Finite Group Databasebeta

← Group #14302975

Character table — Group #14302975

Order 1920.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81
size11222222244444488888888888888888888888881010101012122020202020202020244040404040404040404040404048484848606060606060120120120
order1223446121256101010124121215202020202020303030606060606060606060606060224444444466121244881212121212122424242420202020444444288
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1111111-1-1-1-11-1-1
χ311111111111111111111111111111111111111111111-1-111111111-11111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111111111111111111111-1-1-1-1-1-11111-11-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111
χ51111111111111111111111111111111111111111-1-1-1-111ii−i−i-1-1-1-11-1i−i-1-1ii−i−iii−i−i1111-1-1ii−i−i-1i−i
χ61111111111111111111111111111111111111111-1-1-1-111−i−iii-1-1-1-11-1−ii-1-1−i−iii−i−iii1111-1-1−i−iii-1−ii
χ71111111111111111111111111111111111111111-1-1-1-1-1-1ii−i−i-1-1-1-1-1-1i−i-1-1ii−i−iii−i−i-1-1-1-111−i−iii1−ii
χ81111111111111111111111111111111111111111-1-1-1-1-1-1−i−iii-1-1-1-1-1-1−ii-1-1−i−iii−i−iii-1-1-1-111ii−i−i1i−i
χ9111111111111111-1-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-11111-1-1-1-111-1-1111111-1-1-1
χ10111111111111111-1-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-111-1-1-1-1-1-1111111-1-111-1-1-1-1-111
χ11111111111111111-1-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1111111111-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1111
χ12111111111111111-1-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111-111-1-1-1-1-1-11111-1-111-1-111111-1-1
χ13111111111111111-1-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-111ii−i−i-1-1-1-1-11−ii11ii−i−i−i−iii11-1-1-1-1ii−i−i1−ii
χ14111111111111111-1-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-111−i−iii-1-1-1-1-11i−i11−i−iiiii−i−i11-1-1-1-1−i−iii1i−i
χ15111111111111111-1-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1ii−i−i-1-1-1-111−ii11ii−i−i−i−iii-1-11111−i−iii-1i−i
χ16111111111111111-1-1-11-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−iii-1-1-1-111i−i11−i−iiiii−i−i-1-11111ii−i−i-1−ii
χ172222-2-22-2-222222-200020000-2-2222-2-2-2-20000000022-2-22-2000022-2-2000000000000002-2002-20000000
χ182222-2-22-2-222222-200020000-2-2222-2-2-2-20000000022-2-2-22000022-2-200000000000000-2200-220000000
χ192222-2-22-2-222222-200020000-2-2222-2-2-2-200000000-2-2222-20000-2-222000000000000002-200-220000000
χ202222-2-22-2-222222-200020000-2-2222-2-2-2-200000000-2-222-220000-2-22200000000000000-22002-20000000
