Finite Group Databasebeta

← Group #13155939

Character table — Group #13155939

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11222222222224444444444444444444488888888888888121212121212121212121212242424242424242424242424242424242424242424363636363636363636363636727272216
order1223334466612123336666666612121212121212121236666612121212121212122224666666121266666666681212122424242424242424244466121212121212824244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111-1111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111-1-11111-1-1-1-1-111-1-111111-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1
χ41111111111111111111111111111111111111111111111111-1-11111-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-11
χ511111111111111111111111111111111111111111111111-1-111-1-1-1-111111-1-111-1-1-1-1111111111111-1-111-1-1-1-11111-1-1-1-1
χ611111111111111111111111111111111111111111111111-1-111-1-1-1-111111-1-111-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ711111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11111111111-1-11111-1-1-1-1-1-1-11
χ811111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111-1
χ9222222-2-2222-2-222222222222-2-2-2-2-2-2-2-2-2222222-2-2-2-2-2-2-2-22-20022-2-2000002-20022-2-20000000000000000000000000000
χ10222222-2-2222-2-222222222222-2-2-2-2-2-2-2-2-2222222-2-2-2-2-2-2-2-2-2200-2-22200000-2200-2-2220000000000000000000000000000
χ1122222-12222-1222-1-12-1-1-12-1-122-1-1-1-12222-12-1-1-1-12-1-1-1-1-1-1-12222-1-1-1-1-1-1-1-1222-1-1-1-1-1-102-1-1000000002200-1-1-1-100000000
χ1222222-12222-1222-1-12-1-1-12-1-122-1-1-1-12222-12-1-1-1-12-1-1-1-1-1-1-122-2-2-1-1-1-11111-22211-1-1-1-10-21100000000-2-200111100000000
χ1322222-12222-1222-1-12-1-1-12-1-122-1-1-1-12222-12-1-1-1-12-1-1-1-1-1-1-1-2-2221111-1-1-1-12-2-2-1-1111102-1-100000000-2-200111100000000
χ1422222-12222-1222-1-12-1-1-12-1-122-1-1-1-12222-12-1-1-1-12-1-1-1-1-1-1-1-2-2-2-211111111-2-2-21111110-211000000002200-1-1-1-100000000
χ1522222-1-2-222-1-2-22-1-12-1-1-12-1-12-21111-2-2-2-2-12-1-1-1-1-211111112-200-1-111−i3i3−i3i302-2−i3i3-1-11100−i3i3000000000000−i3i3−i3i300000000
χ1622222-1-2-222-1-2-22-1-12-1-1-12-1-12-21111-2-2-2-2-12-1-1-1-1-211111112-200-1-111i3−i3i3−i302-2i3−i3-1-11100i3−i3000000000000i3−i3i3−i300000000
χ1722222-1-2-222-1-2-22-1-12-1-1-12-1-12-21111-2-2-2-2-12-1-1-1-1-21111111-220011-1-1−i3i3−i3i30-22−i3i311-1-100−i3i3000000000000i3−i3i3−i300000000
χ1822222-1-2-222-1-2-22-1-12-1-1-12-1-12-21111-2-2-2-2-12-1-1-1-1-21111111-220011-1-1i3−i3i3−i30-22i3−i311-1-100i3−i3000000000000−i3i3−i3i300000000
χ192222-1222-12222-12-1-12-1-1-1-12222222-1-1-1-1-1-12-1-1-1-1-1-12-1-1-1-12200222200000-1-100-1-1-1-1200022-1-1-1-1-1-10000000000002-1-10
χ202222-1222-12222-12-1-12-1-1-1-12222222-1-1-1-1-1-12-1-1-1-1-1-12-1-1-1-12200222200000-1-100-1-1-1-1-2000-2-2111111000000000000-2110
χ212222-1222-12222-12-1-12-1-1-1-12222222-1-1-1-1-1-12-1-1-1-1-1-12-1-1-1-1-2-200-2-2-2-20000011001111200022-1-1-1-1-1-1000000000000-2110
χ222222-1222-12222-12-1-12-1-1-1-12222222-1-1-1-1-1-12-1-1-1-1-1-12-1-1-1-1-2-200-2-2-2-20000011001111-2000-2-21111110000000000002-1-10
χ232222-12-2-2-122-2-2-12-1-12-1-1-1-122-2-2-2-2-21111-1-12-1-1-1111-211112-20022-2-200000-1100-1-111000000333−3−3−300000000000003−30
