Finite Group Databasebeta

← Group #13019974

Character table — Group #13019974

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111122224444444444488888888888888810101010161616161616161616202020202020202040404040404040404040404040808080
order12222244444510101010101010488202020204040404040404040222242020202020202020444444444444444888888244
χ111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-11-1-1
χ31111111111111111111111111111111111-1-1-1-1111111111-1-1-1ii−i−i-1-1i−iii−i−i-1-1ii−i−i-1i−i
χ41111111111111111111111111111111111-1-1-1-1111111111-1-1-1−i−iii-1-1−ii−i−iii-1-1−i−iii-1−ii
χ511111111111111111111-1-11111-1-1-1-1-1-1-1-11111-11111-1-1-1-1111111111111111-1-1-1-1-1-1-1-1-1
χ611111111111111111111-1-11111-1-1-1-1-1-1-1-11111-11111-1-1-1-1111-1-1-1-111-1-1-1-1-1-1-1-11111-111
χ711111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1ii−i−i-1-1i−iii−i−i11−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−i−iii-1-1−ii−i−iii11ii−i−i1i−i
χ9111111111-1-111111111-1111111111111111111-1-1-1-1-1-1-1-1-11-1-111111-111-1-1-1-1111111-1-1-1
χ10111111111-1-111111111-1111111111111111111-1-1-1-1-1-1-1-1-11-1-1-1-1-1-11-1-1-1111111-1-1-1-1-111
χ11111111111-1-111111111-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111ii−i−i-11i−i−i−iii-1-1ii−i−i1−ii
χ12111111111-1-111111111-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111−i−iii-11−iiii−i−i-1-1−i−iii1i−i
χ13111111111-1-111111111-1-1-11111-1-1-1-1-1-1-1-111111-1-1-1-111111-1-111111-111-1-1-1-1-1-1-1-1-1-1111
χ14111111111-1-111111111-1-1-11111-1-1-1-1-1-1-1-111111-1-1-1-111111-1-1-1-1-1-11-1-1-11111-1-111111-1-1
χ15111111111-1-111111111-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-111ii−i−i-11i−i−i−iii11−i−iii-1i−i
χ16111111111-1-111111111-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11111-111−i−iii-11−iiii−i−i11ii−i−i-1−ii
χ17222222-2-2-20022222222000-2-2-2-2000000002222000000000-2002222-20-2-20000000000000
χ18222222-2-2-20022222222000-2-2-2-2000000002222000000000-200-2-2-2-2-20220000000000000
χ19222222-2-2-20022222222000-2-2-2-200000000-2-2-2-20000000002002i2i−2i−2i20−2i2i0000000000000
χ20222222-2-2-20022222222000-2-2-2-200000000-2-2-2-2000000000200−2i−2i2i2i202i−2i0000000000000
χ212222-2-222-22222-2-2-2-222-2002-2-22000000002-22-2022-2-20000-2-2-2000022000000000000000
χ222222-2-222-22222-2-2-2-222-2002-2-2200000000-22-22022-2-200002220000-2-2000000000000000
χ232222-2-222-2-2-222-2-2-2-2222002-2-22000000002-22-20-2-2220000-22200002-2000000000000000
χ242222-2-222-2-2-222-2-2-2-2222002-2-2200000000-22-220-2-22200002-2-20000-22000000000000000
χ252222-2-2-2-220022-2-2-2-222000-222-2000000002-22-20000000002000000-20002i−2i2i−2i000000000
χ262222-2-2-2-220022-2-2-2-222000-222-2000000002-22-20000000002000000-2000−2i2i−2i2i000000000
χ272222-2-2-2-220022-2-2-2-222000-222-200000000-22-22000000000-200000020002-2-22000000000
χ282222-2-2-2-220022-2-2-2-222000-222-200000000-22-22000000000-20000002000-222-2000000000
χ292-2-222-2000002-222-2-2-2202−200002222−2−2−2−222-2-20000000000002i−2i2i−2i000000002−2i2−i2i2−i2000
χ302-2-222-2000002-222-2-2-2202−200002222−2−2−2−222-2-2000000000000−2i2i−2i2i000000002−2−i2i2−i2i2000
χ312-2-222-2000002-222-2-2-2202−200002222−2−2−2−2-2-2220000000000002-2-2200000000−222−2−22000
χ322-2-222-2000002-222-2-2-2202−200002222−2−2−2−2-2-222000000000000-222-200000000−22−222−2000
χ332-2-222-2000002-222-2-2-220−220000−2−2−2−2222222-2-20000000000002i−2i2i−2i00000000−22−i2i2−i2i2000
χ342-2-222-2000002-222-2-2-220−220000−2−2−2−2222222-2-2000000000000−2i2i−2i2i00000000−22i2−i2i2−i2000
χ352-2-222-2000002-222-2-2-220−220000−2−2−2−22222-2-2220000000000002-2-22000000002−2−222−2000
χ362-2-222-2000002-222-2-2-220−220000−2−2−2−22222-2-222000000000000-222-2000000002−22−2−22000
