Finite Group Databasebeta

← Group #13019979

Character table — Group #13019979

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111122224444444444488888888888888810101010161616161616161616202020202020202040404040404040404040404040808080
order12222244444510101010101010488202020204040404040404040222221010101020202020444444444444444888888444
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-1-1iii−i−i−i-1-1ii−i−i-1i−i
χ41111111111111111111111111111111111-1-1-1-1111111111-1-1-1−i−iii-1-1−i−i−iiii-1-1−i−iii-1−ii
χ511111111111111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-11111111111111111111-1-1-1-1-1-1-1-1-1
χ611111111111111111111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-11111111-1-1-1-111-1-1-1-1-1-1-1-11111-111
χ711111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1ii−i−i-1-1iii−i−i−i11−i−iii1−ii
χ811111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1−i−iii-1-1−i−i−iiii11ii−i−i1i−i
χ9111111111-1-111111111-1111111111111111111-1-1-1-1-1-1-1-1-11-1-111111-11-1-11-1-1111111-1-1-1
χ10111111111-1-111111111-1111111111111111111-1-1-1-1-1-1-1-1-11-1-1-1-1-1-11-1-111-11111-1-1-1-1-111
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
χ13111111111-1-111111111-1-1-11111-1-1-1-1-1-1-1-1111111111-1-1-1-11-1-111111-11-1-11-1-1-1-1-1-1-1-1111
χ14111111111-1-111111111-1-1-11111-1-1-1-1-1-1-1-1111111111-1-1-1-11-1-1-1-1-1-11-1-111-111-1-111111-1-1
χ15111111111-1-111111111-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-111ii−i−i-11i−i−i−iii11−i−iii-1i−i
χ16111111111-1-111111111-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-111−i−iii-11−iiii−i−i11ii−i−i-1−ii
χ17222222-2-2-20022222222000-2-2-2-2000000002222000000000-2002222-20-200-200000000000
χ18222222-2-2-20022222222000-2-2-2-2000000002222000000000-200-2-2-2-2-20200200000000000
χ19222222-2-2-20022222222000-2-2-2-200000000-2-2-2-20000000002002i2i−2i−2i20−2i002i00000000000
χ20222222-2-2-20022222222000-2-2-2-200000000-2-2-2-2000000000200−2i−2i2i2i202i00−2i00000000000
χ212222-2-222-222222-2-2-2-22-2002-2-22000000002-22-20000022-2-2-2-2-2000022000000000000000
χ222222-2-222-222222-2-2-2-22-2002-2-2200000000-22-220000022-2-22220000-2-2000000000000000
χ232222-2-222-2-2-2222-2-2-2-222002-2-22000000002-22-200000-2-222-22200002-2000000000000000
χ242222-2-222-2-2-2222-2-2-2-222002-2-2200000000-22-2200000-2-2222-2-20000-22000000000000000
χ252222-2-2-2-2200222-2-2-2-22000-222-2000000002-22-20000000002000000-2002i−2i02i−2i000000000
χ262222-2-2-2-2200222-2-2-2-22000-222-2000000002-22-20000000002000000-200−2i2i0−2i2i000000000
χ272222-2-2-2-2200222-2-2-2-22000-222-200000000-22-22000000000-20000002002-20-22000000000
χ282222-2-2-2-2200222-2-2-2-22000-222-200000000-22-22000000000-2000000200-2202-2000000000
χ292-22-22-20000022-222-2-2-20i2−i20000i2i2i2i2−i2−i2−i2−i22-2-220000000000002i−2i2i−2i00000000i2−i22−22−2000
χ302-22-22-20000022-222-2-2-20i2−i20000i2i2i2i2−i2−i2−i2−i22-2-22000000000000−2i2i−2i2i00000000i2−i2−22−22000
χ312-22-22-20000022-222-2-2-20i2−i20000i2i2i2i2−i2−i2−i2−i2-222-20000000000002-2-2200000000−i2i2−i2i2i2−i2000
χ322-22-22-20000022-222-2-2-20i2−i20000i2i2i2i2−i2−i2−i2−i2-222-2000000000000-222-200000000−i2i2i2−i2−i2i2000
χ332-22-22-20000022-222-2-2-20−i2i20000−i2−i2−i2−i2i2i2i2i22-2-220000000000002i−2i2i−2i00000000−i2i2−22−22000
χ342-22-22-20000022-222-2-2-20−i2i20000−i2−i2−i2−i2i2i2i2i22-2-22000000000000−2i2i−2i2i00000000−i2i22−22−2000
χ352-22-22-20000022-222-2-2-20−i2i20000−i2−i2−i2−i2i2i2i2i2-222-20000000000002-2-2200000000i2−i2i2−i2−i2i2000
χ362-22-22-20000022-222-2-2-20−i2i20000−i2−i2−i2−i2i2i2i2i2-222-2000000000000-222-200000000i2−i2−i2i2i2−i2000
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
χ3844444444444-1-1-1-1-1-1-1-14-4-4-1-1-1-1111111110000-41111-1-1-1-1000000000000000000000000
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