χ242222-12-2-2-122-2-2-12-1-12-1-1-1-122-2-2-2-2-21111-1-12-1-1-1111-211112-20022-2-200000-1100-1-111000000−3−3−33330000000000000−330
χ252222-12-2-2-122-2-2-12-1-12-1-1-1-122-2-2-2-2-21111-1-12-1-1-1111-21111-2200-2-222000001-10011-1-1000000333−3−3−30000000000000−330
χ262222-12-2-2-122-2-2-12-1-12-1-1-1-122-2-2-2-2-21111-1-12-1-1-1111-21111-2200-2-222000001-10011-1-1000000−3−3−333300000000000003−30
χ27222-122222-12-1-1-1-122222-12-1-1-122-1-12-1-12-1-1-1-1-1-1-122-1-1-1-1-1002200002222-100-1-100002-1-1-1-1-12-1-12-1-100220000-1-1-1-10000
χ28222-122222-12-1-1-1-122222-12-1-1-122-1-12-1-12-1-1-1-1-1-1-122-1-1-1-1-1002200002222-100-1-10000-2-1-1-111-211-21100-2-2000011110000
χ29222-122222-12-1-1-1-122222-12-1-1-122-1-12-1-12-1-1-1-1-1-1-122-1-1-1-1-100-2-20000-2-2-2-21001100002111-1-12-1-12-1-100-2-2000011110000
χ30222-122222-12-1-1-1-122222-12-1-1-122-1-12-1-12-1-1-1-1-1-1-122-1-1-1-1-100-2-20000-2-2-2-2100110000-211111-211-21100220000-1-1-1-10000
χ3122-22222-222222222-2-2-2-2222-2-22-222222-22-2-2-2-22-22-2-222-2-20000000000000000000000000000000002-20022-2-200000000
χ3222-22222-222222222-2-2-2-2222-2-22-222222-22-2-2-2-22-22-2-222-2-2000000000000000000000000000000000-2200-2-22200000000
χ3322-2222-22222-2-2222-2-2-2-2222-22-22-2-2-2-2-222-2-2-2-222-222-2-222002-2000022-2-22002200000-2-2-2000000000000000000000000
χ3422-2222-22222-2-2222-2-2-2-2222-22-22-2-2-2-2-222-2-2-2-222-222-2-22200-220000-2-222-200-2-200000222000000000000000000000000
χ3522-222-12-222-1222-1-1-21112-1-1-2-2-11-1-1222-2-1-2111-1-2-111-1-1110000−i3i3−i3i3−i3i3i3−i3000−i3i3−i3i3−i3i300i3−i3000000002-200-1-11100000000
χ3622-222-12-222-1222-1-1-21112-1-1-2-2-11-1-1222-2-1-2111-1-2-111-1-1110000−i3i3−i3i3i3−i3−i3i3000i3−i3−i3i3−i3i300−i3i300000000-220011-1-100000000
χ3722-222-12-222-1222-1-1-21112-1-1-2-2-11-1-1222-2-1-2111-1-2-111-1-1110000i3−i3i3−i3−i3i3i3−i3000−i3i3i3−i3i3−i300i3−i300000000-220011-1-100000000
χ3822-222-12-222-1222-1-1-21112-1-1-2-2-11-1-1222-2-1-2111-1-2-111-1-1110000i3−i3i3−i3i3−i3−i3i3000i3−i3i3−i3i3−i300−i3i3000000002-200-1-11100000000
χ3922-222-1-2222-1-2-22-1-1-21112-1-1-221-111-2-2-22-1-2111-121-1-111-1-1002-2−i3i3i3−i3-1-111200-1-1−i3i3i3−i30-211000000000000−i3i3i3−i300000000
χ4022-222-1-2222-1-2-22-1-1-21112-1-1-221-111-2-2-22-1-2111-121-1-111-1-1002-2i3−i3−i3i3-1-111200-1-1i3−i3−i3i30-211000000000000i3−i3−i3i300000000
χ4122-222-1-2222-1-2-22-1-1-21112-1-1-221-111-2-2-22-1-2111-121-1-111-1-100-22−i3i3i3−i311-1-1-20011−i3i3i3−i302-1-1000000000000i3−i3−i3i300000000
χ4222-222-1-2222-1-2-22-1-1-21112-1-1-221-111-2-2-22-1-2111-121-1-111-1-100-22i3−i3−i3i311-1-1-20011i3−i3−i3i302-1-1000000000000−i3i3i3−i300000000
χ4322-2-122-222-1211-1-12-2-2-2-2-12-11-1-2211-2112-11111-1-1-22-111-1-1002-2000022-2-2-100-1-1000001113−303−303−30000000033−3−30000
χ4422-2-122-222-1211-1-12-2-2-2-2-12-11-1-2211-2112-11111-1-1-22-111-1-1002-2000022-2-2-100-1-100000111−330−330−3300000000−3−3330000
χ4522-2-122-222-1211-1-12-2-2-2-2-12-11-1-2211-2112-11111-1-1-22-111-1-100-220000-2-2221001100000-1-1-13−303−303−300000000−3−3330000
χ4622-2-122-222-1211-1-12-2-2-2-2-12-11-1-2211-2112-11111-1-1-22-111-1-100-220000-2-2221001100000-1-1-1−330−330−330000000033−3−30000
χ474444-2-244-24-244-2-21-2-211-21-244-2-2-2-2-2-2-2-21-2-2111-211-211114400-2-2-2-200000-2-20011110000000000000000000000000000