χ21222-122-1-1-12-1222-12-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222002222-1-1-1-10222-1-1-1-1-1-1-1-1-1-10000000000000
χ22222-122-1-1-12-1222-12-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222200-2-2-2-2-1-1-1-102-2-2-1-1111111110000000000000
χ23222-122-1-1-12-1222-12-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2002i2i−2i−2i11110-22i−2i11−i−iii−i−iii0000000000000
χ24222-122-1-1-12-1222-12-1-1-1222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-200−2i−2i2i2i11110-2−2i2i11ii−i−iii−i−i0000000000000
χ25222-122-1-1-12-1222-1-211-1-2-2-2-222-1-1-1-1-1-1-1111111112222002222-1-1-1-10-2-2-211-1-1-1-111110000000000000
χ26222-122-1-1-12-1222-1-211-1-2-2-2-222-1-1-1-1-1-1-111111111222200-2-2-2-2-1-1-1-10-222111111-1-1-1-10000000000000
χ27222-122-1-1-12-1222-1-211-1-2-2-2-222-1-1-1-1-1-1-111111111-2-2-2-2002i2i−2i−2i111102−2i2i-1-1−i−iiiii−i−i0000000000000
χ28222-122-1-1-12-1222-1-211-1-2-2-2-222-1-1-1-1-1-1-111111111-2-2-2-200−2i−2i2i2i1111022i−2i-1-1ii−i−i−i−iii0000000000000
χ2922-222-22222-2-2-22-2000200002-22-2-222-2-2000000002-22-2002i−2i2i−2i2-2-220000002i−2i2i−2i00000000000000000
χ3022-222-22222-2-2-22-2000200002-22-2-222-2-2000000002-22-200−2i2i−2i2i2-2-22000000−2i2i−2i2i00000000000000000
χ3122-222-22222-2-2-22-2000200002-22-2-222-2-200000000-22-22002-2-22-222-20000002-2-2200000000000000000
χ3222-222-22222-2-2-22-2000200002-22-2-222-2-200000000-22-2200-222-2-222-2000000-222-200000000000000000
χ3322-22-222-2-22-2-2-22200020000-222-2-2-2-222000000002-2-220000002-22-2000000000000000000002i−2i2i−2i000
χ3422-22-222-2-22-2-2-22200020000-222-2-2-2-222000000002-2-220000002-22-200000000000000000000−2i2i−2i2i000
χ3522-22-222-2-22-2-2-22200020000-222-2-2-2-22200000000-222-2000000-22-22000000000000000000002-2-22000
χ3622-22-222-2-22-2-2-22200020000-222-2-2-2-22200000000-222-2000000-22-2200000000000000000000-222-2000
χ3722-2-12-2-1-1-121-2-22103−3-100002-2-111-1-1113333−3−3−3−32-22-2002i−2i2i−2i-111-100003−3−ii−ii−i3i3−i3i30000000000000
χ3822-2-12-2-1-1-121-2-22103−3-100002-2-111-1-1113333−3−3−3−32-22-200−2i2i−2i2i-111-100003−3i−ii−ii3−i3i3−i30000000000000
χ3922-2-12-2-1-1-121-2-22103−3-100002-2-111-1-1113333−3−3−3−3-22-22002-2-221-1-110000−33-111-1−333−30000000000000
χ4022-2-12-2-1-1-121-2-22103−3-100002-2-111-1-1113333−3−3−3−3-22-2200-222-21-1-110000−331-1-113−3−330000000000000
χ4122-2-12-2-1-1-121-2-2210−33-100002-2-111-1-111−3−3−3−333332-22-2002i−2i2i−2i-111-10000−33−ii−iii3−i3i3−i30000000000000
