Finite Group Databasebeta

← Group #13019758

Character table — Group #13019758

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size111122444444448888810101010101016161616161616161616162020202020202032324040404040404040404040404040408080
order12224444445101010220202020224444481010202020404040404448888202048888888888888848
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-111
χ31111111111111111111111111-1-111111-1-1-1-11111111-1-11111111-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111-1-111111-1-1-1-1111-1-1-1-1-1-11-1-1-1-1-1-111111111-1-1
χ51111111111111111111-1-1-1-1-1-111111111111-1-1-1ii−i−i11-1iii−i−i−iii−i−iii−i−i-1-1
χ61111111111111111111-1-1-1-1-1-111111111111-1-1-1−i−iii11-1−i−i−iiii−i−iii−i−iii-1-1
χ71111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1ii−i−i-1-1-1iii−i−i−i−i−iii−i−iii11
χ81111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1−i−iii-1-1-1−i−i−iiiiii−i−iii−i−i11
χ91111111-1-111111-111111111111-1-1-1-1-11-1-1-1-1-1-11111111-11-1-11-1-11111-1-1-1-11-1
χ101111111-1-111111-111111111111-1-1-1-1-11-1-1-1-1-1-11-1-1-1-111-1-111-111-1-1-1-111111-1
χ111111111-1-111111-11111111111-11-1-1-1-111111-1-111111-1-1-11-1-11-1-1-1-1-1-11111-11
χ121111111-1-111111-11111111111-11-1-1-1-111111-1-11-1-1-1-1-1-1-1-111-1111111-1-1-1-1-11
χ131111111-1-111111-11111-1-1-1-1-1-11-1-1-1-1-11-1-1-1-111-1ii−i−i111i−i−i−iiiii−i−i−i−iii-11
χ141111111-1-111111-11111-1-1-1-1-1-11-1-1-1-1-11-1-1-1-111-1−i−iii111−iiii−i−i−i−iiiii−i−i-11
χ151111111-1-111111-11111-1-1-1-1-1-1-11-1-1-1-11111111-1ii−i−i-1-11i−i−i−iii−i−iiiii−i−i1-1
χ161111111-1-111111-11111-1-1-1-1-1-1-11-1-1-1-11111111-1−i−iii-1-11−iiii−i−iii−i−i−i−iii1-1
χ17222222-222-22222-22-2-2222-222-200-2-222-2000022-2000000-20000000000000000
χ18222222-222-22222-22-2-22-2-22-2-2200-2-222-20000-2-2200000020000000000000000
χ19222222-2-2-2-2222222-2-2222-222-20022-2-2-20000-2-2-200000020000000000000000
χ20222222-2-2-2-2222222-2-22-2-22-2-220022-2-2-20000222000000-20000000000000000
χ212222-2-2200-222220-222-222-2-2-2-2000000-200000022i2i−2i−2i000−2i002i000000000000
χ222222-2-2200-222220-222-222-2-2-2-2000000-20000002−2i−2i2i2i0002i00−2i000000000000
χ232222-2-2200-222220-222-2-2-22222000000-2000000-22222000-200-2000000000000
χ242222-2-2200-222220-222-2-2-22222000000-2000000-2-2-2-2-20002002000000000000
χ252222-2-2-200222220-2-2-2-2222-2-220000002000000-2000000002i−2i02i−2i0000000000
χ262222-2-2-200222220-2-2-2-2222-2-220000002000000-200000000−2i2i0−2i2i0000000000
χ272222-2-2-200222220-2-2-2-2-2-2-222-200000020000002000000002-20-220000000000
χ282222-2-2-200222220-2-2-2-2-2-2-222-20000002000000200000000-2202-20000000000
χ292-22-2-2202i−2i022-2-20-20022-202-2000002i−2i000002i−2i00000000000000i2−i2i2−i22−22−200
χ302-22-2-2202i−2i022-2-20-20022-202-2000002i−2i000002i−2i00000000000000−i2i2−i2i2−22−2200
χ312-22-2-2202i−2i022-2-20-2002-220-22000002i−2i00000−2i2i000000000000002−2−22−i2i2i2−i200
χ322-22-2-2202i−2i022-2-20-2002-220-22000002i−2i00000−2i2i00000000000000−222−2i2−i2−i2i200
χ332-22-2-220−2i2i022-2-20-20022-202-200000−2i2i00000−2i2i00000000000000i2−i2i2−i2−22−2200
χ342-22-2-220−2i2i022-2-20-20022-202-200000−2i2i00000−2i2i00000000000000−i2i2−i2i22−22−200
χ352-22-2-220−2i2i022-2-20-2002-220-2200000−2i2i000002i−2i000000000000002−2−22i2−i2−i2i200
χ362-22-2-220−2i2i022-2-20-2002-220-2200000−2i2i000002i−2i00000000000000−222−2−i2i2i2−i200
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
χ394444444-4-44-1-1-1-1-4-1-1-1-10000004-41111-111110000000-1-100000000000000000
χ404444444-4-44-1-1-1-1-4-1-1-1-1000000-441111-1-1-1-1-100000001100000000000000000
χ41444444-444-4-1-1-1-1-4-111-10000000011-1-1155−5−500000005−500000000000000000
χ42444444-444-4-1-1-1-1-4-111-10000000011-1-11−5−5550000000−5500000000000000000
χ43444444-4-4-4-4-1-1-1-14-111-100000000-1-111155−5−50000000−5500000000000000000
χ44444444-4-4-4-4-1-1-1-14-111-100000000-1-1111−5−55500000005−500000000000000000
χ454-44-44-4000044-4-40400-44-40-4400000000000000000000000000000000000000
χ464-44-44-4000044-4-40400-4-4404-400000000000000000000000000000000000000
χ474-4-440000004-4-440000000400-4000000000000002i2−2i22i2−2i20000000000000000000
χ484-4-440000004-4-440000000400-400000000000000−2i22i2−2i22i20000000000000000000
χ494-4-440000004-4-440000000-40040000000000000022−22−22220000000000000000000
χ504-4-440000004-4-440000000-400400000000000000−222222−220000000000000000000
χ518888-8-8800-8-2-2-2-202-2-220000000000002000000000000000000000000000000
χ528888-8-8-8008-2-2-2-202222000000000000-2000000000000000000000000000000
χ5388-8-80000008-88-8000000000000000000000000000000000000000000000000
χ5488-8-8000000-22-220025−2500000000000000ζ7−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
χ5588-8-8000000-22-220025−2500000000000000−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
χ5688-8-8000000-22-2200−252500000000000000−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
χ5788-8-8000000-22-2200−252500000000000000ζ7−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
χ588-88-88-80000-2-2220-20020000000025−25000000000000000000000000000000000
χ598-88-88-80000-2-2220-200200000000−2525000000000000000000000000000000000
χ608-88-8-8808i−8i0-2-2220200-20000000000−2i2i0000000000000000000000000000000
χ618-88-8-880−8i8i0-2-2220200-200000000002i−2i0000000000000000000000000000000
χ6216-16-1616000000-444-4000000000000000000000000000000000000000000000000

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