Finite Group Databasebeta

← Group #13156263

Character table — Group #13156263

Order 1728.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90
size11222222222224444444444444444444488888888888888181824242424242424242424242424242424242424242424242424242436363636363636363672727272216
order12233344666121233366666666121212121212121212366666121212121212121288488121212121212121224242424242424242424242424242424248882424242461224244
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11111-1-1-1-11
χ31111111111111111111111111111111111111111111111111-111-1-1-1-1-1-1-1-11111111111111111-1-11-1-11111-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111-1
χ511111111111111111111111111111111111111111111111-1-111-11111111111-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-111-1-1-1
χ611111111111111111111111111111111111111111111111-1-11-1111111111-1-111-1-1-1-1-1-1111111-1-1-111-1-1-1-1-1-111-1
χ711111111111111111111111111111111111111111111111-1-1-11-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111
χ811111111111111111111111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-111-1-11
χ9222222-2-2222-2-222222222222-2-2-2-2-2-2-2-2-2222222-2-2-2-2-2-2-2-2000000000000000000000000000000002i−2i0000002i−2i0
χ10222222-2-2222-2-222222222222-2-2-2-2-2-2-2-2-2222222-2-2-2-2-2-2-2-200000000000000000000000000000000−2i2i000000−2i2i0
χ1122222-12222-1222-1-122-1-1-12-1-1-12-122-1-122-12-1-1-1-12-1-1-1-1-1-1-10022022-1-1-1-1-1-12200-1-1-1-1-1-1000000220000000-1-1000
χ1222222-12222-1222-1-122-1-1-12-1-1-12-122-1-122-12-1-1-1-12-1-1-1-1-1-1-1002-2022-1-1-1-1-1-1-2-200111111000000-2-2000000011000
χ1322222-12222-1222-1-122-1-1-12-1-1-12-122-1-122-12-1-1-1-12-1-1-1-1-1-1-100-220-2-21111112200-1-1-1-1-1-1000000-2-2000000011000
χ1422222-12222-1222-1-122-1-1-12-1-1-12-122-1-122-12-1-1-1-12-1-1-1-1-1-1-100-2-20-2-2111111-2-200111111000000220000000-1-1000
χ152222-12222-1222-12-12-12-1-1-12-12-12-1-1222-1-1-12-1-1-1-12-1-1-1-1-1-100202-1-122-1-1-1-10022000000-1-1-1-1-1-100022000000-1-10
χ162222-12222-1222-12-12-12-1-1-12-12-12-1-1222-1-1-12-1-1-1-12-1-1-1-1-1-10020-2-1-122-1-1-1-100-2-2000000111111000-2-2000000110
χ172222-12222-1222-12-12-12-1-1-12-12-12-1-1222-1-1-12-1-1-1-12-1-1-1-1-1-100-20211-2-211110022000000-1-1-1-1-1-1000-2-2000000110
χ182222-12222-1222-12-12-12-1-1-12-12-12-1-1222-1-1-12-1-1-1-12-1-1-1-1-1-100-20-211-2-2111100-2-200000011111100022000000-1-10
χ192222-12-2-22-12-2-2-12-12-12-1-1-12-1-21-211-2-2-21-1-12-1-1-11-211111100000−i3i300−i3−i3i3i30000000000333−3−3−30002i−2i000000−ii0
χ202222-12-2-22-12-2-2-12-12-12-1-1-12-1-21-211-2-2-21-1-12-1-1-11-211111100000−i3i300−i3−i3i3i30000000000−3−3−3333000−2i2i000000i−i0
χ212222-12-2-22-12-2-2-12-12-12-1-1-12-1-21-211-2-2-21-1-12-1-1-11-211111100000i3−i300i3i3−i3−i30000000000333−3−3−3000−2i2i000000i−i0
