Finite Group Databasebeta

← Group #13017775

Character table — Group #13017775

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111122444444448888888888888888810101010101016161616161616161620202040404040404040404040404040404040408080
order12224444445101010224442020202020202020202020202244441010101020202020204442244488888888888844
χ111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1ii−i−iii−i−iii−i−ii−i
χ41111111111111111111111111111111-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1−i−iii−i−iii−i−iii−ii
χ5111111111111111-1-1-1-111111111-1-1-1-111111111-1-11-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1
χ6111111111111111-1-1-1-111111111-1-1-1-111111111-1-11-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111
χ7111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-11-1-1-1-1-1-1-1-11111ii−i−i−i−iiiii−i−i−ii
χ8111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-11-1-1-1-1-1-1-1-11111−i−iiiii−i−i−i−iiii−i
χ911111111-1-11111-11-1-111111-1-1-1-11111111111-1-1111-1-1-1-1-1-11-111-1-11111-1-1-1-1-1-1-1-111
χ1011111111-1-11111-11-1-111111-1-1-1-11111111111-1-1111-1-1-1-1-1-11-111-1-1-1-1-1-111111111-1-1
χ1111111111-1-11111-11-1-111111-1-1-1-11111-1-1-1-1-1-1-1-1111-1-1-1-111-11-1-111ii−i−i−i−iii−i−iiii−i
χ1211111111-1-11111-11-1-111111-1-1-1-11111-1-1-1-1-1-1-1-1111-1-1-1-111-11-1-111−i−iiiii−i−iii−i−i−ii
χ1311111111-1-11111-1-111-11111-1-1-1-1-1-1-1-1111111-1-1-1-111111-1-11-1-1-11111111111-1-1-1-1-1-1
χ1411111111-1-11111-1-111-11111-1-1-1-1-1-1-1-1111111-1-1-1-111111-1-11-1-1-111-1-1-1-1-1-1-1-1111111
χ1511111111-1-11111-1-111-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1111-1-1ii−i−iii−i−i−i−iii−ii
χ1611111111-1-11111-1-111-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1111-1-1−i−iii−i−iiiii−i−ii−i
χ17222222-2-2222222-2000022-2-222220000222-2-22-2-200-2000022-2-2000000000000000000
χ18222222-2-2222222-2000022-2-222220000-2-2-222-2-2-200-20000-2-222000000000000000000
χ19222222-2-2-2-222222000022-2-2-2-2-2-20000222-2-222200-20000-2-2-22000000000000000000
χ20222222-2-2-2-222222000022-2-2-2-2-2-20000-2-2-222-22200-20000222-2000000000000000000
χ212222-2-22-2002222002-20-2-2-2-20000000022-2-2-2-20000222-2-20020002-200000000000000
χ222222-2-22-2002222002-20-2-2-2-200000000-2-222220000222-2-200-2000-2200000000000000
χ232222-2-22-200222200-220-2-2-2-20000000022-2-2-2-200002-2-222002000-2200000000000000
χ242222-2-22-200222200-220-2-2-2-200000000-2-2222200002-2-22200-20002-200000000000000
χ252222-2-2-220022220200-2-2-2220000-2-2-2-222-222-20022-2000000-20-220000000000000000
χ262222-2-2-220022220200-2-2-2220000-2-2-2-2-2-22-2-220022-2000000202-20000000000000000
χ272222-2-2-220022220-2002-2-2220000222222-222-200-2-2-2000000-202-20000000000000000
χ282222-2-2-220022220-2002-2-22200002222-2-22-2-2200-2-2-200000020-220000000000000000
χ292-22-22-2002i−2i22-2-2000002-2002i2i−2i−2i00002-2-20020000000002i−2i000000i2−i2i2−i200002−22−200
χ302-22-22-2002i−2i22-2-2000002-2002i2i−2i−2i00002-2-20020000000002i−2i000000−i2i2−i2i20000−22−2200
χ312-22-22-2002i−2i22-2-2000002-2002i2i−2i−2i0000-22200-2000000000−2i2i0000002−2−220000−i2i2i2−i200
χ322-22-22-2002i−2i22-2-2000002-2002i2i−2i−2i0000-22200-2000000000−2i2i000000−222−20000i2−i2−i2i200
χ332-22-22-200−2i2i22-2-2000002-200−2i−2i2i2i00002-2-2002000000000−2i2i000000i2−i2i2−i20000−22−2200
χ342-22-22-200−2i2i22-2-2000002-200−2i−2i2i2i00002-2-2002000000000−2i2i000000−i2i2−i2i200002−22−200
