-1-12-1-1-1-1000022002222000000-2110-2-2001111000-1-1-1-1-1-10000-200110
χ172222-1222-12222-12-12-12-1-1-1-122222-1-1-1-12-1-12-1-1-1-1-1-12-1-1-1-10000-2-200-2-2-2-20000002-1-102200-1-1-1-10001111110000-200110
χ182222-1222-12222-12-12-12-1-1-1-122222-1-1-1-12-1-12-1-1-1-1-1-12-1-1-1-10000-2-200-2-2-2-2000000-2110-2-20011110001111110000200-1-10
χ192222-12-2-2-122-2-2-12-12-12-1-1-1-12-2-2-2-21111-2-1-12-1-1-1111-2111100002i−2i002i2i−2i−2i0000000−i3i300000−i3−i3i3i3000−i−i−iiii00000003−30
χ202222-12-2-2-122-2-2-12-12-12-1-1-1-12-2-2-2-21111-2-1-12-1-1-1111-2111100002i−2i002i2i−2i−2i0000000i3−i300000i3i3−i3−i3000−i−i−iiii0000000−330
χ212222-12-2-2-122-2-2-12-12-12-1-1-1-12-2-2-2-21111-2-1-12-1-1-1111-211110000−2i2i00−2i−2i2i2i0000000−i3i300000−i3−i3i3i3000iii−i−i−i0000000−330
χ222222-12-2-2-122-2-2-12-12-12-1-1-1-12-2-2-2-21111-2-1-12-1-1-1111-211110000−2i2i00−2i−2i2i2i0000000i3−i300000i3i3−i3−i3000iii−i−i−i00000003−30
χ23222-122222-12-1-1-1-12-12222-12-1-12-1-12-1-122-1-1-1-1-1-1-122-1-1-1-1-122-1-122-1-1-1-1-1-122-1-1-1-1000200-1-100002-1-12-1-12-1-12-1-10000000
χ24222-122222-12-1-1-1-12-12222-12-1-12-1-12-1-122-1-1-1-1-1-1-122-1-1-1-1-122-1-1-2-2-1-11111-2-21111000200-1-100002-1-1-211-211-2110000000
χ25222-122222-12-1-1-1-12-12222-12-1-12-1-12-1-122-1-1-1-1-1-1-122-1-1-1-1-1-2-2112211-1-1-1-1-2-21111000-200110000-2112-1-12-1-1-2110000000
χ26222-122222-12-1-1-1-12-12222-12-1-12-1-12-1-122-1-1-1-1-1-1-122-1-1-1-1-1-2-211-2-211111122-1-1-1-1000-200110000-211-211-2112-1-10000000
χ27222-122-2-22-1211-1-12-12222-12-11-211-211-2-2-1-1-1-1-1-11-2-21111100−i3i32i−2i−i3i3−i−iii0033−3−3000000−i3i300000−i3i32i−i−i−2iii03−30000000
χ28222-122-2-22-1211-1-12-12222-12-11-211-211-2-2-1-1-1-1-1-11-2-21111100−i3i3−2i2i−i3i3ii−i−i00−3−333000000−i3i300000−i3i3−2iii2i−i−i0−330000000
χ29222-122-2-22-1211-1-12-12222-12-11-211-211-2-2-1-1-1-1-1-11-2-21111100i3−i32i−2ii3−i3−i−iii00−3−333000000i3−i300000i3−i32i−i−i−2iii0−330000000
χ30222-122-2-22-1211-1-12-12222-12-11-211-211-2-2-1-1-1-1-1-11-2-21111100i3−i3−2i2ii3−i3ii−i−i0033−3−3000000i3−i300000i3−i3−2iii2i−i−i03−30000000
χ3122-22222-222222222-2-2-2-2-2222-2222222-2-22-2-2-2-22-22-2-222-2-2000000000000222222000000000000000000000-2-2-20000000
χ3222-22222-222222222-2-2-2-2-2222-2222222-2-22-2-2-2-22-22-2-222-2-2000000000000-2-2-2-2-2-20000000000000000000002220000000
χ3322-2222-22222-2-2222-2-2-2-2-22222-2-2-2-2-2-2222-2-2-2-222-222-2-2222-22200-2-20000000000000200220000-2-2-20000000000000000
χ3422-2222-22222-2-2222-2-2-2-2-22222-2-2-2-2-2-2222-2-2-2-222-222-2-222-22-2-200220000000000000-200-2-200002220000000000000000
χ3522-222-1-2222-1-2-22-1-1-2-21112-1-12111-2-2-22-1-1-2111-121-1-111-1-12-22200-2-20000000000000-1−i3i3-1-1−i3i3−i3i311100000000000−i3i3000