χ222222-12-2-22-12-2-2-12-12-12-1-1-12-1-21-211-2-2-21-1-12-1-1-11-211111100000i3−i300i3i3−i3−i30000000000−3−3−33330002i−2i000000−ii0
χ23222-12222-122-1-1-1-12-12222-1-12222-1-1-1-1-12-1-1-1-1-1-1-1-122-1-1-1-12202200000000-1-1-1-122-1-1-1-12-1-12-1-100200-1-1-1-100000
χ24222-12222-122-1-1-1-12-12222-1-12222-1-1-1-1-12-1-1-1-1-1-1-1-122-1-1-1-1220-2-2000000001111-2-21111-211-21100200-1-1-1-100000
χ25222-12222-122-1-1-1-12-12222-1-12222-1-1-1-1-12-1-1-1-1-1-1-1-122-1-1-1-1-2-202-200000000-1-11122-1-1-1-1-211-21100-200111100000
χ26222-12222-122-1-1-1-12-12222-1-12222-1-1-1-1-12-1-1-1-1-1-1-1-122-1-1-1-1-2-20-220000000011-1-1-2-211112-1-12-1-100-200111100000
χ2722-22222-222222222-2-2-2-2-2222-2222222-2-22-2-2-2-22-2-22-222-2-2000000000000000000000000000002-200000002-2000
χ2822-22222-222222222-2-2-2-2-2222-2222222-2-22-2-2-2-22-2-22-222-2-200000000000000000000000000000-220000000-22000
χ2922-2222-22222-2-2222-2-2-2-2-22222-2-2-2-2-2-2222-2-2-2-2222-22-2-2222200000000000000000000000000000-20022-2-200000
χ3022-2222-22222-2-2222-2-2-2-2-22222-2-2-2-2-2-2222-2-2-2-2222-22-2-222-2-200000000000000000000000000000200-2-22200000
χ3122-222-12-222-1222-1-1-2-21112-1-112-122-1-1-2-2-1-2111-1-21-11-1-1110000000−i3i3−i3i3−i3i30000−i3i3−i3−i3i3i30000002-20000000-11000
χ3222-222-12-222-1222-1-1-2-21112-1-112-122-1-1-2-2-1-2111-1-21-11-1-1110000000−i3i3−i3i3−i3i30000i3−i3i3i3−i3−i3000000-2200000001-1000
χ3322-222-12-222-1222-1-1-2-21112-1-112-122-1-1-2-2-1-2111-1-21-11-1-1110000000i3−i3i3−i3i3−i30000−i3i3−i3−i3i3i3000000-2200000001-1000
χ3422-222-12-222-1222-1-1-2-21112-1-112-122-1-1-2-2-1-2111-1-21-11-1-1110000000i3−i3i3−i3i3−i30000i3−i3i3i3−i3−i30000002-20000000-11000
χ3522-2-122-22-12211-1-121-2-2-2-2-1-122-2-21111-12-11111-1-1-1-2211-1-122000000000003−33−3003−33−303−303−300-200-1-11100000
χ3622-2-122-22-12211-1-121-2-2-2-2-1-122-2-21111-12-11111-1-1-1-2211-1-12200000000000−33−3300−33−330−330−3300-200-1-11100000
χ3722-2-122-22-12211-1-121-2-2-2-2-1-122-2-21111-12-11111-1-1-1-2211-1-1-2-2000000000003−3−33003−33−30−330−330020011-1-100000
χ3822-2-122-22-12211-1-121-2-2-2-2-1-122-2-21111-12-11111-1-1-1-2211-1-1-2-200000000000−333−300−33−3303−303−30020011-1-100000
χ3944444-2-4-444-2-4-44-2-244-2-2-24-2-22-42-4-422-4-4-24-2-2-2-2-422222220000000000000000000000000000000000000000000
χ404444-2-2444-2-244-2-214-2-211-2-21-2-2-2-2-2-2-24-21-2-2111-2-211111100400-2-2-2-21111000000000000000000000000000000
χ414444-2-2444-2-244-2-214-2-211-2-21-2-2-2-2-2-2-24-21-2-2111-2-211111100-4002222-1-1-1-1000000000000000000000000000000
χ424444-2-2-4-44-2-2-4-4-2-214-2-211-2-212222222-421-2-211122-1-1-1-1-1-100000−2i32i300i3i3−i3−i3000000000000000000000000000000
χ434444-2-2-4-44-2-2-4-4-2-214-2-211-2-212222222-421-2-211122-1-1-1-1-1-1000002i3−2i300−i3−i3i3i3000000000000000000000000000000