χ352-22-22-200−2i2i22-2-2000002-200−2i−2i2i2i0000-22200-20000000002i−2i0000002−2−220000i2−i2−i2i200
χ362-22-22-200−2i2i22-2-2000002-200−2i−2i2i2i0000-22200-20000000002i−2i000000−222−20000−i2i2i2−i200
χ374444444444-1-1-1-144444-1-1-1-1-1-1-1-1-1-1-1-1000000-1-1-1-1-1-1-1-1-10000000000000000000000
χ384444444444-1-1-1-14-4-4-4-4-1-1-1-1-1-1-1-11111000000-1-111-111110000000000000000000000
χ3944444444-4-4-1-1-1-1-44-4-44-1-1-1-11111-1-1-1-100000011-1-1-111110000000000000000000000
χ4044444444-4-4-1-1-1-1-4-444-4-1-1-1-1111111110000001111-1-1-1-1-10000000000000000000000
χ41444444-4-444-1-1-1-1-40000-1-111-1-1-1-155−5−5000000115−515−55−50000000000000000000000
χ42444444-4-444-1-1-1-1-40000-1-111-1-1-1-1−5−55500000011−551−55−550000000000000000000000
χ43444444-4-4-4-4-1-1-1-140000-1-111111155−5−5000000-1-15−51−55−550000000000000000000000
χ44444444-4-4-4-4-1-1-1-140000-1-1111111−5−555000000-1-1−5515−55−50000000000000000000000
χ454444-4-44-400-1-1-1-1004-4011115−55−555−5−50000005−5−55-1-1-1110000000000000000000000
χ464444-4-44-400-1-1-1-1004-401111−55−55−5−555000000−555−5-1-1-1110000000000000000000000
χ474444-4-44-400-1-1-1-100-44011115−55−5−5−5550000005−55−5-111-1-10000000000000000000000
χ484444-4-44-400-1-1-1-100-4401111−55−5555−5−5000000−55−55-111-1-10000000000000000000000
χ494444-4-4-4400-1-1-1-10400-411-1-15−55−51111000000−55-1-11−555−50000000000000000000000
χ504444-4-4-4400-1-1-1-10400-411-1-1−55−5511110000005−5-1-115−5−550000000000000000000000
χ514444-4-4-4400-1-1-1-10-400411-1-15−55−5-1-1-1-1000000−551115−5−550000000000000000000000
χ524444-4-4-4400-1-1-1-10-400411-1-1−55−55-1-1-1-10000005−5111−555−50000000000000000000000
χ5344-4-40000004-4-44000000000000000000004i−4i0000000000000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39000000
χ5444-4-40000004-4-44000000000000000000004i−4i00000000000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39000000
χ5544-4-40000004-4-4400000000000000000000−4i4i0000000000000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37000000
χ5644-4-40000004-4-4400000000000000000000−4i4i00000000000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37000000
χ574-44-4-44000044-4-400000-4400000000004-4400-40000000000000000000000000000000
χ584-44-4-44000044-4-400000-440000000000-44-40040000000000000000000000000000000
χ598-88-88-8008i−8i-2-22200000-2200−2i−2i2i2i00000000000000000000000000000000000000000
χ608-88-88-800−8i8i-2-22200000-22002i2i−2i−2i00000000000000000000000000000000000000000
χ618-88-8-880000-2-222000002-2002i5−2i5−2i52i500000000000000000000000000000000000000000
χ628-88-8-880000-2-222000002-200−2i52i52i5−2i500000000000000000000000000000000000000000
χ638-8-880000008-88-8000000000000000000000000000000000000000000000000000000
χ648-8-88000000-22-22000000025−250000−2ζ6+2ζ14−2ζ22+2ζ382ζ6−2ζ14+2ζ22−2ζ382ζ6−2ζ14−2ζ22+2ζ38−2ζ6+2ζ14+2ζ22−2ζ380000000000000000000000000000000000000
χ658-8-88000000-22-22000000025−2500002ζ6−2ζ14+2ζ22−2ζ38−2ζ6+2ζ14−2ζ22+2ζ38−2ζ6+2ζ14+2ζ22−2ζ382ζ6−2ζ14−2ζ22+2ζ380000000000000000000000000000000000000
χ668-8-88000000-22-220000000−252500002ζ6−2ζ14−2ζ22+2ζ38−2ζ6+2ζ14+2ζ22−2ζ382ζ6−2ζ14+2ζ22−2ζ38−2ζ6+2ζ14−2ζ22+2ζ380000000000000000000000000000000000000
χ678-8-88000000-22-220000000−25250000−2ζ6+2ζ14+2ζ22−2ζ382ζ6−2ζ14−2ζ22+2ζ38−2ζ6+2ζ14−2ζ22+2ζ382ζ6−2ζ14+2ζ22−2ζ380000000000000000000000000000000000000
χ681616-16-16000000-444-4000000000000000000000000000000000000000000000000000000

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