Finite Group Databasebeta

← Group #13019728

Character table — Group #13019728

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size111122444444448888810101010101016161616161616161616162020202020202032324040404040404040404040404040408080
order12224444445101010420202020444444482020202020404040402448888202024444888888888848
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-111
χ31111111111111111111111111-1-111111-1-1-1-11111111-1-11-1-1-1-1-1-1-1-1111111-1-1
χ41111111111111111111111111-1-111111-1-1-1-1111-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1
χ51111111111111111111-1-1-1-1-1-111111111111-1-1-1ii−i−i11-1ii−i−iii−i−iiii−i−i−i-1-1
χ61111111111111111111-1-1-1-1-1-111111111111-1-1-1−i−iii11-1−i−iii−i−iii−i−i−iiii-1-1
χ71111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1ii−i−i-1-1-1−i−iii−i−iiiiii−i−i−i11
χ81111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1−i−iii-1-1-1ii−i−iii−i−i−i−i−iiii11
χ911111111-1-11111-111111111111-1-1-11-1-1-1-1-1-11-1-1111111-1-1-1-1-111111-1-11-1-11-1
χ1011111111-1-11111-111111111111-1-1-11-1-1-1-1-1-11-1-1-1-1-1-111-11111-1-1-1-1-111-1111-1
χ1111111111-1-11111-11111111111-11-1-11-1-111111-1-11111-1-1-11111-1-1-1-11-1-11-1-1-11
χ1211111111-1-11111-11111111111-11-1-11-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-111-11
χ1311111111-1-11111-11111-1-1-1-1-1-11-1-1-11-1-1-1-1-1-1-111ii−i−i111−i−iiiii−i−ii−i−i−iii-11
χ1411111111-1-11111-11111-1-1-1-1-1-11-1-1-11-1-1-1-1-1-1-111−i−iii111ii−i−i−i−iii−iiii−i−i-11
χ1511111111-1-11111-11111-1-1-1-1-1-1-11-1-11-1-11111-111ii−i−i-1-11ii−i−i−i−iiii−i−i−iii1-1
χ1611111111-1-11111-11111-1-1-1-1-1-1-11-1-11-1-11111-111−i−iii-1-11−i−iiiii−i−i−iiii−i−i1-1
χ17222222-2-2222222-2-2-22222-2-2220022-2-2-20000-222000000-20000000000000000
χ18222222-2-2222222-2-2-222-2-222-2-20022-2-2-200002-2-200000020000000000000000
χ19222222-2-2-2-222222-2-22222-2-22200-2-2-2220000-2-2-200000020000000000000000
χ20222222-2-2-2-222222-2-222-2-222-2-200-2-2-2220000222000000-20000000000000000
χ212222-2-22-20022220-2-2-2-22222-2-200002000000-20000000000000000002i−2i02i−2i00
χ222222-2-22-20022220-2-2-2-22222-2-200002000000-2000000000000000000−2i2i0−2i2i00
χ232222-2-22-20022220-2-2-2-2-2-2-2-2220000200000020000000000000000002-20-2200
χ242222-2-22-20022220-2-2-2-2-2-2-2-222000020000002000000000000000000-2202-200
χ252222-2-2-22002222022-2-222-2-2-2-20000-20000002002i2i−2i−2i00000000000−2i002i0000
χ262222-2-2-22002222022-2-222-2-2-2-20000-2000000200−2i−2i2i2i000000000002i00−2i0000
χ272222-2-2-22002222022-2-2-2-222220000-2000000-200222200000000000-200-20000
χ282222-2-2-22002222022-2-2-2-222220000-2000000-200-2-2-2-20000000000020020000
χ292-2-22-22002-22-22-20002-22i−2i002i−2i002-2000000002i−2i00000001−i−1+i1+i−1−i1−i−1+i1+i−1−i00000000
χ302-2-22-22002-22-22-20002-22i−2i002i−2i002-2000000002i−2i0000000−1+i1−i−1−i1+i−1+i1−i−1−i1+i00000000
χ312-2-22-22002-22-22-20002-2−2i2i00−2i2i002-200000000−2i2i00000001+i−1−i1−i−1+i1+i−1−i1−i−1+i00000000
χ322-2-22-22002-22-22-20002-2−2i2i00−2i2i002-200000000−2i2i0000000−1−i1+i−1+i1−i−1−i1+i−1+i1−i00000000
χ332-2-22-2200-222-22-20002-22i−2i002i−2i00-2200000000−2i2i00000001−i−1+i1+i−1−i−1+i1−i−1−i1+i00000000
χ342-2-22-2200-222-22-20002-22i−2i002i−2i00-2200000000−2i2i0000000−1+i1−i−1−i1+i1−i−1+i1+i−1−i00000000
χ352-2-22-2200-222-22-20002-2−2i2i00−2i2i00-22000000002i−2i00000001+i−1−i1−i−1+i−1−i1+i−1+i1−i00000000
χ362-2-22-2200-222-22-20002-2−2i2i00−2i2i00-22000000002i−2i0000000−1−i1+i−1+i1−i1+i−1−i1−i−1+i00000000
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
χ3944444444-4-4-1-1-1-1-4-1-1-1-10000004-411-11111110000000-1-100000000000000000
χ4044444444-4-4-1-1-1-1-4-1-1-1-1000000-4411-111-1-1-1-100000001100000000000000000
χ41444444-4-444-1-1-1-1-411-1-100000000-1-111155−5−500000005−500000000000000000
χ42444444-4-444-1-1-1-1-411-1-100000000-1-1111−5−5550000000−5500000000000000000
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
χ4544-4-40000004-4-4400000004i−4i00000000000000002+2i−2−2i2−2i−2+2i0000000000000000000
χ4644-4-40000004-4-4400000004i−4i0000000000000000−2−2i2+2i−2+2i2−2i0000000000000000000
χ4744-4-40000004-4-440000000−4i4i00000000000000002−2i−2+2i2+2i−2−2i0000000000000000000
χ4844-4-40000004-4-440000000−4i4i0000000000000000−2+2i2−2i−2−2i2+2i0000000000000000000
χ494-4-444-400004-44-4000-444i−4i00−4i4i0000000000000000000000000000000000000
χ504-4-444-400004-44-4000-44−4i4i004i−4i0000000000000000000000000000000000000
χ518888-8-88-800-2-2-2-2022220000000000-200000000000000000000000000000000
χ528888-8-8-8800-2-2-2-20-2-2220000000000200000000000000000000000000000000
χ538-88-800000088-8-8000000000000000000000000000000000000000000000000
χ548-88-8000000-2-222025−25000000000000000−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
χ558-88-8000000-2-222025−25000000000000000ζ7+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
χ568-88-8000000-2-2220−2525000000000000000ζ7+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
χ578-88-8000000-2-2220−2525000000000000000−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
χ588-8-888-80000-22-220002-2000000000002i5−2i5000000000000000000000000000000
χ598-8-888-80000-22-220002-200000000000−2i52i5000000000000000000000000000000
χ608-8-88-88008-8-22-22000-2200000000-22000000000000000000000000000000000
χ618-8-88-8800-88-22-22000-22000000002-2000000000000000000000000000000000
χ621616-16-16000000-444-4000000000000000000000000000000000000000000000000

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