Finite Group Databasebeta

← Group #13156252

Character table — Group #13156252

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size112222222222244444444444444444444888888888888881212181824242424242424242424242424242424242424242424242424243636363636727272727272108108
order122333446661212333666666121212121212121212121236666661212121212121224886666881212121224242424242424242424242424242424824242424441212121288
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-111
χ31111111111111111111111111111111111111111111111111-1-111111-1111111-1-1111111-1-1-1-1-1-1-1-1-1-1-11-111-1-1-1-1
χ41111111111111111111111111111111111111111111111111-1-11111-111111-1-111-1-1-1-1-1-1111111-1-1-1-1-1-11-1-111-1-1
χ511111111111111111111111111111111111111111111111-1-111-1-1-1-111-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-1
χ611111111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1
χ711111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11-1-11111
χ811111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-11-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-11-111-1-111
χ9222222-2-2222-2-2222222222-2-2-2-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-2000000000000000000000000000000000000000002i−2i
χ10222222-2-2222-2-2222222222-2-2-2-2-2-2-2-2-2-2-22222222-2-2-2-2-2-2-200000000000000000000000000000000000000000−2i2i
χ1122222-12222-1222-1-122-12-1-12-1-1-12-122-1-12-12-1-1-1-1-12-1-1-1-1-1-122002-1-1-1022-1-1-10022000000-1-1-1-1-1-1000000200-1-100
χ1222222-12222-1222-1-122-12-1-12-1-1-12-122-1-12-12-1-1-1-1-12-1-1-1-1-1-122002-1-1-10-22-1-1-100-2-2000000111111000000-2001100
χ1322222-12222-1222-1-122-12-1-12-1-1-12-122-1-12-12-1-1-1-1-12-1-1-1-1-1-1-2-200-211102-21110022000000-1-1-1-1-1-1000000-2001100
χ1422222-12222-1222-1-122-12-1-12-1-1-12-122-1-12-12-1-1-1-1-12-1-1-1-1-1-1-2-200-21110-2-211100-2-2000000111111000000200-1-100
χ152222-12222-1222-12-12-12-12-1-12-1-1-12-1-1222-1-12-1-1-1-1-12-1-1-1-1-12200-12-1-120-12-1-12200-1-1-1-1-1-10000000000020-1-10000
χ162222-12222-1222-12-12-12-12-1-12-1-1-12-1-1222-1-12-1-1-1-1-12-1-1-1-1-12200-12-1-1-20-12-1-1-2-20011111100000000000-20110000
χ172222-12222-1222-12-12-12-12-1-12-1-1-12-1-1222-1-12-1-1-1-1-12-1-1-1-1-1-2-2001-211201-2112200-1-1-1-1-1-100000000000-20110000
χ182222-12222-1222-12-12-12-12-1-12-1-1-12-1-1222-1-12-1-1-1-1-12-1-1-1-1-1-2-2001-211-201-211-2-2001111110000000000020-1-10000
χ19222-12222-122-1-1-1-12-122-1-12222222-1-1-1-1-1-1-1-12-1-1-1-1-12-1-1-1-100220000220000-1-1-1-122-1-1-1-122-1-1-1-12-1-1-1-100000000
χ20222-12222-122-1-1-1-12-122-1-12222222-1-1-1-1-1-1-1-12-1-1-1-1-12-1-1-1-100220000-2-200001111-2-21111-2-211112-1-1-1-100000000
χ21222-12222-122-1-1-1-12-122-1-12222222-1-1-1-1-1-1-1-12-1-1-1-1-12-1-1-1-100-2-200002-20000-1-11122-1-1-1-1-2-21111-2111100000000