χ44444-244-4-4-24422-2-24-24444-2-24-4-4-422222-4-2-2-2-2-2-222-4-422220000000000000000000000000000000000000000000
χ45444-24-244-24-2-2-2-21-2-24-2-2-2-21-2-24-2-2-211-241-21111-21-2-211110004000000000-2-200-2-2111100000000000000000000
χ46444-24-244-24-2-2-2-21-2-24-2-2-2-21-2-24-2-2-211-241-21111-21-2-21111000-4000000000220022-1-1-1-100000000000000000000
χ47444-24-2-4-4-24-222-21-2-24-2-2-2-21-22-4222-1-12-41-211112-122-1-1-1-100000000000000000003i−3i−3i3i00000000000000000000
χ48444-24-2-4-4-24-222-21-2-24-2-2-2-21-22-4222-1-12-41-211112-122-1-1-1-10000000000000000000−3i3i3i−3i00000000000000000000
χ49444-2-2444-2-24-2-21-2-2-2-24-2-21-2-24-2411-2-2-2-211-21111-2-2-21111000040000000000-2-2000000-211-21100000000000000
χ50444-2-2444-2-24-2-21-2-2-2-24-2-21-2-24-2411-2-2-2-211-21111-2-2-211110000-40000000000220000002-1-12-1-100000000000000
χ51444-2-24-4-4-2-24221-2-2-2-24-2-21-2-2-42-4-1-1222211-2111-1222-1-1-1-10000000000000000000000023−3−3−233300000000000000
χ52444-2-24-4-4-2-24221-2-2-2-24-2-21-2-2-42-4-1-1222211-2111-1222-1-1-1-100000000000000000000000−233323−3−300000000000000
χ5344-444-2-4444-2-4-44-2-2-4-42224-2-2-2-42-4-42244-2-4222-24-22-222-2-20000000000000000000000000000000000000000000
χ5444-44-244-44-2444-24-2-42-422-24-2-4-24-2-244-42-22-422-22-4-22-2-2220000000000000000000000000000000000000000000
χ5544-44-24-444-24-4-4-24-2-42-422-24-242-422-4-44-2-22-422-2-242-222-2-20000000000000000000000000000000000000000000
χ5644-44-2-24-44-2-244-2-21-422-1-1-2-212-2-2-2-2-2-2-42122-1-11221-111-1-10000000−2i32i3i3−i3i3−i3000000000000000000000000000000
χ5744-44-2-24-44-2-244-2-21-422-1-1-2-212-2-2-2-2-2-2-42122-1-11221-111-1-100000002i3−2i3−i3i3−i3i3000000000000000000000000000000
χ5844-44-2-2-444-2-2-4-4-2-21-422-1-1-2-21-22222224-2122-1-11-2-2-11-1-1110000000003-3-33000000000000000000000000000000
χ5944-44-2-2-444-2-2-4-4-2-21-422-1-1-2-21-22222224-2122-1-11-2-2-11-1-111000000000-333-3000000000000000000000000000000
χ6044-4-2444-4-244-2-2-2-242-4-4-4-4-2-24-444-2-2-2-22-4-22222-2224-4-2-2220000000000000000000000000000000000000000000
χ6144-4-24-24-4-24-2-2-2-21-22-4222-21-224-2-2-2112-412-1-1-112-1-2211-1-100000000000000000−2i32i3i3i3−i3−i300000000000000000000
χ6244-4-24-24-4-24-2-2-2-21-22-4222-21-224-2-2-2112-412-1-1-112-1-2211-1-1000000000000000002i3−2i3−i3−i3i3i300000000000000000000
χ6344-4-24-2-44-24-222-21-22-4222-21-2-2-4222-1-1-2412-1-1-11-212-2-1-111000000000000023−230000−33−3300000000000000000000
χ6444-4-24-2-44-24-222-21-22-4222-21-2-2-4222-1-1-2412-1-1-11-212-2-1-1110000000000000−232300003−33−300000000000000000000
χ6544-4-2-244-4-2-24-2-21-2-222-4221-2-2-4-2411-2-2221-12-1-11-12-2211-1-10000000000000000000000003-30-3300000000000000
χ6644-4-2-244-4-2-24-2-21-2-222-4221-2-2-4-2411-2-2221-12-1-11-12-2211-1-1000000000000000000000000-3303-300000000000000