χ484444-2-244-24-244-2-21-2-211-21-244-2-2-2-2-2-2-2-21-2-2111-211-21111-4-4002222000002200-1-1-1-10000000000000000000000000000
χ494444-2-2-4-4-24-2-4-4-2-21-2-211-21-24-4222222221-2-21112-1-12-1-1-1-14-400-2-22200000-220011-1-10000000000000000000000000000
χ504444-2-2-4-4-24-2-4-4-2-21-2-211-21-24-4222222221-2-21112-1-12-1-1-1-1-440022-2-2000002-200-1-1110000000000000000000000000000
χ51444-244-4-44-2422-2-244444-24-2-22-4-422-422-4-2-2-2-2-2-22-4-4222220000000000000000000000000000000000000000000000000
χ52444-24-2444-2-2-2-2-21-24-2-2-2-2-21-2-2-2-2114-2-241-21111-2-2-21111100440000-2-2-2-2-2001100000-211000000000000000000000000
χ53444-24-2444-2-2-2-2-21-24-2-2-2-2-21-2-2-2-2114-2-241-21111-2-2-21111100-4-400002222200-1-1000002-1-1000000000000000000000000
χ54444-24-2-4-44-2-222-21-24-2-2-2-2-21-2222-1-1-422-41-21111222-1-1-1-1-100000000−2i32i3−2i32i3000i3−i3000000i3−i3000000000000000000000000
χ55444-24-2-4-44-2-222-21-24-2-2-2-2-21-2222-1-1-422-41-21111222-1-1-1-1-1000000002i3−2i32i3−2i3000−i3i3000000−i3i3000000000000000000000000
χ56444-2-2444-2-24-2-21-2-2-24-2-21-2-2-2-244-2-2-211-211-21111-2-2-211110000000000000000000004000-2-2-211-2110000000000000000
χ57444-2-2444-2-24-2-21-2-2-24-2-21-2-2-2-244-2-2-211-211-21111-2-2-21111000000000000000000000-4000222-1-12-1-10000000000000000
χ58444-2-24-4-4-2-24221-2-2-24-2-21-2-2-22-4-4222-1-1211-2111-1222-1-1-1-100000000000000000000000000023−3−3−23330000000000000000
χ59444-2-24-4-4-2-24221-2-2-24-2-21-2-2-22-4-4222-1-1211-2111-1222-1-1-1-1000000000000000000000000000−233323−3−30000000000000000
χ6044-44-244-4-24444-24-22-422-2-24-4-44-444-2-2-22-22-422-22-22-4-2-2220000000000000000000000000000000000000000000000000
χ6144-44-24-44-244-4-4-24-22-422-2-24-44-44-4-4222-2-22-422-2-22-2422-2-20000000000000000000000000000000000000000000000000
χ6244-44-2-24-4-24-244-2-2122-1-1-21-2-4-4-22-2-2-2-2-22122-1-1121-1211-1-10000−2i32i3−2i32i3000000000i3−i3i3−i30000000000000000000000000000
χ6344-44-2-24-4-24-244-2-2122-1-1-21-2-4-4-22-2-2-2-2-22122-1-1121-1211-1-100002i3−2i32i3−2i3000000000−i3i3−i3i30000000000000000000000000000
χ6444-44-2-2-44-24-2-4-4-2-2122-1-1-21-2-442-222222-2122-1-11-2-11-2-1-1110000−2i32i32i3−2i3000000000i3−i3−i3i30000000000000000000000000000
χ6544-44-2-2-44-24-2-4-4-2-2122-1-1-21-2-442-222222-2122-1-11-2-11-2-1-11100002i3−2i3−2i32i3000000000−i3i3i3−i30000000000000000000000000000
χ6644-4-2444-44-24-2-2-2-24-4-4-4-4-24-2224-4-2-24-2-2-4-22222-224-42-2-2220000000000000000000000000000000000000000000000000
χ6744-4-24-24-44-2-2-2-2-21-2-4222-2-2122-22114-2-2-412-1-1-112-22-111-1-100000000−2i32i32i3−2i3000i3−i3000000−i3i3000000000000000000000000
χ6844-4-24-24-44-2-2-2-2-21-2-4222-2-2122-22114-2-2-412-1-1-112-22-111-1-1000000002i3−2i3−2i32i3000−i3i3000000i3−i3000000000000000000000000
χ6944-4-24-2-444-2-222-21-2-4222-2-212-22-2-1-1-422412-1-1-11-22-21-1-111004-40000-2-222-20011000002-1-1000000000000000000000000
χ7044-4-24-2-444-2-222-21-2-4222-2-212-22-2-1-1-422412-1-1-11-22-21-1-11100-44000022-2-2200-1-100000-211000000000000000000000000
χ7144-4-2-244-4-2-24-2-21-2-22-4221-2-2224-4-2-2-21121-12-1-11-1-22211-1-100000000000000000000000000003-30-330000000000000000
χ7244-4-2-244-4-2-24-2-21-2-22-4221-2-2224-4-2-2-21121-12-1-11-1-22211-1-10000000000000000000000000000-3303-30000000000000000