χ22222-12222-122-1-1-1-12-122-1-12222222-1-1-1-1-1-1-1-12-1-1-1-1-12-1-1-1-100-2-20000-22000011-1-1-2-2111122-1-1-1-1-2111100000000
χ2322-22222-222222222-2-2-2222-2-2-2-2222222-22-2-2-2-2-22-2-2222-2-22-200222200-2-2-2-200000000000000000000000000000
χ2422-22222-222222222-2-2-2222-2-2-2-2222222-22-2-2-2-2-22-2-2222-2-2-2200-2-2-2-200222200000000000000000000000000000
χ2522-2222-22222-2-2222-2-2-22222222-2-2-2-2-2-222-2-2-2-2-2222-2-2-222002200000000000000000000000000-222-2-200000000
χ2622-2222-22222-2-2222-2-2-22222222-2-2-2-2-2-222-2-2-2-2-2222-2-2-22200-2-2000000000000000000000000002-2-22200000000
χ2722-222-12-222-1222-1-1-2-212-1-1-21112-122-1-1-2-1-21111-1-21-1-1-1112-2002-1-1-100-21110000000000−i3i3−i3−i3i3i3000000000−i3i300
χ2822-222-12-222-1222-1-1-2-212-1-1-21112-122-1-1-2-1-21111-1-21-1-1-1112-2002-1-1-100-21110000000000i3−i3i3i3−i3−i3000000000i3−i300
χ2922-222-12-222-1222-1-1-2-212-1-1-21112-122-1-1-2-1-21111-1-21-1-1-111-2200-2111002-1-1-10000000000−i3i3−i3−i3i3i3000000000i3−i300
χ3022-222-12-222-1222-1-1-2-212-1-1-21112-122-1-1-2-1-21111-1-21-1-1-111-2200-2111002-1-1-10000000000i3−i3i3i3−i3−i3000000000−i3i300
χ3122-22-122-22-1222-12-1-21-2-12-11-211-12-1-122-2-11-2111-11-2-1-1-1112-200-12-1-1001-2110000−i3i3−i3−i3i3i30000000000000−i3i30000
χ3222-22-122-22-1222-12-1-21-2-12-11-211-12-1-122-2-11-2111-11-2-1-1-1112-200-12-1-1001-2110000i3−i3i3i3−i3−i30000000000000i3−i30000
χ3322-22-122-22-1222-12-1-21-2-12-11-211-12-1-122-2-11-2111-11-2-1-1-111-22001-21100-12-1-10000−i3i3−i3−i3i3i30000000000000i3−i30000
χ3422-22-122-22-1222-12-1-21-2-12-11-211-12-1-122-2-11-2111-11-2-1-1-111-22001-21100-12-1-10000i3−i3i3i3−i3−i30000000000000−i3i30000
χ3522-2-122-22-12211-1-121-2-2-1-122222-2-21111-1-111-211-1-1-1-211-1-1002200000000003−33−3003−33−3003−33−3-2-1-11100000000
χ3622-2-122-22-12211-1-121-2-2-1-122222-2-21111-1-111-211-1-1-1-211-1-100220000000000−33−3300−33−3300−33−33-2-1-11100000000
χ3722-2-122-22-12211-1-121-2-2-1-122222-2-21111-1-111-211-1-1-1-211-1-100-2-200000000003−3−33003−33−300−33−33211-1-100000000
χ3822-2-122-22-12211-1-121-2-2-1-122222-2-21111-1-111-211-1-1-1-211-1-100-2-20000000000−333−300−33−33003−33−3211-1-100000000
χ3944444-2-4-444-2-4-44-2-244-24-2-2-4222-42-4-422-4-24-2-2-2-2-2-42222220000000000000000000000000000000000000000000
χ404444-24-4-44-24-4-4-24-24-24-24-22-4222-422-4-4-4-2-24-2-2-2-22-4222220000000000000000000000000000000000000000000
χ414444-2-2444-2-244-2-214-2-2-2-21-2-211-2-2-2-2-2-241-2-21111-2-2111114400-2-21100-2-21100000000000000000000000000000
χ424444-2-2444-2-244-2-214-2-2-2-21-2-211-2-2-2-2-2-241-2-21111-2-211111-4-40022-1-10022-1-100000000000000000000000000000
χ434444-2-2-4-44-2-2-4-4-2-214-2-2-2-2122-1-1222222-41-2-2111122-1-1-1-1-10000003-300003-300000000000000000000000000000