χ4222-2-12-2-1-1-121-2-2210−33-100002-2-111-1-111−3−3−3−333332-22-200−2i2i−2i2i-111-10000−33i−ii−i−i3i3−i3i30000000000000
χ4322-2-12-2-1-1-121-2-2210−33-100002-2-111-1-111−3−3−3−33333-22-22002-2-221-1-1100003−3-111-13−3−330000000000000
χ4422-2-12-2-1-1-121-2-2210−33-100002-2-111-1-111−3−3−3−33333-22-2200-222-21-1-1100003−31-1-11−333−30000000000000
χ45444444444-14-1-1-14444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000440000000040000000000000-1-1-1-1000000000
χ46444444444-14-1-1-14444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000-4-400000000-400000000000001111000000000
χ47444444444-14-1-1-14-4-4-4-11111-1-1-1-1-1-1-1-1-11111111100004400000000-40000000000000-1-111000000000
χ48444444444-14-1-1-14-4-4-4-11111-1-1-1-1-1-1-1-1-1111111110000-4-4000000004000000000000011-1-1000000000
χ494444-4-44-4-4-14-1-1-1-4000-1−5−55511-1-1-11111−5−555−5−55500004-40000000000000000000000-11−55000000000
χ504444-4-44-4-4-14-1-1-1-4000-1−5−55511-1-1-11111−5−555−5−5550000-4400000000000000000000001-15−5000000000
χ514444-4-44-4-4-14-1-1-1-4000-155−5−511-1-1-1111155−5−555−5−500004-40000000000000000000000-115−5000000000
χ524444-4-44-4-4-14-1-1-1-4000-155−5−511-1-1-1111155−5−555−5−50000-4400000000000000000000001-1−55000000000
χ53444-2-4-4-2224-24442000-20000-4-4-2-2-222220000000044-4-4000000-2-222000000000000000000000000000
χ54444-2-4-4-2224-24442000-20000-4-4-2-2-2222200000000-4-44400000022-2-2000000000000000000000000000
χ5544-4-2-44-22242-4-44-2000-20000-44-22222-2-2000000004-4-44000000-22-22000000000000000000000000000
χ5644-4-2-44-22242-4-44-2000-20000-44-22222-2-200000000-444-40000002-22-2000000000000000000000000000
χ57888-488-4-4-4-2-4-2-2-2-48-4-41-2-2-2-2-2-211111111111111100000000000000000000000000000000000000000
χ58888-488-4-4-4-2-4-2-2-2-4-84412222-2-21111111-1-1-1-1-1-1-1-100000000000000000000000000000000000000000
χ59888-4-8-8-444-2-4-2-2-240001−25−25252522111-1-1-1-155−5−555−5−500000000000000000000000000000000000000000
χ60888-4-8-8-444-2-4-2-2-2400012525−25−2522111-1-1-1-1−5−555−5−55500000000000000000000000000000000000000000
χ6188-888-8888-2-822-2-8000-20000-22-222-2-2220000000000000000000000000000000000000000000000000
χ6288-88-888-8-8-2-822-28000-200002-2-22222-2-20000000000000000000000000000000000000000000000000
χ6388-8-48-8-4-4-4-2422-24043−4310000-221-1-111-1-1−3−3−3−3333300000000000000000000000000000000000000000
χ6488-8-48-8-4-4-4-2422-240−434310000-221-1-111-1-13333−3−3−3−300000000000000000000000000000000000000000