χ3622-222-1-2222-1-2-22-1-1-2-21112-1-12111-2-2-22-1-1-2111-121-1-111-1-12-22200-2-20000000000000-1i3−i3-1-1i3−i3i3−i311100000000000i3−i3000
χ3722-222-1-2222-1-2-22-1-1-2-21112-1-12111-2-2-22-1-1-2111-121-1-111-1-1-22-2-2002200000000000001−i3i311−i3i3−i3i3-1-1-100000000000i3−i3000
χ3822-222-1-2222-1-2-22-1-1-2-21112-1-12111-2-2-22-1-1-2111-121-1-111-1-1-22-2-2002200000000000001i3−i311i3−i3i3−i3-1-1-100000000000−i3i3000
χ3922-2-1222-22-12-1-1-1-121-2-2-2-2-12-112-1-12-1-1-2-2-11111-112-21-1-11100−i3i300i3−i3−i3i3−i3i322-1-1-1-1000000−i3i300000i3−i30−i3i30−i3i3-2110000000
χ4022-2-1222-22-12-1-1-1-121-2-2-2-2-12-112-1-12-1-1-2-2-11111-112-21-1-11100−i3i300i3−i3i3−i3i3−i3-2-21111000000−i3i300000i3−i30i3−i30i3−i32-1-10000000
χ4122-2-1222-22-12-1-1-1-121-2-2-2-2-12-112-1-12-1-1-2-2-11111-112-21-1-11100i3−i300−i3i3−i3i3−i3i3-2-21111000000i3−i300000−i3i30−i3i30−i3i32-1-10000000
χ4222-2-1222-22-12-1-1-1-121-2-2-2-2-12-112-1-12-1-1-2-2-11111-112-21-1-11100i3−i300−i3i3i3−i3i3−i322-1-1-1-1000000i3−i300000−i3i30i3−i30i3−i3-2110000000
χ4322-2-122-222-1211-1-121-2-2-2-2-12-1-1-211-21122-11111-1-1-22-111-1-12-2-1-100113−3−330033−3−3000200-1-10000-21103−30−330−330000000
χ4422-2-122-222-1211-1-121-2-2-2-2-12-1-1-211-21122-11111-1-1-22-111-1-12-2-1-10011−333−300−3−333000200-1-10000-2110−3303−303−30000000
χ4522-2-122-222-1211-1-121-2-2-2-2-12-1-1-211-21122-11111-1-1-22-111-1-1-221100-1-13−3−3300−3−333000-2001100002-1-103−30−3303−30000000
χ4622-2-122-222-1211-1-121-2-2-2-2-12-1-1-211-21122-11111-1-1-22-111-1-1-221100-1-1−333−30033−3−3000-2001100002-1-10−3303−30−330000000
χ4744444-2-4-444-2-4-44-2-244-2-2-24-2-2-4222-4-4-4-42-24-2-2-2-2-422222220000000000000000000000000000000000000000000000000
χ484444-2-244-24-244-2-214-2-211-21-24-2-2-2-2-2-2-2-21-2-2111-211-211110000000000000000004-2-20-2-20011110000000000000000000
χ494444-2-244-24-244-2-214-2-211-21-24-2-2-2-2-2-2-2-21-2-2111-211-21111000000000000000000-42202200-1-1-1-10000000000000000000
χ504444-2-2-4-4-24-2-4-4-2-214-2-211-21-2-4222222221-2-21112-1-12-1-1-1-10000000000000000000−2i32i300000i3i3−i3−i30000000000000000000
χ514444-2-2-4-4-24-2-4-4-2-214-2-211-21-2-4222222221-2-21112-1-12-1-1-1-100000000000000000002i3−2i300000−i3−i3i3i30000000000000000000
χ52444-24-2444-2-2-2-2-21-2-24-2-2-2-2-21-2-2114-2-24-21-21111-2-2-21111144-2-200-2-20000000000000-200110000-2110000000000000000
χ53444-24-2444-2-2-2-2-21-2-24-2-2-2-2-21-2-2114-2-24-21-21111-2-2-211111-4-42200220000000000000200-1-100002-1-10000000000000000
χ54444-24-2-4-44-2-222-21-2-24-2-2-2-2-2122-1-1-422-421-21111222-1-1-1-1-100−2i32i300−2i32i30000000000000000i3−i300000i3−i30000000000000000
