Finite Group Databasebeta

← Group #13156255

Character table — Group #13156255

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11222222222224444444444444444444488888888888888121212121212121212121212181818181818242424242424242424242424242424242424242424363636727272727272216
order1223334466612123336666666612121212121212121236666612121212121212122466881212242424248824242424466612121212121212121212122424242424248242488242424244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111-1111-1-11-1-111-1-1-1-1111111111-1-1-1-1-1-1-1
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
χ4111111111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1111-1-11-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1111
χ511111111111111111111111111111111111111111111111-1-1-1-111-1-11111-1-1-1-1-1-11-1-1-111-111-1-11111111111-1-1-1-11-1-111-1
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
χ711111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-111-111-1-11111-1-1-1-1-1-1111-1-1-1-1-1-11
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
χ1122222-12222-1222-1-122-1-1-12-1-12-1-1-12222-1-12-1-1-1-12-1-1-1-1-1-1-12222002200000000002-1-1-122-1-1-1-1-1-1-1-1-100000000020-1-1000
χ1222222-12222-1222-1-122-1-1-12-1-12-1-1-12222-1-12-1-1-1-12-1-1-1-1-1-1-1222200220000000000-2-1-1-1-2-2-111-1-11111000000000-2011000
χ1322222-12222-1222-1-122-1-1-12-1-12-1-1-12222-1-12-1-1-1-12-1-1-1-1-1-1-1-2-2-2-200-2-200000000002111221-1-111-1-1-1-1000000000-2011000
χ1422222-12222-1222-1-122-1-1-12-1-12-1-1-12222-1-12-1-1-1-12-1-1-1-1-1-1-1-2-2-2-200-2-20000000000-2111-2-211111111100000000020-1-1000
χ152222-1222-122-1-1-12-12-1222-1-12-12-1-12-1-122-1-1-1-1-1-1-1-122-1-1-1-122-1-122-1-1-1-1-1-122-1-1-1-102-1-100200-1-100002-1-12-1-12-1-10000000
χ162222-1222-122-1-1-12-12-1222-1-12-12-1-12-1-122-1-1-1-1-1-1-1-122-1-1-1-122-1-1-2-2-1-11111-2-2111102-1-100200-1-10000-211-211-2110000000
χ172222-1222-122-1-1-12-12-1222-1-12-12-1-12-1-122-1-1-1-1-1-1-1-122-1-1-1-1-2-2112211-1-1-1-1-2-211110-21100-2001100002-1-12-1-1-2110000000
χ182222-1222-122-1-1-12-12-1222-1-12-12-1-12-1-122-1-1-1-1-1-1-1-122-1-1-1-1-2-211-2-211111122-1-1-1-10-21100-200110000-211-2112-1-10000000
χ192222-12-2-2-12211-12-12-1222-1-121-211-211-2-2-1-1-1-1-1-111-2-2111100−i3i32i−2i−i3i3−i−iii0033−3−300−i3i300000−i3i300002i−i−i−2iii03−30000000
χ202222-12-2-2-12211-12-12-1222-1-121-211-211-2-2-1-1-1-1-1-111-2-2111100−i3i3−2i2i−i3i3ii−i−i00−3−33300−i3i300000−i3i30000−2iii2i−i−i0−330000000
χ212222-12-2-2-12211-12-12-1222-1-121-211-211-2-2-1-1-1-1-1-111-2-2111100i3−i32i−2ii3−i3−i−iii00−3−33300i3−i300000i3−i300002i−i−i−2iii0−330000000
χ222222-12-2-2-12211-12-12-1222-1-121-211-211-2-2-1-1-1-1-1-111-2-2111100i3−i3−2i2ii3−i3ii−i−i0033−3−300i3−i300000i3−i30000−2iii2i−i−i03−30000000