χ7344-4-2-24-44-2-24221-2-22-4221-2-22-2-44222-1-1-21-12-1-1112-2-2-1-111000000000000000000000000023−230−330−330000000000000000
χ7444-4-2-24-44-2-24221-2-22-4221-2-22-2-44222-1-1-21-12-1-1112-2-2-1-1110000000000000000000000000−232303−303−30000000000000000
χ754-4044400-4-4-4004440000-4-4-4000000000040000-400000000000000000000000000000000000000000002i−2i00002i−2i2i−2i0000
χ764-4044400-4-4-4004440000-4-4-4000000000040000-40000000000000000000000000000000000000000000−2i2i0000−2i2i−2i2i0000
χ774-40-24400-42-423−23-2-2400002-42000023−23023−230-200002000023−2300000000000000000000000000000000000002i−2i0000ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ11−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ110000
χ784-40-24400-42-423−23-2-2400002-42000023−23023−230-200002000023−230000000000000000000000000000000000000−2i2i0000−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ11ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ110000
χ794-40-24400-42-4−2323-2-2400002-420000−23230−23230-2000020000−232300000000000000000000000000000000000002i−2i0000−ζ2+ζ7+ζ10+ζ11ζ2−ζ7−ζ10−ζ11ζ2+ζ7−ζ10+ζ11−ζ2−ζ7+ζ10−ζ110000
χ804-40-24400-42-4−2323-2-2400002-420000−23230−23230-2000020000−23230000000000000000000000000000000000000−2i2i0000ζ2−ζ7−ζ10−ζ11−ζ2+ζ7+ζ10+ζ11−ζ2−ζ7+ζ10−ζ11ζ2+ζ7−ζ10+ζ110000
χ81888-4-4-488-4-4-4-4-4222-4-422222-4-4-4-422-422-4-122-1-1-12222-1-1-1-10000000000000000000000000000000000000000000000000
χ82888-4-4-4-8-8-4-4-444222-4-422222-4444-2-24-2-24-122-1-1-1-2-2-2-211110000000000000000000000000000000000000000000000000
χ8388-8-4-4-48-8-4-4-4-4-422244-2-222244-4422-4224-1-2-211-1-22-2-2-1-1110000000000000000000000000000000000000000000000000
χ8488-8-4-4-4-88-4-4-44422244-2-22224-44-4-2-24-2-2-4-1-2-211-12-22211-1-10000000000000000000000000000000000000000000000000
χ858-8088-400-8-84008-4-40000-8440000000000-400004000000000000000000000000000000000000000000000000000000000
χ868-808-48004-8-800-48-4000044-80000000000-400004000000000000000000000000000000000000000000000000000000000
χ878-808-4-4004-8400-4-42006-64-2400000000002006-6-2000000000000000000000000000000000000000000000000000000000
χ888-808-4-4004-8400-4-4200-664-240000000000200-66-2000000000000000000000000000000000000000000000000000000000
χ898-80-48-400-84443−43-42-4000044-20000−2323043−43020000-20000−2323000000000000000000000000000000000000000000000000000
χ908-80-48-400-844−4343-42-4000044-2000023−230−4343020000-2000023−23000000000000000000000000000000000000000000000000000
χ918-80-4-480044-843−432-4-40000-244000043−430−2323020000-20000−2323000000000000000000000000000000000000000000000000000
χ928-80-4-480044-8−43432-4-40000-2440000−4343023−23020000-2000023−23000000000000000000000000000000000000000000000000000
χ938-80-4-4-40044443−43222006-6-2-2-20000−23230−23230-100-33100003−333−330000000000000000000000000000000000000000000000000
χ948-80-4-4-40044443−4322200-66-2-2-20000−23230−23230-1003-3100003−3−33330000000000000000000000000000000000000000000000000
χ958-80-4-4-400444−4343222006-6-2-2-2000023−23023−230-100-3310000−33−33330000000000000000000000000000000000000000000000000
χ968-80-4-4-400444−434322200-66-2-2-2000023−23023−230-1003-310000−3333−330000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.