Finite Group Databasebeta

← Group #13019950

Character table — Group #13019950

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111122224444444444488888888888888810101010161616161616161616202020202020202040404040404040404040404040808080
order12222244444510101010101010488202020204040404040404040444442020202020202020444488884888888888888488
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-11-1-1
χ31111111111111111111111111111111111-1-1-1-1111111111-1-1-1-1ii−i−i-1-1-1iii−i−i−iii−i−i-1i−i
χ41111111111111111111111111111111111-1-1-1-1111111111-1-1-1-1−i−iii-1-1-1−i−i−iiii−i−iii-1−ii
χ511111111111111111111-1-11111-1-1-1-1-1-1-1-11111-11111-1-1-1-1111111111-1-1111111-1-1-1-1-1-1-1
χ611111111111111111111-1-11111-1-1-1-1-1-1-1-11111-11111-1-1-1-11111-1-1-1-11-1-1-1-1-1-1-1-11111-111
χ711111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1ii−i−i-111iii−i−i−i−i−iii1−ii
χ811111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1−i−iii-111−i−i−iiiiii−i−i1i−i
χ911111111-1-1111111111-1111111111111111111-1-1-1-1-1-1-1-1-11-1-111111-1111-1-11-1-11111-1-1-1
χ1011111111-1-1111111111-1111111111111111111-1-1-1-1-1-1-1-1-11-1-11-1-1-1-1-111-111-111-1-1-1-1-111
χ1111111111-1-1111111111-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1ii−i−i1-1-1i−i−i−iiiii−i−i1−ii
χ1211111111-1-1111111111-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1−i−iii1-1-1−iiii−i−i−i−iii1i−i
χ1311111111-1-1111111111-1-1-11111-1-1-1-1-1-1-1-111111-1-1-1-111111-1-111111-1-1-11-1-11-1-1-1-1-1-1111
χ1411111111-1-1111111111-1-1-11111-1-1-1-1-1-1-1-111111-1-1-1-111111-1-11-1-1-1-1-1-1-1-111-11111111-1-1
χ1511111111-1-1111111111-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-111-1ii−i−i111i−i−i−iii−i−iii-1i−i
χ1611111111-1-1111111111-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-111-1−i−iii111−iiii−i−iii−i−i-1−ii
χ17222222-2-200-222222222000-2-2-2-2000000002222000000000-200-22222000-200-2000000000
χ18222222-2-200-222222222000-2-2-2-2000000002222000000000-200-2-2-2-2-20002002000000000
χ19222222-2-200-222222222000-2-2-2-200000000-2-2-2-200000000020022i2i−2i−2i000−2i002i000000000
χ20222222-2-200-222222222000-2-2-2-200000000-2-2-2-20000000002002−2i−2i2i2i0002i00−2i000000000
χ212222-2-22222-222-2-2-2-222-2002-2-22000000002-22-2022-2-20000-2-2-2200002000000000000000
χ222222-2-22222-222-2-2-2-222-2002-2-2200000000-22-22022-2-20000222-20000-2000000000000000
χ232222-2-222-2-2-222-2-2-2-2222002-2-22000000002-22-20-2-2220000-22220000-2000000000000000
χ242222-2-222-2-2-222-2-2-2-2222002-2-2200000000-22-220-2-22200002-2-2-200002000000000000000
χ252222-2-2-2-200222-2-2-2-222000-222-2000000002-22-2000000000200-2000000002i−2i02i−2i0000000
χ262222-2-2-2-200222-2-2-2-222000-222-2000000002-22-2000000000200-200000000−2i2i0−2i2i0000000
χ272222-2-2-2-200222-2-2-2-222000-222-200000000-22-22000000000-2002000000002-20-220000000