χ23222-122222-1222-1-12-122-1-1-12-12222-1-1-1-12-1-12-1-1-1-12-1-1-1-1-1-10000220022220000002000-1-102200-1-1-1-1-1-1-1-1-1-10000200-1-10
χ24222-122222-1222-1-12-122-1-1-12-12222-1-1-1-12-1-12-1-1-1-12-1-1-1-1-1-1000022002222000000-2000110-2-2001111-1-1-1-1-1-10000-200110
χ25222-122222-1222-1-12-122-1-1-12-12222-1-1-1-12-1-12-1-1-1-12-1-1-1-1-1-10000-2-200-2-2-2-20000002000-1-102200-1-1-1-11111110000-200110
χ26222-122222-1222-1-12-122-1-1-12-12222-1-1-1-12-1-12-1-1-1-12-1-1-1-1-1-10000-2-200-2-2-2-2000000-2000110-2-20011111111110000200-1-10
χ27222-122-2-22-12-2-2-1-12-122-1-1-12-1-2-2-2-21111-2-1-12-1-1-11-211111100002i−2i002i2i−2i−2i0000000000−i3i300000−i3−i3i3i3−i−i−iiii00000003−30
χ28222-122-2-22-12-2-2-1-12-122-1-1-12-1-2-2-2-21111-2-1-12-1-1-11-211111100002i−2i002i2i−2i−2i0000000000i3−i300000i3i3−i3−i3−i−i−iiii0000000−330
χ29222-122-2-22-12-2-2-1-12-122-1-1-12-1-2-2-2-21111-2-1-12-1-1-11-21111110000−2i2i00−2i−2i2i2i0000000000−i3i300000−i3−i3i3i3iii−i−i−i0000000−330
χ30222-122-2-22-12-2-2-1-12-122-1-1-12-1-2-2-2-21111-2-1-12-1-1-11-21111110000−2i2i00−2i−2i2i2i0000000000i3−i300000i3i3−i3−i3iii−i−i−i00000003−30
χ3122-22222-222222222-2-2-2-2-2222-2222222-2-22-2-2-2-22-2-22-222-2-2000000000000222222000000000000000000000-2-2-20000000
χ3222-22222-222222222-2-2-2-2-2222-2222222-2-22-2-2-2-22-2-22-222-2-2000000000000-2-2-2-2-2-20000000000000000000002220000000
χ3322-2222-22222-2-2222-2-2-2-2-22222-2-2-2-2-2-2222-2-2-2-2222-22-2-2222-22200-2-20000000000022200-200-2-200000000000000000000
χ3422-2222-22222-2-2222-2-2-2-2-22222-2-2-2-2-2-2222-2-2-2-2222-22-2-222-22-2-2002200000000000-2-2-2002002200000000000000000000
χ3522-222-1-2222-1-2-22-1-1-2-21112-1-12111-2-2-22-1-1-2111-12-11-111-1-12-22200-2-200000000000-1-1-1001−i3i311−i3i3−i3i300000000000−i3i3000
χ3622-222-1-2222-1-2-22-1-1-2-21112-1-12111-2-2-22-1-1-2111-12-11-111-1-12-22200-2-200000000000-1-1-1001i3−i311i3−i3i3−i300000000000i3−i3000
χ3722-222-1-2222-1-2-22-1-1-2-21112-1-12111-2-2-22-1-1-2111-12-11-111-1-1-22-2-200220000000000011100-1−i3i3-1-1−i3i3−i3i300000000000i3−i3000
χ3822-222-1-2222-1-2-22-1-1-2-21112-1-12111-2-2-22-1-1-2111-12-11-111-1-1-22-2-200220000000000011100-1i3−i3-1-1i3−i3i3−i300000000000−i3i3000
χ3922-22-122-2-122-1-1-12-1-21-2-2-2-1-1212-1-12-1-1-2-2-11111-1112-2-1-11100−i3i300i3−i3−i3i3−i3i322-1-1-1-100−i3i300000i3−i300000−i3i30−i3i3-2110000000
χ4022-22-122-2-122-1-1-12-1-21-2-2-2-1-1212-1-12-1-1-2-2-11111-1112-2-1-11100−i3i300i3−i3i3−i3i3−i3-2-2111100−i3i300000i3−i300000i3−i30i3−i32-1-10000000
χ4122-22-122-2-122-1-1-12-1-21-2-2-2-1-1212-1-12-1-1-2-2-11111-1112-2-1-11100i3−i300−i3i3−i3i3−i3i3-2-2111100i3−i300000−i3i300000−i3i30−i3i32-1-10000000
χ4222-22-122-2-122-1-1-12-1-21-2-2-2-1-1212-1-12-1-1-2-2-11111-1112-2-1-11100i3−i300−i3i3i3−i3i3−i322-1-1-1-100i3−i300000−i3i300000i3−i30i3−i3-2110000000
