Finite Group Databasebeta

← Group #13019769

Character table — Group #13019769

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size111122444444448888810101010101016161616161616161616162020202020202032324040404040404040404040404040408080
order12224444445101010420202020224444282020202020404040402248888101048888888888888828
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-111
χ31111111111111111111111111-1-111111-1-1-1-11111111-1-11-1-1-1-1111111-1-1-1-1-1-1
χ41111111111111111111111111-1-111111-1-1-1-1111-1-1-1-1-1-111111-1-1-1-1-1-11111-1-1
χ51111111111111111111-1-1-1-1-1-111111111111-1-1-1ii−i−i11-1ii−i−iiii−i−i−iii−i−i-1-1
χ61111111111111111111-1-1-1-1-1-111111111111-1-1-1−i−iii11-1−i−iii−i−i−iiii−i−iii-1-1
χ71111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1ii−i−i-1-1-1−i−iiiiii−i−i−i−i−iii11
χ81111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1−i−iii-1-1-1ii−i−i−i−i−iiiiii−i−i11
χ91111111-1-111111-111111111111-11-1-1-1-1-1-1-1-1-1-11111111-111111-1-11-1-1-1-1-1-11-1
χ101111111-1-111111-111111111111-11-1-1-1-1-1-1-1-1-1-11-1-1-1-111-1-1-1-1-1-111-11111111-1
χ111111111-1-111111-11111111111-111-1-1-1-11111-1-111111-1-1-1-1-1-1-11-1-11-1-11111-11
χ121111111-1-111111-11111111111-111-1-1-1-11111-1-11-1-1-1-1-1-1-11111-111-111-1-1-1-1-11
χ131111111-1-111111-11111-1-1-1-1-1-11-11-1-1-1-1-1-1-1-111-1ii−i−i111ii−i−ii−i−i−iii−i−iii-11
χ141111111-1-111111-11111-1-1-1-1-1-11-11-1-1-1-1-1-1-1-111-1−i−iii111−i−iii−iiii−i−iii−i−i-11
χ151111111-1-111111-11111-1-1-1-1-1-1-111-1-1-1-1111111-1ii−i−i-1-11−i−iiii−i−i−iiiii−i−i1-1
χ161111111-1-111111-11111-1-1-1-1-1-1-111-1-1-1-1111111-1−i−iii-1-11ii−i−i−iiii−i−i−i−iii1-1
χ17222222-222-22222-2-2-222222-2-2200-222-2-2000022-2000000-20000000000000000
χ18222222-222-22222-2-2-222-2-2-222-200-222-2-20000-2-2200000020000000000000000
χ19222222-2-2-2-222222-2-222222-2-2200-2-2-2220000-2-2-200000020000000000000000
χ20222222-2-2-2-222222-2-222-2-2-222-200-2-2-2220000222000000-20000000000000000
χ212222-2-2200-222220-2-2-2-222-222-20020000000000-20000000000002i−2i02i−2i000000
χ222222-2-2200-222220-2-2-2-222-222-20020000000000-2000000000000−2i2i0−2i2i000000
χ232222-2-2200-222220-2-2-2-2-2-22-2-22002000000000020000000000002-20-22000000
χ242222-2-2200-222220-2-2-2-2-2-22-2-2200200000000002000000000000-2202-2000000
χ252222-2-2-20022222022-2-222-2-2-2-200-2000000000022i2i−2i−2i0000000−2i002i00000000
χ262222-2-2-20022222022-2-222-2-2-2-200-200000000002−2i−2i2i2i00000002i00−2i00000000
χ272222-2-2-20022222022-2-2-2-2222200-20000000000-222220000000-200-200000000
χ282222-2-2-20022222022-2-2-2-2222200-20000000000-2-2-2-2-20000000200200000000
χ2922-2-2-2202-202-22-2000-222-2200-20002-20000002-200000000i2−i2i2−i2000000i2−i2i2−i200
χ3022-2-2-2202-202-22-2000-222-2200-20002-20000002-200000000−i2i2−i2i2000000−i2i2−i2i200
χ3122-2-2-2202-202-22-2000-22-22-20020002-2000000-22000000002−2−220000002−2−2200
χ3222-2-2-2202-202-22-2000-22-22-20020002-2000000-2200000000−222−2000000−222−200
χ3322-2-2-220-2202-22-2000-222-2200-2000-22000000-2200000000i2−i2i2−i2000000−i2i2−i2i200
χ3422-2-2-220-2202-22-2000-222-2200-2000-22000000-2200000000−i2i2−i2i2000000i2−i2i2−i200
χ3522-2-2-220-2202-22-2000-22-22-2002000-220000002-2000000002−2−22000000−222−200
χ3622-2-2-220-2202-22-2000-22-22-2002000-220000002-200000000−222−20000002−2−2200
χ374444444444-1-1-1-14-1-1-1-100000044-1-1-1-1-1-1-1-1-10000000-1-100000000000000000
χ384444444444-1-1-1-14-1-1-1-1000000-4-4-1-1-1-1-1111100000001100000000000000000
χ394444444-4-44-1-1-1-1-4-1-1-1-10000004-4-1111111110000000-1-100000000000000000
χ404444444-4-44-1-1-1-1-4-1-1-1-1000000-44-11111-1-1-1-100000001100000000000000000
χ41444444-444-4-1-1-1-1-411-1-1000000001-1-11155−5−500000005−500000000000000000
χ42444444-444-4-1-1-1-1-411-1-1000000001-1-111−5−5550000000−5500000000000000000
χ43444444-4-4-4-4-1-1-1-1411-1-100000000111-1-155−5−50000000−5500000000000000000
χ44444444-4-4-4-4-1-1-1-1411-1-100000000111-1-1−5−55500000005−500000000000000000
χ4544-4-44-400004-44-40004-44-4-40040000000000000000000000000000000000000
χ4644-4-44-400004-44-40004-4-44400-40000000000000000000000000000000000000
χ474-44-40000004-4-44000000004-40000000000000002i2−2i22i2−2i20000000000000000000
χ484-44-40000004-4-44000000004-4000000000000000−2i22i2−2i22i20000000000000000000
χ494-44-40000004-4-4400000000-4400000000000000022−22−22220000000000000000000
χ504-44-40000004-4-4400000000-44000000000000000−222222−220000000000000000000
χ518888-8-8800-8-2-2-2-20222200000000-20000000000000000000000000000000000
χ528888-8-8-8008-2-2-2-20-2-2220000000020000000000000000000000000000000000
χ5388-8-88-80000-22-22000-22000000000002i5−2i5000000000000000000000000000000
χ5488-8-88-80000-22-22000-2200000000000−2i52i5000000000000000000000000000000
χ5588-8-8-8808-80-22-220002-2000000000-2200000000000000000000000000000000
χ5688-8-8-880-880-22-220002-20000000002-200000000000000000000000000000000
χ578-8-8800000088-8-8000000000000000000000000000000000000000000000000
χ588-8-88000000-2-222025−25000000000000000ζ7−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−ζ3900000000000000000000000000
χ598-8-88000000-2-222025−25000000000000000−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+ζ3900000000000000000000000000
χ608-8-88000000-2-2220−2525000000000000000−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+ζ3900000000000000000000000000
χ618-8-88000000-2-2220−2525000000000000000ζ7−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−ζ3900000000000000000000000000
χ6216-1616-16000000-444-4000000000000000000000000000000000000000000000000

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