χ6588-8-4-88-444-2422-2-4000100002-21-1-1-1-111−15−1515151515−15−1500000000000000000000000000000000000000000
χ6688-8-4-88-444-2422-2-4000100002-21-1-1-1-1111515−15−15−15−15151500000000000000000000000000000000000000000
χ678-80800-8008000-800008000000-80000000000000000000000000000000000000000000000000000000
χ688-80800-800-20−252520000-2−2ζ14+2ζ26−2ζ34+2ζ462ζ14−2ζ26+2ζ34−2ζ462ζ2+2ζ22−2ζ38−2ζ58−2ζ2−2ζ22+2ζ38+2ζ58002−25250000−2ζ14+2ζ26−2ζ34+2ζ462ζ14−2ζ26+2ζ34−2ζ462ζ2+2ζ22−2ζ38−2ζ58−2ζ2−2ζ22+2ζ38+2ζ58−2ζ14+2ζ26−2ζ34+2ζ462ζ14−2ζ26+2ζ34−2ζ462ζ2+2ζ22−2ζ38−2ζ58−2ζ2−2ζ22+2ζ38+2ζ5800000000000000000000000000000000000000000
χ698-80800-800-20−252520000-22ζ14−2ζ26+2ζ34−2ζ46−2ζ14+2ζ26−2ζ34+2ζ46−2ζ2−2ζ22+2ζ38+2ζ582ζ2+2ζ22−2ζ38−2ζ58002−252500002ζ14−2ζ26+2ζ34−2ζ46−2ζ14+2ζ26−2ζ34+2ζ46−2ζ2−2ζ22+2ζ38+2ζ582ζ2+2ζ22−2ζ38−2ζ582ζ14−2ζ26+2ζ34−2ζ46−2ζ14+2ζ26−2ζ34+2ζ46−2ζ2−2ζ22+2ζ38+2ζ582ζ2+2ζ22−2ζ38−2ζ5800000000000000000000000000000000000000000
χ708-80800-800-2025−2520000-22ζ2+2ζ22−2ζ38−2ζ58−2ζ2−2ζ22+2ζ38+2ζ582ζ14−2ζ26+2ζ34−2ζ46−2ζ14+2ζ26−2ζ34+2ζ4600225−2500002ζ2+2ζ22−2ζ38−2ζ58−2ζ2−2ζ22+2ζ38+2ζ582ζ14−2ζ26+2ζ34−2ζ46−2ζ14+2ζ26−2ζ34+2ζ462ζ2+2ζ22−2ζ38−2ζ58−2ζ2−2ζ22+2ζ38+2ζ582ζ14−2ζ26+2ζ34−2ζ46−2ζ14+2ζ26−2ζ34+2ζ4600000000000000000000000000000000000000000
χ718-80800-800-2025−2520000-2−2ζ2−2ζ22+2ζ38+2ζ582ζ2+2ζ22−2ζ38−2ζ58−2ζ14+2ζ26−2ζ34+2ζ462ζ14−2ζ26+2ζ34−2ζ4600225−250000−2ζ2−2ζ22+2ζ38+2ζ582ζ2+2ζ22−2ζ38−2ζ58−2ζ14+2ζ26−2ζ34+2ζ462ζ14−2ζ26+2ζ34−2ζ46−2ζ2−2ζ22+2ζ38+2ζ582ζ2+2ζ22−2ζ38−2ζ58−2ζ14+2ζ26−2ζ34+2ζ462ζ14−2ζ26+2ζ34−2ζ4600000000000000000000000000000000000000000
χ728-80-400443−438000-80000-400000040043−43000000000000000000000000000000000000000000000000000
χ738-80-400443−43-20−2525200001−2ζ14+2ζ26−2ζ34+2ζ462ζ14−2ζ26+2ζ34−2ζ462ζ2+2ζ22−2ζ38−2ζ58−2ζ2−2ζ22+2ζ38+2ζ5800-15−5−33−1515−ζ7+ζ14−ζ23−ζ26+ζ34+ζ43−ζ46+ζ47ζ7−ζ14+ζ23+ζ26−ζ34−ζ43+ζ46−ζ47−ζ2−ζ11−ζ19−ζ22+ζ31+ζ38+ζ58+ζ59ζ2+ζ11+ζ19+ζ22−ζ31−ζ38−ζ58−ζ59ζ7+ζ14+ζ23−ζ26+ζ34−ζ43−ζ46−ζ47−ζ7−ζ14−ζ23+ζ26−ζ34+ζ43+ζ46+ζ47−ζ2+ζ11+ζ19−ζ22−ζ31+ζ38+ζ58−ζ59ζ2−ζ11−ζ19+ζ22+ζ31−ζ38−ζ58+ζ5900000000000000000000000000000000000000000
χ748-80-400443−43-20−25252000012ζ14−2ζ26+2ζ34−2ζ46−2ζ14+2ζ26−2ζ34+2ζ46−2ζ2−2ζ22+2ζ38+2ζ582ζ2+2ζ22−2ζ38−2ζ5800-15−5−33−1515ζ7−ζ14+ζ23+ζ26−ζ34−ζ43+ζ46−ζ47−ζ7+ζ14−ζ23−ζ26+ζ34+ζ43−ζ46+ζ47ζ2+ζ11+ζ19+ζ22−ζ31−ζ38−ζ58−ζ59−ζ2−ζ11−ζ19−ζ22+ζ31+ζ38+ζ58+ζ59−ζ7−ζ14−ζ23+ζ26−ζ34+ζ43+ζ46+ζ47ζ7+ζ14+ζ23−ζ26+ζ34−ζ43−ζ46−ζ47ζ2−ζ11−ζ19+ζ22+ζ31−ζ38−ζ58+ζ59−ζ2+ζ11+ζ19−ζ22−ζ31+ζ38+ζ58−ζ5900000000000000000000000000000000000000000