χ4322-22-12-22-12211-12-1-21-2-2-2-1-12-1-211-21122-11111-1-1-1-2211-1-12-2-1-100113−3−330033−3−302-1-100-20011000003−30−330−330000000
χ4422-22-12-22-12211-12-1-21-2-2-2-1-12-1-211-21122-11111-1-1-1-2211-1-12-2-1-10011−333−300−3−33302-1-100-2001100000−3303−303−30000000
χ4522-22-12-22-12211-12-1-21-2-2-2-1-12-1-211-21122-11111-1-1-1-2211-1-1-221100-1-13−3−3300−3−3330-21100200-1-1000003−30−3303−30000000
χ4622-22-12-22-12211-12-1-21-2-2-2-1-12-1-211-21122-11111-1-1-1-2211-1-1-221100-1-1−333−30033−3−30-21100200-1-100000−3303−30−330000000
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
χ484444-2-244-24-2-2-2-2-214-2-2-2-2-21-2-2-2114-2-24-21-21111-21-2-2111144-2-200-2-200000000000-21100-2001100000000000000000000
χ494444-2-244-24-2-2-2-2-214-2-2-2-2-21-2-2-2114-2-24-21-21111-21-2-21111-4-4220022000000000002-1-100200-1-100000000000000000000
χ504444-2-2-4-4-24-222-2-214-2-2-2-2-21-222-1-1-422-421-211112-122-1-1-1-100−2i32i300−2i32i3000000000000i3−i300000i3−i300000000000000000000
χ514444-2-2-4-4-24-222-2-214-2-2-2-2-21-222-1-1-422-421-211112-122-1-1-1-1002i3−2i3002i3−2i3000000000000−i3i300000−i3i300000000000000000000
χ52444-24-2444-2-244-21-2-24-211-2-214-2-2-2-2-2-2-2-21-2-2111-2-21111110000000000000000004000-2-20-2-20011110000000000000000
χ53444-24-2444-2-244-21-2-24-211-2-214-2-2-2-2-2-2-2-21-2-2111-2-2111111000000000000000000-40002202200-1-1-1-10000000000000000
χ54444-24-2-4-44-2-2-4-4-21-2-24-211-2-21-4222222221-2-211122-1-1-1-1-1-10000000000000000000000−2i32i300000i3i3−i3−i30000000000000000
χ55444-24-2-4-44-2-2-4-4-21-2-24-211-2-21-4222222221-2-211122-1-1-1-1-1-100000000000000000000002i3−2i300000−i3−i3i3i30000000000000000
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
χ6044-444-24-444-2444-2-2-4-42224-2-2-4-2-2-2444-42-2-4222-2-42-22-2-2220000000000000000000000000000000000000000000000000
χ6144-44-2-24-4-24-2-2-2-2-21-42222-21-22-2114-2-2-4212-1-1-112-1-2211-1-100−2i32i3002i3−2i3000000000000i3−i300000−i3i300000000000000000000
χ6244-44-2-24-4-24-2-2-2-2-21-42222-21-22-2114-2-2-4212-1-1-112-1-2211-1-1002i3−2i300−2i32i3000000000000−i3i300000i3−i300000000000000000000
χ6344-44-2-2-44-24-222-2-21-42222-21-2-22-1-1-4224-212-1-1-11-212-2-1-1114-4-2-2002200000000000-21100200-1-100000000000000000000
χ6444-44-2-2-44-24-222-2-21-42222-21-2-22-1-1-4224-212-1-1-11-212-2-1-111-442200-2-2000000000002-1-100-2001100000000000000000000
χ6544-4-2444-44-2444-2-242-4-422-24-2-4444-2-2-22-4-22-422-22-4-22-2-2220000000000000000000000000000000000000000000000000
χ6644-4-244-444-24-4-4-2-242-4-422-24-24-4-4-4222-24-22-422-2-242-222-2-20000000000000000000000000000000000000000000000000
χ6744-4-24-24-44-2-244-21-22-42-1-1-2-21-4-2-2-2-2-2-222122-1-11221-111-1-1000000000000000000000000000003-3-330000000000000000