χ40444444444-4-4-1-1-1-1-1-1-1-1-4-4-4-1-1-1-11111111100004-1-1-1-11111000000000000000000000000
χ414444-4-444-444-1-1-11111-1-400-111-155−5−555−5−50000055−5−5-1-111000000000000000000000000
χ424444-4-444-444-1-1-11111-1-400-111-1−5−555−5−55500000−5−555-1-111000000000000000000000000
χ434444-4-444-4-4-4-1-1-11111-1400-111-155−5−555−5−500000−5−55511-1-1000000000000000000000000
χ444444-4-444-4-4-4-1-1-11111-1400-111-1−5−555−5−5550000055−5−511-1-1000000000000000000000000
χ454-44-4-440000044-4-4-444-400000000000000044-4-4000000000000000000000000000000000
χ464-44-4-440000044-4-4-444-4000000000000000-4-444000000000000000000000000000000000
χ474-4-44004-404-44-4-400004000-4004000000000000000004-400000000000000000000000000
χ484-4-44004-404-4-1115−55−5-100015−5-1−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−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36-115−5000000000000000000000000
χ494-4-44004-404-4-1115−55−5-100015−5-1ζ4−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+ζ3600000ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36-115−5000000000000000000000000
χ504-4-44004-404-4-111−55−55-10001−55-1−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−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36-11−55000000000000000000000000
χ514-4-44004-404-4-111−55−55-10001−55-1ζ4+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−ζ3600000ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36-11−55000000000000000000000000
χ524-4-44004-40-444-4-400004000-400400000000000000000-4400000000000000000000000000
χ534-4-44004-40-44-1115−55−5-100015−5-1−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−ζ3600000ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ36ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ361-1−55000000000000000000000000
χ544-4-44004-40-44-1115−55−5-100015−5-1ζ4−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−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ36−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ361-1−55000000000000000000000000
χ554-4-44004-40-44-111−55−55-10001−55-1−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+ζ3600000ζ4+ζ12−ζ28−ζ36−ζ4−ζ12+ζ28+ζ36−ζ4+ζ12−ζ28+ζ36ζ4−ζ12+ζ28−ζ361-15−5000000000000000000000000
χ564-4-44004-40-44-111−55−55-10001−55-1ζ4+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−ζ4−ζ12+ζ28+ζ36ζ4+ζ12−ζ28−ζ36ζ4−ζ12+ζ28−ζ36−ζ4+ζ12−ζ28+ζ361-15−5000000000000000000000000
χ574-4-4400-440004-4-400004000400-400000000000000000000004-4000000000000000000000
χ584-4-4400-440004-4-400004000400-40000000000000000000000-44000000000000000000000
χ59888888-8-8-800-2-2-2-2-2-2-2-20002222000000000000000000000000000000000000000000000
χ608888-8-8-8-8800-2-2-22222-20002-2-22000000000000000000000000000000000000000000000
χ6188-8-800000008-880000-80000000000000000000000000000000000000000000000000000
χ6288-8-80000000-22-225−25−252520000000−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
χ6388-8-80000000-22-225−25−252520000000ζ7−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
χ6488-8-80000000-22-2−252525−2520000000ζ7−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
χ6588-8-80000000-22-2−252525−2520000000−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
χ668-88-88-800000-2-22-2-222204i2−4i20000−i2−i2−i2−i2i2i2i2i20000000000000000000000000000000000000
χ678-88-88-800000-2-22-2-22220−4i24i20000i2i2i2i2−i2−i2−i2−i20000000000000000000000000000000000000
χ688-88-8-8800000-2-2222-2-220000000i10i10−i10−i10−i10−i10i10i100000000000000000000000000000000000000
χ698-88-8-8800000-2-2222-2-220000000−i10−i10i10i10i10i10−i10−i100000000000000000000000000000000000000
χ708-8-8800-88000-22225−2525−25-2000-2−25252000000000000000000000000000000000000000000000
χ718-8-8800-88000-222−2525−2525-2000-225−252000000000000000000000000000000000000000000000

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