χ55444-24-2-4-44-2-222-21-2-24-2-2-2-2-2122-1-1-422-421-21111222-1-1-1-1-1002i3−2i3002i3−2i30000000000000000−i3i300000−i3i30000000000000000
χ56444-2-2444-2-24-2-21-2-2-2-24-2-21-2-2-24-2-2-211-2411-21111-2-2-2111100004400-2-2-2-2000000000000000000000-211-2110000000000
χ57444-2-2444-2-24-2-21-2-2-2-24-2-21-2-2-24-2-2-211-2411-21111-2-2-211110000-4-40022220000000000000000000002-1-12-1-10000000000
χ58444-2-24-4-4-2-24221-2-2-2-24-2-21-2-22-4222-1-12-411-2111-1222-1-1-1-100004i−4i00−2i−2i2i2i000000000000000000000−2iii2i−i−i0000000000
χ59444-2-24-4-4-2-24221-2-2-2-24-2-21-2-22-4222-1-12-411-2111-1222-1-1-1-10000−4i4i002i2i−2i−2i0000000000000000000002i−i−i−2iii0000000000
χ6044-444-24-444-2444-2-2-4-42224-2-2-4-2-2-2444-42-2-4222-2-4-222-2-2220000000000000000000000000000000000000000000000000
χ6144-44-244-4-24444-24-2-42-422-2-24-4444-2-2-22-4-22-422-22-22-4-2-2220000000000000000000000000000000000000000000000000
χ6244-44-24-44-244-4-4-24-2-42-422-2-244-4-4-4222-24-22-422-2-22-2422-2-20000000000000000000000000000000000000000000000000
χ6344-44-2-24-4-24-244-2-21-422-1-1-21-2-4-2-2-2-2-2-222122-1-1121-1211-1-1000000000000000000000000003-3-330000000000000000000
χ6444-44-2-24-4-24-244-2-21-422-1-1-21-2-4-2-2-2-2-2-222122-1-1121-1211-1-100000000000000000000000000-333-30000000000000000000
χ6544-44-2-2-44-24-2-4-4-2-21-422-1-1-21-24222222-2-2122-1-11-2-11-2-1-1110000000000000000000000−2i32i300i3−i3i3−i30000000000000000000
χ6644-44-2-2-44-24-2-4-4-2-21-422-1-1-21-24222222-2-2122-1-11-2-11-2-1-11100000000000000000000002i3−2i300−i3i3−i3i30000000000000000000
χ6744-4-24-24-44-2-2-2-2-21-22-4222-2-212-2114-2-2-4212-1-1-112-22-111-1-100−2i32i3002i3−2i30000000000000000i3−i300000−i3i30000000000000000
χ6844-4-24-24-44-2-2-2-2-21-22-4222-2-212-2114-2-2-4212-1-1-112-22-111-1-1002i3−2i300−2i32i30000000000000000−i3i300000i3−i30000000000000000
χ6944-4-24-2-444-2-222-21-22-4222-2-21-22-1-1-4224-212-1-1-11-22-21-1-1114-4-2-200220000000000000-2001100002-1-10000000000000000
χ7044-4-24-2-444-2-222-21-22-4222-2-21-22-1-1-4224-212-1-1-11-22-21-1-111-442200-2-20000000000000200-1-10000-2110000000000000000
χ7144-4-2-244-4-2-24-2-21-2-222-4221-2-224-2-2-2112-41-12-1-11-1-22211-1-100000000−2i32i3−2i32i30000000000000000000000i3−i30i3−i30000000000
χ7244-4-2-244-4-2-24-2-21-2-222-4221-2-224-2-2-2112-41-12-1-11-1-22211-1-1000000002i3−2i32i3−2i30000000000000000000000−i3i30−i3i30000000000
χ7344-4-2-24-44-2-24221-2-222-4221-2-2-2-4222-1-1-241-12-1-1112-2-2-1-1110000000023−23−23230000000000000000000000−3303−30000000000
χ7444-4-2-24-44-2-24221-2-222-4221-2-2-2-4222-1-1-241-12-1-1112-2-2-1-11100000000−232323−2300000000000000000000003−30−330000000000
χ754-4044400-4-4-40044400000-4-4-400000000040000-40000000000000000000022−2222−2222−220000000000000000000000000000000