χ444444-2-2-4-44-2-2-4-4-2-214-2-2-2-2122-1-1222222-41-2-2111122-1-1-1-1-1000000-330000-3300000000000000000000000000000
χ45444-244-4-4-24422-2-24-244-2-24-4-4-4-4-4-422222-2-2-24-2-2-222-422220000000000000000000000000000000000000000000
χ46444-24-244-24-2-2-2-21-2-24-2-21-24-2-2-24-2-2-211-21-21-2111-21-211110000000004000000-2-2000000-2-211110000000000000
χ47444-24-244-24-2-2-2-21-2-24-2-21-24-2-2-24-2-2-211-21-21-2111-21-21111000000000-40000002200000022-1-1-1-10000000000000
χ48444-24-2-4-4-24-222-21-2-24-2-21-2-4222-4222-1-121-21-21112-12-1-1-1-1000000000000000000000000003i−3i−3i3i0000000000000
χ49444-24-2-4-4-24-222-21-2-24-2-21-2-4222-4222-1-121-21-21112-12-1-1-1-100000000000000000000000000−3i3i3i−3i0000000000000
χ50444-2-2444-2-24-2-21-2-2-2-241-2-2-24-2-2-2411-2-2-211-2-21111-2-2111100000000400000-2-200-2-211110000000000000000000
χ51444-2-2444-2-24-2-21-2-2-2-241-2-2-24-2-2-2411-2-2-211-2-21111-2-2111100000000-400000220022-1-1-1-10000000000000000000
χ52444-2-24-4-4-2-24221-2-2-2-241-2-22-4222-4-1-122211-2-2111-122-1-1-1-1000000000000000000003i−3i−3i3i0000000000000000000
χ53444-2-24-4-4-2-24221-2-2-2-241-2-22-4222-4-1-122211-2-2111-122-1-1-1-100000000000000000000−3i3i3i−3i0000000000000000000
χ5444-444-2-4444-2-4-44-2-2-4-424-2-24-2-2-2-42-4-4224-2-42222-24-2222-2-20000000000000000000000000000000000000000000
χ5544-44-24-444-24-4-4-24-2-42-4-24-2-24-2-22-422-4-44-22-4222-2-24222-2-20000000000000000000000000000000000000000000
χ5644-44-2-24-44-2-244-2-21-422-2-2122-1-1-2-2-2-2-2-2-4122-1-1-1122111-1-14-400-2-2110022-1-100000000000000000000000000000
χ5744-44-2-24-44-2-244-2-21-422-2-2122-1-1-2-2-2-2-2-2-4122-1-1-1122111-1-1-440022-1-100-2-21100000000000000000000000000000
χ5844-44-2-2-444-2-2-4-4-2-21-422-2-21-2-2112222224122-1-1-11-2-2-1-1-1110000003-30000-3300000000000000000000000000000
χ5944-44-2-2-444-2-2-4-4-2-21-422-2-21-2-2112222224122-1-1-11-2-2-1-1-111000000-3300003-300000000000000000000000000000
χ6044-4-2444-4-244-2-2-2-242-4-4-2-24-4-4-4-444-2-2-2-22-222-422-2224-2-2220000000000000000000000000000000000000000000
χ6144-4-24-24-4-24-2-2-2-21-22-42-21-2-42224-2-2-211212-12-1-112-1-211-1-1000000000000000000000000−2i32i3i3i3−i3−i30000000000000
χ6244-4-24-24-4-24-2-2-2-21-22-42-21-2-42224-2-2-211212-12-1-112-1-211-1-10000000000000000000000002i3−2i3−i3−i3i3i30000000000000
χ6344-4-24-2-44-24-222-21-22-42-21-24-2-2-2-4222-1-1-212-12-1-11-212-1-111000000000000000023−2300000000−33−330000000000000
χ6444-4-24-2-44-24-222-21-22-42-21-24-2-2-2-4222-1-1-212-12-1-11-212-1-1110000000000000000−2323000000003−33−30000000000000
χ6544-4-2-244-4-2-24-2-21-2-222-41-2-22-422-2411-2-221-122-1-11-12-211-1-1000000000000000000−2i32i3i3i3−i3−i30000000000000000000
χ6644-4-2-244-4-2-24-2-21-2-222-41-2-22-422-2411-2-221-122-1-11-12-211-1-10000000000000000002i3−2i3−i3−i3i3i30000000000000000000