χ6744-4-2-24-44-2-24221-2-222-4221-2-242-4-1-122-2-21-12-1-111-22-2-1-11100000000000000023−230000000−330−3300000000000000
χ6844-4-2-24-44-2-24221-2-222-4221-2-242-4-1-122-2-21-12-1-111-22-2-1-111000000000000000−232300000003−303−300000000000000
χ694-4044400-4-4-40044400000-4-4-400000000040000-40000000022−220000000000000000000000000000000022−220000000
χ704-4044400-4-4-40044400000-4-4-400000000040000-400000000−222200000000000000000000000000000000−22220000000
χ714-40-244002-4-423−23-2-240000022-400023−2323−2300-200002000023−230022−2200000000000000000000000000000000−226−600000
χ724-40-244002-4-423−23-2-240000022-400023−2323−2300-200002000023−2300−2222000000000000000000000000000000002−2−6600000
χ734-40-244002-4-4−2323-2-240000022-4000−2323−232300-2000020000−23230022−2200000000000000000000000000000000−22−6600000
χ744-40-244002-4-4−2323-2-240000022-4000−2323−232300-2000020000−232300−2222000000000000000000000000000000002−26−600000
χ75888-4-4-488-4-4-4-4-4222-4-4-422222-4-4-42222-4-4-122-1-1-12222-1-1-1-10000000000000000000000000000000000000000000
χ76888-4-4-4-8-8-4-4-444222-4-4-422222444-2-2-2-244-122-1-1-1-2-2-2-211110000000000000000000000000000000000000000000
χ7788-8-4-4-48-8-4-4-4-4-4222444-2-22224-4-4222244-1-2-211-1-2-22-2-1-1110000000000000000000000000000000000000000000
χ7888-8-4-4-4-88-4-4-444222444-2-2222-444-2-2-2-2-4-4-1-2-211-122-2211-1-10000000000000000000000000000000000000000000
χ798-8088-400-8-84008-4-400000-844000000000-400004000000000000000000000000000000000000000000000000000
χ808-808-4800-84-800-48-4000004-84000000000-400004000000000000000000000000000000000000000000000000000
χ818-808-4-400-84400-4-420006-644-20000000002006-6-2000000000000000000000000000000000000000000000000000
χ828-808-4-400-84400-4-42000-6644-2000000000200-66-2000000000000000000000000000000000000000000000000000
χ838-80-48-4004-8443−43-42-4000004-2400043−43−23230020000-20000−2323000000000000000000000000000000000000000000000
χ848-80-48-4004-84−4343-42-4000004-24000−434323−230020000-2000023−23000000000000000000000000000000000000000000000
χ858-80-4-480044-843−432-4-400000-244000−232343−430020000-20000−2323000000000000000000000000000000000000000000000
χ868-80-4-480044-8−43432-4-400000-24400023−23−43430020000-2000023−23000000000000000000000000000000000000000000000
χ878-80-4-4-40044443−432220006-6-2-2-2000−2323−232300-100-33100003−333−330000000000000000000000000000000000000000000
χ888-80-4-4-40044443−43222000-66-2-2-2000−2323−232300-1003-3100003−3−33330000000000000000000000000000000000000000000
χ898-80-4-4-400444−43432220006-6-2-2-200023−2323−2300-100-3310000−33−33330000000000000000000000000000000000000000000
χ908-80-4-4-400444−4343222000-66-2-2-200023−2323−2300-1003-310000−3333−330000000000000000000000000000000000000000000

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