χ764-4044400-4-4-40044400000-4-4-400000000040000-400000000000000000000−2222−2222−22220000000000000000000000000000000
χ774-40-24400-42-423−23-2-24000002-420023−23023−2300-200002000023−230000000000000022−222ζ13−2ζ23−2ζ13+2ζ232ζ5−2ζ7−2ζ5+2ζ70000000000000000000000000000000
χ784-40-24400-42-423−23-2-24000002-420023−23023−2300-200002000023−2300000000000000−2222−2ζ13+2ζ232ζ13−2ζ23−2ζ5+2ζ72ζ5−2ζ70000000000000000000000000000000
χ794-40-24400-42-4−2323-2-24000002-4200−23230−232300-2000020000−23230000000000000022−222ζ5−2ζ7−2ζ5+2ζ72ζ13−2ζ23−2ζ13+2ζ230000000000000000000000000000000
χ804-40-24400-42-4−2323-2-24000002-4200−23230−232300-2000020000−232300000000000000−2222−2ζ5+2ζ72ζ5−2ζ7−2ζ13+2ζ232ζ13−2ζ230000000000000000000000000000000
χ81888-4-4-488-4-4-4-4-4222-4-4-422222-4-422-422-4-4-122-1-1-12222-1-1-1-10000000000000000000000000000000000000000000000000
χ82888-4-4-4-8-8-4-4-444222-4-4-42222244-2-24-2-244-122-1-1-1-2-2-2-211110000000000000000000000000000000000000000000000000
χ8388-8-4-4-48-8-4-4-4-4-4222444-2-22224-422-42244-1-2-211-1-22-2-2-1-1110000000000000000000000000000000000000000000000000
χ8488-8-4-4-4-88-4-4-444222444-2-2222-44-2-24-2-2-4-4-1-2-211-12-22211-1-10000000000000000000000000000000000000000000000000
χ858-8088-400-8-84008-4-400000-844000000000-400004000000000000000000000000000000000000000000000000000000000
χ868-808-48004-8-800-48-40000044-8000000000-400004000000000000000000000000000000000000000000000000000000000
χ878-808-4-4004-8400-4-420006-64-240000000002006-6-2000000000000000000000000000000000000000000000000000000000
χ888-808-4-4004-8400-4-42000-664-24000000000200-66-2000000000000000000000000000000000000000000000000000000000
χ898-80-48-400-84443−43-42-40000044-200−2323043−430020000-20000−2323000000000000000000000000000000000000000000000000000
χ908-80-48-400-844−4343-42-40000044-20023−230−43430020000-2000023−23000000000000000000000000000000000000000000000000000
χ918-80-4-480044-843−432-4-400000-2440043−430−23230020000-20000−2323000000000000000000000000000000000000000000000000000
χ928-80-4-480044-8−43432-4-400000-24400−4343023−230020000-2000023−23000000000000000000000000000000000000000000000000000
χ938-80-4-4-40044443−432220006-6-2-2-200−23230−232300-100-33100003−333−330000000000000000000000000000000000000000000000000
χ948-80-4-4-40044443−43222000-66-2-2-200−23230−232300-1003-3100003−3−33330000000000000000000000000000000000000000000000000
χ958-80-4-4-400444−43432220006-6-2-2-20023−23023−2300-100-3310000−33−33330000000000000000000000000000000000000000000000000
χ968-80-4-4-400444−4343222000-66-2-2-20023−23023−2300-1003-310000−3333−330000000000000000000000000000000000000000000000000

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