χ6744-4-2-24-44-2-24221-2-222-41-2-2-24-2-22-4-1-122-21-122-1-111-22-1-1110000000000000023−230000−33−330000000000000000000
χ6844-4-2-24-44-2-24221-2-222-41-2-2-24-2-22-4-1-122-21-122-1-111-22-1-11100000000000000−232300003−33−30000000000000000000
χ694-4044400-4-4-400444000-4-4-400000000000400000-400000000022−2200000000000000000000000000022−220000000000
χ704-4044400-4-4-400444000-4-4-400000000000400000-4000000000−2222000000000000000000000000000−22220000000000
χ714-40-244002-4-423−23-2-2400022-400000023−2323−230-200000200023−23000022−22000000000000000000000000000−226−600000000
χ724-40-244002-4-423−23-2-2400022-400000023−2323−230-200000200023−230000−22220000000000000000000000000002−2−6600000000
χ734-40-244002-4-4−2323-2-2400022-4000000−2323−23230-2000002000−2323000022−22000000000000000000000000000−22−6600000000
χ744-40-244002-4-4−2323-2-2400022-4000000−2323−23230-2000002000−23230000−22220000000000000000000000000002−26−600000000
χ75888-4-4-488-4-4-4-4-4222-4-4-4222-4-422-4-42222-4-1222-1-1-1222-1-1-1-10000000000000000000000000000000000000000000
χ76888-4-4-4-8-8-4-4-444222-4-4-422244-2-244-2-2-2-24-1222-1-1-1-2-2-211110000000000000000000000000000000000000000000
χ7788-8-4-4-48-8-4-4-4-4-422244422244-2-2-4-422224-1-2-2-211-1-2-22-1-1110000000000000000000000000000000000000000000
χ7888-8-4-4-4-88-4-4-444222444222-4-42244-2-2-2-2-4-1-2-2-211-122-211-1-10000000000000000000000000000000000000000000
χ798-8088-400-8-84008-4-4000-84400000000000-400000400000000000000000000000000000000000000000000000000
χ808-808-4800-84-800-48-40004-8400000000000-400000400000000000000000000000000000000000000000000000000
χ818-808-4-400-84400-4-4200044-2006i−6i0000000200000-2000006i−6i0000000000000000000000000000000000000000000
χ828-808-4-400-84400-4-4200044-200−6i6i0000000200000-200000−6i6i0000000000000000000000000000000000000000000
χ838-80-48-4004-8443−43-42-40004-2400000043−43−23230200000-2000−2323000000000000000000000000000000000000000000000
χ848-80-48-4004-84−4343-42-40004-24000000−434323−230200000-200023−23000000000000000000000000000000000000000000000
χ858-80-4-480044-843−432-4-4000-244000000−232343−430200000-2000−2323000000000000000000000000000000000000000000000
χ868-80-4-480044-8−43432-4-4000-24400000023−23−43430200000-200023−23000000000000000000000000000000000000000000000
χ878-80-4-4-40044443−43222000-2-2-2006i−6i00−2323−23230-1000−3i33i310003−3−3i3i0000000000000000000000000000000000000000000
χ888-80-4-4-40044443−43222000-2-2-200−6i6i00−2323−23230-10003i3−3i310003−33i−3i0000000000000000000000000000000000000000000
χ898-80-4-4-400444−4343222000-2-2-2006i−6i0023−2323−230-10003i3−3i31000−33−3i3i0000000000000000000000000000000000000000000
χ908-80-4-4-400444−4343222000-2-2-200−6i6i0023−2323−230-1000−3i33i31000−333i−3i0000000000000000000000000000000000000000000

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