χ758-80-400443−43-2025−252000012ζ2+2ζ22−2ζ38−2ζ58−2ζ2−2ζ22+2ζ38+2ζ582ζ14−2ζ26+2ζ34−2ζ46−2ζ14+2ζ26−2ζ34+2ζ4600-1−55−3315−15−ζ2−ζ11−ζ19−ζ22+ζ31+ζ38+ζ58+ζ59ζ2+ζ11+ζ19+ζ22−ζ31−ζ38−ζ58−ζ59ζ7−ζ14+ζ23+ζ26−ζ34−ζ43+ζ46−ζ47−ζ7+ζ14−ζ23−ζ26+ζ34+ζ43−ζ46+ζ47−ζ2+ζ11+ζ19−ζ22−ζ31+ζ38+ζ58−ζ59ζ2−ζ11−ζ19+ζ22+ζ31−ζ38−ζ58+ζ59−ζ7−ζ14−ζ23+ζ26−ζ34+ζ43+ζ46+ζ47ζ7+ζ14+ζ23−ζ26+ζ34−ζ43−ζ46−ζ4700000000000000000000000000000000000000000
χ768-80-400443−43-2025−25200001−2ζ2−2ζ22+2ζ38+2ζ582ζ2+2ζ22−2ζ38−2ζ58−2ζ14+2ζ26−2ζ34+2ζ462ζ14−2ζ26+2ζ34−2ζ4600-1−55−3315−15ζ2+ζ11+ζ19+ζ22−ζ31−ζ38−ζ58−ζ59−ζ2−ζ11−ζ19−ζ22+ζ31+ζ38+ζ58+ζ59−ζ7+ζ14−ζ23−ζ26+ζ34+ζ43−ζ46+ζ47ζ7−ζ14+ζ23+ζ26−ζ34−ζ43+ζ46−ζ47ζ2−ζ11−ζ19+ζ22+ζ31−ζ38−ζ58+ζ59−ζ2+ζ11+ζ19−ζ22−ζ31+ζ38+ζ58−ζ59ζ7+ζ14+ζ23−ζ26+ζ34−ζ43−ζ46−ζ47−ζ7−ζ14−ζ23+ζ26−ζ34+ζ43+ζ46+ζ4700000000000000000000000000000000000000000
χ778-80-4004−43438000-80000-4000000400−4343000000000000000000000000000000000000000000000000000
χ788-80-4004−4343-20−2525200001−2ζ14+2ζ26−2ζ34+2ζ462ζ14−2ζ26+2ζ34−2ζ462ζ2+2ζ22−2ζ38−2ζ58−2ζ2−2ζ22+2ζ38+2ζ5800-15−53−315−15ζ7+ζ14+ζ23−ζ26+ζ34−ζ43−ζ46−ζ47−ζ7−ζ14−ζ23+ζ26−ζ34+ζ43+ζ46+ζ47−ζ2+ζ11+ζ19−ζ22−ζ31+ζ38+ζ58−ζ59ζ2−ζ11−ζ19+ζ22+ζ31−ζ38−ζ58+ζ59−ζ7+ζ14−ζ23−ζ26+ζ34+ζ43−ζ46+ζ47ζ7−ζ14+ζ23+ζ26−ζ34−ζ43+ζ46−ζ47−ζ2−ζ11−ζ19−ζ22+ζ31+ζ38+ζ58+ζ59ζ2+ζ11+ζ19+ζ22−ζ31−ζ38−ζ58−ζ5900000000000000000000000000000000000000000
χ798-80-4004−4343-20−25252000012ζ14−2ζ26+2ζ34−2ζ46−2ζ14+2ζ26−2ζ34+2ζ46−2ζ2−2ζ22+2ζ38+2ζ582ζ2+2ζ22−2ζ38−2ζ5800-15−53−315−15−ζ7−ζ14−ζ23+ζ26−ζ34+ζ43+ζ46+ζ47ζ7+ζ14+ζ23−ζ26+ζ34−ζ43−ζ46−ζ47ζ2−ζ11−ζ19+ζ22+ζ31−ζ38−ζ58+ζ59−ζ2+ζ11+ζ19−ζ22−ζ31+ζ38+ζ58−ζ59ζ7−ζ14+ζ23+ζ26−ζ34−ζ43+ζ46−ζ47−ζ7+ζ14−ζ23−ζ26+ζ34+ζ43−ζ46+ζ47ζ2+ζ11+ζ19+ζ22−ζ31−ζ38−ζ58−ζ59−ζ2−ζ11−ζ19−ζ22+ζ31+ζ38+ζ58+ζ5900000000000000000000000000000000000000000
χ808-80-4004−4343-2025−252000012ζ2+2ζ22−2ζ38−2ζ58−2ζ2−2ζ22+2ζ38+2ζ582ζ14−2ζ26+2ζ34−2ζ46−2ζ14+2ζ26−2ζ34+2ζ4600-1−553−3−1515−ζ2+ζ11+ζ19−ζ22−ζ31+ζ38+ζ58−ζ59ζ2−ζ11−ζ19+ζ22+ζ31−ζ38−ζ58+ζ59−ζ7−ζ14−ζ23+ζ26−ζ34+ζ43+ζ46+ζ47ζ7+ζ14+ζ23−ζ26+ζ34−ζ43−ζ46−ζ47−ζ2−ζ11−ζ19−ζ22+ζ31+ζ38+ζ58+ζ59ζ2+ζ11+ζ19+ζ22−ζ31−ζ38−ζ58−ζ59ζ7−ζ14+ζ23+ζ26−ζ34−ζ43+ζ46−ζ47−ζ7+ζ14−ζ23−ζ26+ζ34+ζ43−ζ46+ζ4700000000000000000000000000000000000000000
χ818-80-4004−4343-2025−25200001−2ζ2−2ζ22+2ζ38+2ζ582ζ2+2ζ22−2ζ38−2ζ58−2ζ14+2ζ26−2ζ34+2ζ462ζ14−2ζ26+2ζ34−2ζ4600-1−553−3−1515ζ2−ζ11−ζ19+ζ22+ζ31−ζ38−ζ58+ζ59−ζ2+ζ11+ζ19−ζ22−ζ31+ζ38+ζ58−ζ59ζ7+ζ14+ζ23−ζ26+ζ34−ζ43−ζ46−ζ47−ζ7−ζ14−ζ23+ζ26−ζ34+ζ43+ζ46+ζ47ζ2+ζ11+ζ19+ζ22−ζ31−ζ38−ζ58−ζ59−ζ2−ζ11−ζ19−ζ22+ζ31+ζ38+ζ58+ζ59−ζ7+ζ14−ζ23−ζ26+ζ34+ζ43−ζ46+ζ47ζ7−ζ14+ζ23+ζ26−ζ34−ζ43+ζ46−ζ4700000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 60 (ζ60 = 1); i = ζ15.