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
χ39444444444-4-4-1-1-1-1-1-1-1-1-444-1-1-1-1-1-1-1-1-1-1-1-10000-411111111000000000000000000000000
χ40444444444-4-4-1-1-1-1-1-1-1-1-4-4-4-1-1-1-111111111000041111-1-1-1-1000000000000000000000000
χ414444-4-444-444-1-11111-1-1-400-111-155−5−555−5−500000-1-11155−5−5000000000000000000000000
χ424444-4-444-444-1-11111-1-1-400-111-1−5−555−5−55500000-1-111−5−555000000000000000000000000
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
χ454-44-4004-404i−4i4-400004-4000-400400000000000004i−4i000000000000000000000000000000
χ464-44-4004-404i−4i-115−55−5-1100015−5-1−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ3600000−iii5−i5−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38000000000000000000000000
χ474-44-4004-404i−4i-115−55−5-1100015−5-1ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ3600000−iii5−i5ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38000000000000000000000000
χ484-44-4004-404i−4i-11−55−55-110001−55-1−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ3600000−ii−i5i5−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38000000000000000000000000
χ494-44-4004-404i−4i-11−55−55-110001−55-1ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ3600000−ii−i5i5ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38000000000000000000000000
χ504-44-4004-40−4i4i4-400004-4000-40040000000000000−4i4i000000000000000000000000000000
χ514-44-4004-40−4i4i-115−55−5-1100015−5-1−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ3600000i−i−i5i5ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38000000000000000000000000
χ524-44-4004-40−4i4i-115−55−5-1100015−5-1ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ3600000i−i−i5i5−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38000000000000000000000000
χ534-44-4004-40−4i4i-11−55−55-110001−55-1−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ3600000i−ii5−i5ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38000000000000000000000000
χ544-44-4004-40−4i4i-11−55−55-110001−55-1ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ3600000i−ii5−i5−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38000000000000000000000000
χ554-44-400-440004-400004-4000400-400000000000000000000004i−4i000000000000000000000
χ564-44-400-440004-400004-4000400-40000000000000000000000−4i4i000000000000000000000
χ574-4-44-44000004-4-4-444-440000000000000004-4-44000000000000000000000000000000000
χ584-4-44-44000004-4-4-444-44000000000000000-444-4000000000000000000000000000000000
χ59888888-8-8-800-2-2-2-2-2-2-2-20002222000000000000000000000000000000000000000000000
χ608888-8-8-8-8800-2-22222-2-20002-2-22000000000000000000000000000000000000000000000
χ6188-8-80000000880000-8-80000000000000000000000000000000000000000000000000000
χ6288-8-80000000-2-225−25−2525220000000ζ7+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
χ6388-8-80000000-2-225−25−2525220000000−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
χ6488-8-80000000-2-2−252525−25220000000−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
χ6588-8-80000000-2-2−252525−25220000000ζ7+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
χ668-88-800-88000-2225−2525−25-22000-2−25252000000000000000000000000000000000000000000000
χ678-88-800-88000-22−2525−2525-22000-225−252000000000000000000000000000000000000000000000
χ688-8-888-800000-22-2-2222-2042−420000−2−2−2−222220000000000000000000000000000000000000
χ698-8-888-800000-22-2-2222-20−424200002222−2−2−2−20000000000000000000000000000000000000
χ708-8-88-8800000-2222-2-22-200000001010−10−10−10−1010100000000000000000000000000000000000000
χ718-8-88-8800000-2222-2-22-20000000−10−1010101010−10−100000000000000000000000000000000000000

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