χ282222-2-2-2-200222-2-2-2-222000-222-200000000-22-22000000000-200200000000-2202-20000000
χ2922-2-22-2000002222-2-2-2-202−200002222−2−2−2−222-2-200000000000002-22-202−20000002−22−2000
χ3022-2-22-2000002222-2-2-2-202−200002222−2−2−2−222-2-20000000000000-22-2202−2000000−22−22000
χ3122-2-22-2000002222-2-2-2-202−200002222−2−2−2−2-2-22200000000000002i−2i−2i2i0−22000000i2−i2−i2i2000
χ3222-2-22-2000002222-2-2-2-202−200002222−2−2−2−2-2-2220000000000000−2i2i2i−2i0−22000000−i2i2i2−i2000
χ3322-2-22-2000002222-2-2-2-20−220000−2−2−2−2222222-2-200000000000002-22-20−22000000−22−22000
χ3422-2-22-2000002222-2-2-2-20−220000−2−2−2−2222222-2-20000000000000-22-220−220000002−22−2000
χ3522-2-22-2000002222-2-2-2-20−220000−2−2−2−22222-2-22200000000000002i−2i−2i2i02−2000000−i2i2i2−i2000
χ3622-2-22-2000002222-2-2-2-20−220000−2−2−2−22222-2-2220000000000000−2i2i2i−2i02−2000000i2−i2−i2i2000
χ3744444444444-1-1-1-1-1-1-1-1444-1-1-1-1-1-1-1-1-1-1-1-100004-1-1-1-1-1-1-1-1000000000000000000000000
χ3844444444444-1-1-1-1-1-1-1-14-4-4-1-1-1-1111111110000-4-1-1-1-11111000000000000000000000000
χ3944444444-4-44-1-1-1-1-1-1-1-1-444-1-1-1-1-1-1-1-1-1-1-1-10000-411111111000000000000000000000000
χ4044444444-4-44-1-1-1-1-1-1-1-1-4-4-4-1-1-1-111111111000041111-1-1-1-1000000000000000000000000
χ414444-4-44444-4-1-11111-1-1-400-111-155−5−555−5−500000-1-11155−5−5000000000000000000000000
χ424444-4-44444-4-1-11111-1-1-400-111-1−5−555−5−55500000-1-111−5−555000000000000000000000000
χ434444-4-444-4-4-4-1-11111-1-1400-111-155−5−555−5−50000011-1-1−5−555000000000000000000000000
χ444444-4-444-4-4-4-1-11111-1-1400-111-1−5−555−5−5550000011-1-155−5−5000000000000000000000000
χ4544-4-4-440000044-4-444-4-40000000000000004-4-44000000000000000000000000000000000
χ4644-4-4-440000044-4-444-4-4000000000000000-444-4000000000000000000000000000000000
χ474-4-44004-44i−4i04-40000-44000400-400000000000004i−4i000000000000000000000000000000
χ484-4-44004-44i−4i0-115−55−51-1000-15−51−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ3800000−iii5−i5−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36000000000000000000000000
χ494-4-44004-44i−4i0-115−55−51-1000-15−51ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ3800000−iii5−i5ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36000000000000000000000000
χ504-4-44004-44i−4i0-11−55−551-1000-1−551ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ3800000−ii−i5i5ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36000000000000000000000000
χ514-4-44004-44i−4i0-11−55−551-1000-1−551−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ3800000−ii−i5i5−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36000000000000000000000000
χ524-4-44004-4−4i4i04-40000-44000400-40000000000000−4i4i000000000000000000000000000000
χ534-4-44004-4−4i4i0-115−55−51-1000-15−51−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ3800000i−i−i5i5ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36000000000000000000000000