χ6844-4-24-24-44-2-244-21-22-42-1-1-2-21-4-2-2-2-2-2-222122-1-11221-111-1-100000000000000000000000000000-333-30000000000000000
χ6944-4-24-2-444-2-2-4-4-21-22-42-1-1-2-214222222-2-2122-1-11-2-2-11-1-1110000000000000000000000000−2i32i300i3−i3i3−i30000000000000000
χ7044-4-24-2-444-2-2-4-4-21-22-42-1-1-2-214222222-2-2122-1-11-2-2-11-1-11100000000000000000000000002i3−2i300−i3i3−i3i30000000000000000
χ7144-4-2-244-4-2-24-2-21-2-222-4221-2-224-2-2-2112-41-12-1-11-12-2211-1-100000000−2i32i3−2i32i30000000000000000000000i3−i30i3−i30000000000
χ7244-4-2-244-4-2-24-2-21-2-222-4221-2-224-2-2-2112-41-12-1-11-12-2211-1-1000000002i3−2i32i3−2i30000000000000000000000−i3i30−i3i30000000000
χ7344-4-2-24-44-2-24221-2-222-4221-2-2-2-4222-1-1-241-12-1-111-22-2-1-1110000000023−23−23230000000000000000000000−3303−30000000000
χ7444-4-2-24-44-2-24221-2-222-4221-2-2-2-4222-1-1-241-12-1-111-22-2-1-11100000000−232323−2300000000000000000000003−30−330000000000
χ754-4044400-4-4-40044400000-4-4-400000000040000-40000000000000000000022−2222−2222−220000000000000000000000000000000
χ764-4044400-4-4-40044400000-4-4-400000000040000-400000000000000000000−2222−2222−22220000000000000000000000000000000
χ774-404-24002-4-423−23-24-20000022-40023−23023−2300-200002000023−230000000000000022−222ζ13−2ζ23−2ζ13+2ζ232ζ5−2ζ7−2ζ5+2ζ70000000000000000000000000000000
χ784-404-24002-4-423−23-24-20000022-40023−23023−2300-200002000023−2300000000000000−2222−2ζ13+2ζ232ζ13−2ζ23−2ζ5+2ζ72ζ5−2ζ70000000000000000000000000000000
χ794-404-24002-4-4−2323-24-20000022-400−23230−232300-2000020000−23230000000000000022−222ζ5−2ζ7−2ζ5+2ζ72ζ13−2ζ23−2ζ13+2ζ230000000000000000000000000000000
χ804-404-24002-4-4−2323-24-20000022-400−23230−232300-2000020000−232300000000000000−2222−2ζ5+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
χ8388-8-4-4-48-8-4-4-4-4-4222444-2-22224-422-42244-1-2-211-1-2-22-2-1-1110000000000000000000000000000000000000000000000000
χ8488-8-4-4-4-88-4-4-444222444-2-2222-44-2-24-2-2-4-4-1-2-211-122-2211-1-10000000000000000000000000000000000000000000000000
χ858-8088-400-8-84008-4-400000-844000000000-400004000000000000000000000000000000000000000000000000000000000
χ868-808-4-4004-8443−43-4-42000004-2400−2323043−430020000-20000−2323000000000000000000000000000000000000000000000000000
χ878-808-4-4004-84−4343-4-42000004-240023−230−43430020000-2000023−23000000000000000000000000000000000000000000000000000
χ888-80-48800-84-800-4-48000004-84000000000-400004000000000000000000000000000000000000000000000000000000000
χ898-80-48-400-84400-42-40006-644-20000000002006-6-2000000000000000000000000000000000000000000000000000000000
χ908-80-48-400-84400-42-4000-6644-2000000000200-66-2000000000000000000000000000000000000000000000000000000000
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.