Finite Group Databasebeta

← Group #13019942

Character table — Group #13019942

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71
size111122224444444444488888888888888810101010161616161616161616202020202020202040404040404040404040404040808080
order12222244224510101010101010288202020204040404040404040444441010101020202020444488884888888888888488
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
χ212222-2-22222-222-2-2-2-222-2002-2-220000000022-2-2022-2-20000-2-2-2200002000000000000000
χ222222-2-22222-222-2-2-2-222-2002-2-2200000000-2-222022-2-20000222-20000-2000000000000000
χ232222-2-222-2-2-222-2-2-2-2222002-2-220000000022-2-20-2-2220000-22220000-2000000000000000
χ242222-2-222-2-2-222-2-2-2-2222002-2-2200000000-2-2220-2-22200002-2-2-200002000000000000000
χ252222-2-2-2-200222-2-2-2-222000-222-20000000022-2-2000000000200-2000000002i−2i02i−2i0000000
χ262222-2-2-2-200222-2-2-2-222000-222-20000000022-2-2000000000200-200000000−2i2i0−2i2i0000000
χ272222-2-2-2-200222-2-2-2-222000-222-200000000-2-222000000000-2002000000002-20-220000000
χ282222-2-2-2-200222-2-2-2-222000-222-200000000-2-222000000000-200200000000-2202-20000000
χ292-22-22-2000002-222-2-2-2202−200002222−2−2−2−22i−2i2i−2i0000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ390i2−i20000001+i−1−i1−i−1+i000
χ302-22-22-2000002-222-2-2-2202−200002222−2−2−2−22i−2i2i−2i00000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ390i2−i2000000−1−i1+i−1+i1−i000
χ312-22-22-2000002-222-2-2-2202−200002222−2−2−2−2−2i2i−2i2i0000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ370−i2i2000000−1+i1−i−1−i1+i000
χ322-22-22-2000002-222-2-2-2202−200002222−2−2−2−2−2i2i−2i2i00000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ370−i2i20000001−i−1+i1+i−1−i000
χ332-22-22-2000002-222-2-2-220−220000−2−2−2−222222i−2i2i−2i0000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ390−i2i2000000−1−i1+i−1+i1−i000
χ342-22-22-2000002-222-2-2-220−220000−2−2−2−222222i−2i2i−2i00000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ390−i2i20000001+i−1−i1−i−1+i000
χ352-22-22-2000002-222-2-2-220−220000−2−2−2−22222−2i2i−2i2i0000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ370i2−i20000001−i−1+i1+i−1−i000
χ362-22-22-2000002-222-2-2-220−220000−2−2−2−22222−2i2i−2i2i00000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ370i2−i2000000−1+i1−i−1−i1+i000
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
χ4544-4-4004-44-404-400004-4000400-400000000000004-4000000000000000000000000000000
χ4644-4-4004-44-40-115−55−5-11000-15−51−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−ζ3800000-115−5−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38000000000000000000000000
χ4744-4-4004-44-40-115−55−5-11000-15−51ζ6−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+ζ3800000-115−5ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38000000000000000000000000
χ4844-4-4004-44-40-11−55−55-11000-1−551ζ6−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+ζ3800000-11−55ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38000000000000000000000000
χ4944-4-4004-44-40-11−55−55-11000-1−551−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−ζ3800000-11−55−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38000000000000000000000000
χ5044-4-4004-4-4404-400004-4000400-40000000000000-44000000000000000000000000000000
χ5144-4-4004-4-440-115−55−5-11000-15−51−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−ζ38000001-1−55ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38000000000000000000000000
χ5244-4-4004-4-440-115−55−5-11000-15−51ζ6−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+ζ38000001-1−55−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38000000000000000000000000
χ5344-4-4004-4-440-11−55−55-11000-1−551ζ6−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+ζ38000001-15−5−ζ6+ζ14+ζ22−ζ38ζ6−ζ14−ζ22+ζ38−ζ6+ζ14−ζ22+ζ38ζ6−ζ14+ζ22−ζ38000000000000000000000000
χ5444-4-4004-4-440-11−55−55-11000-1−551−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−ζ38000001-15−5ζ6−ζ14−ζ22+ζ38−ζ6+ζ14+ζ22−ζ38ζ6−ζ14+ζ22−ζ38−ζ6+ζ14−ζ22+ζ38000000000000000000000000
χ5544-4-400-440004-400004-4000-400400000000000000000000004i−4i000000000000000000000
χ5644-4-400-440004-400004-4000-40040000000000000000000000−4i4i000000000000000000000
χ574-44-4-44000004-4-4-444-440000000000000004i−4i−4i4i000000000000000000000000000000000
χ584-44-4-44000004-4-4-444-44000000000000000−4i4i4i−4i000000000000000000000000000000000
χ59888888-8-800-8-2-2-2-2-2-2-2-20002222000000000000000000000000000000000000000000000
χ608888-8-8-8-8008-2-22222-2-20002-2-22000000000000000000000000000000000000000000000
χ6188-8-800-88000-2225−2525−25-220002−2525-2000000000000000000000000000000000000000000000
χ6288-8-800-88000-22−2525−2525-22000225−25-2000000000000000000000000000000000000000000000
χ638-88-88-800000-22-2-2222-2042−420000−2−2−2−222220000000000000000000000000000000000000
χ648-88-88-800000-22-2-2222-20−424200002222−2−2−2−20000000000000000000000000000000000000
χ658-88-8-8800000-2222-2-22-200000001010−10−10−10−1010100000000000000000000000000000000000000
χ668-88-8-8800000-2222-2-22-20000000−10−1010101010−10−100000000000000000000000000000000000000
χ678-8-880000000880000-8-80000000000000000000000000000000000000000000000000000
χ688-8-880000000-2-225−25−2525220000000−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
χ698-8-880000000-2-225−25−2525220000000ζ7−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
χ708-8-880000000-2-2−252525−25220000000ζ7−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
χ718-8-880000000-2-2−252525−25220000000−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

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