χ544-4-44004-4−4i4i0-115−55−51-1000-15−51ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ3800000i−i−i5i5−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36000000000000000000000000
χ554-4-44004-4−4i4i0-11−55−551-1000-1−551ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ3800000i−ii5−i5−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36000000000000000000000000
χ564-4-44004-4−4i4i0-11−55−551-1000-1−551−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ3800000i−ii5−i5ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36000000000000000000000000
χ574-4-4400-440004-40000-44000-400400000000000000000000004-4000000000000000000000
χ584-4-4400-440004-40000-44000-40040000000000000000000000-44000000000000000000000
χ59888888-8-800-8-2-2-2-2-2-2-2-20002222000000000000000000000000000000000000000000000
χ608888-8-8-8-8008-2-22222-2-20002-2-22000000000000000000000000000000000000000000000
χ6188-8-88-800000-2-2-2-22222042−420000−2−2−2−222220000000000000000000000000000000000000
χ6288-8-88-800000-2-2-2-222220−424200002222−2−2−2−20000000000000000000000000000000000000
χ6388-8-8-8800000-2-222-2-22200000001010−10−10−10−1010100000000000000000000000000000000000000
χ6488-8-8-8800000-2-222-2-2220000000−10−1010101010−10−100000000000000000000000000000000000000
χ658-88-800000008-800008-80000000000000000000000000000000000000000000000000000
χ668-88-80000000-2225−25−2525-220000000−ζ7+ζ13−ζ21+ζ23+ζ29−ζ31−ζ37+ζ39ζ7−ζ13+ζ21−ζ23−ζ29+ζ31+ζ37−ζ39−ζ7+ζ13+ζ21+ζ23−ζ29+ζ31−ζ37−ζ39ζ7−ζ13−ζ21−ζ23+ζ29−ζ31+ζ37+ζ39ζ7−ζ13+ζ21−ζ23−ζ29+ζ31+ζ37−ζ39−ζ7+ζ13−ζ21+ζ23+ζ29−ζ31−ζ37+ζ39ζ7−ζ13−ζ21−ζ23+ζ29−ζ31+ζ37+ζ39−ζ7+ζ13+ζ21+ζ23−ζ29+ζ31−ζ37−ζ390000000000000000000000000000000000000
χ678-88-80000000-2225−25−2525-220000000ζ7−ζ13+ζ21−ζ23−ζ29+ζ31+ζ37−ζ39−ζ7+ζ13−ζ21+ζ23+ζ29−ζ31−ζ37+ζ39ζ7−ζ13−ζ21−ζ23+ζ29−ζ31+ζ37+ζ39−ζ7+ζ13+ζ21+ζ23−ζ29+ζ31−ζ37−ζ39−ζ7+ζ13−ζ21+ζ23+ζ29−ζ31−ζ37+ζ39ζ7−ζ13+ζ21−ζ23−ζ29+ζ31+ζ37−ζ39−ζ7+ζ13+ζ21+ζ23−ζ29+ζ31−ζ37−ζ39ζ7−ζ13−ζ21−ζ23+ζ29−ζ31+ζ37+ζ390000000000000000000000000000000000000
χ688-88-80000000-22−252525−25-220000000ζ7−ζ13−ζ21−ζ23+ζ29−ζ31+ζ37+ζ39−ζ7+ζ13+ζ21+ζ23−ζ29+ζ31−ζ37−ζ39−ζ7+ζ13−ζ21+ζ23+ζ29−ζ31−ζ37+ζ39ζ7−ζ13+ζ21−ζ23−ζ29+ζ31+ζ37−ζ39−ζ7+ζ13+ζ21+ζ23−ζ29+ζ31−ζ37−ζ39ζ7−ζ13−ζ21−ζ23+ζ29−ζ31+ζ37+ζ39ζ7−ζ13+ζ21−ζ23−ζ29+ζ31+ζ37−ζ39−ζ7+ζ13−ζ21+ζ23+ζ29−ζ31−ζ37+ζ390000000000000000000000000000000000000
χ698-88-80000000-22−252525−25-220000000−ζ7+ζ13+ζ21+ζ23−ζ29+ζ31−ζ37−ζ39ζ7−ζ13−ζ21−ζ23+ζ29−ζ31+ζ37+ζ39ζ7−ζ13+ζ21−ζ23−ζ29+ζ31+ζ37−ζ39−ζ7+ζ13−ζ21+ζ23+ζ29−ζ31−ζ37+ζ39ζ7−ζ13−ζ21−ζ23+ζ29−ζ31+ζ37+ζ39−ζ7+ζ13+ζ21+ζ23−ζ29+ζ31−ζ37−ζ39−ζ7+ζ13−ζ21+ζ23+ζ29−ζ31−ζ37+ζ39ζ7−ζ13+ζ21−ζ23−ζ29+ζ31+ζ37−ζ390000000000000000000000000000000000000
χ708-8-8800-88000-2225−2525−252-20002−2525-2000000000000000000000000000000000000000000000
χ718-8-8800-88000-22−2525−25252-2000225−25-2000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 40 (ζ40 = 1); i = ζ10.