Finite Group Databasebeta

← Group #13017748

Character table — Group #13017748

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111122444444448888888888888888810101010101016161616161616161620202040404040404040404040404040404040408080
order12224444445101010244442020202020202020202020202244441010202020202020202242444444448888888888
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
χ5111111111111111-1-1-1-1-1-1-1-111111111111111111-1-1-1-1-1-1111-1-11-1-11111-1-1-1-11111-1-1
χ6111111111111111-1-1-1-1-1-1-1-111111111111111111-1-1-1-1-1-1111-1-11-1-1-1-1-1-11111-1-1-1-111
χ7111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-111-111ii−i−i−i−iiiii−i−i−ii
χ8111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-111-111−i−iiiii−i−i−i−iiii−i
χ911111111-1-11111-11-1-1111111111-1-1-1-1111111-1-1111-1-1-1-1-1-1111-1-1-11111-1-1-1-1-1-1-1-111
χ1011111111-1-11111-11-1-1111111111-1-1-1-1111111-1-1111-1-1-1-1-1-1111-1-1-1-1-1-1-111111111-1-1
χ1111111111-1-11111-11-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-111-1-1-1111ii−i−i−i−iii−i−iiii−i
χ1211111111-1-11111-11-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-1-111-1-1-1111−i−iiiii−i−iii−i−i−ii
χ1311111111-1-11111-1-111-1-1-1-1-11111-1-1-1-1111111-1-11-1-11111-1-11-1-1-11111111111-1-1-1-1-1-1
χ1411111111-1-11111-1-111-1-1-1-1-11111-1-1-1-1111111-1-11-1-11111-1-11-1-1-111-1-1-1-1-1-1-1-1111111
χ1511111111-1-11111-1-111-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-1111111-1111-1-1ii−i−iii−i−i−i−iii−ii
χ1611111111-1-11111-1-111-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11-1-1111111-1111-1-1−i−iii−i−iiiii−i−ii−i
χ17222222-2-2222222-20000000022-2-2222222-2-2-2-2-2-2-2000000-2-220020000000000000000
χ18222222-2-2222222-20000000022-2-22222-2-22222-2-2-200000022-200-20000000000000000
χ19222222-2-2-2-2222220000000022-2-2-2-2-2-222-2-2-2-222-200000022200-20000000000000000
χ20222222-2-2-2-2222220000000022-2-2-2-2-2-2-2-2222222-2000000-2-2-20020000000000000000
χ212222-2-22-2002222002-200000-2-2-2-200002222-2-20020022-2-200-20002-200000000000000
χ222222-2-22-2002222002-200000-2-2-2-20000-2-2-2-2220020022-2-2002000-2200000000000000
χ232222-2-22-200222200-2200000-2-2-2-200002222-2-200200-2-22200-2000-2200000000000000
χ242222-2-22-200222200-2200000-2-2-2-20000-2-2-2-22200200-2-2220020002-200000000000000
χ252222-2-2-220022220200-22222-2-222000022-2-22200-2-2-2000000-22-200000000000000000
χ262222-2-2-220022220200-22222-2-2220000-2-222-2-200-2-2-20000002-2200000000000000000
χ272222-2-2-220022220-2002-2-2-2-2-2-222000022-2-22200-222000000-2-2200000000000000000
χ282222-2-2-220022220-2002-2-2-2-2-2-2220000-2-222-2-200-22200000022-200000000000000000
χ292-22-22-2002i−2i2-22-20000000002-2002i2i−2i−2i002i−2i2i−2i0000000002-20000001+i−1−i1−i−1+i00001−i−1+i1+i−1−i00
χ302-22-22-2002i−2i2-22-20000000002-2002i2i−2i−2i002i−2i2i−2i0000000002-2000000−1−i1+i−1+i1−i0000−1+i1−i−1−i1+i00
χ312-22-22-2002i−2i2-22-20000000002-2002i2i−2i−2i00−2i2i−2i2i000000000-220000001−i−1+i1+i−1−i0000−1−i1+i−1+i1−i00
χ322-22-22-2002i−2i2-22-20000000002-2002i2i−2i−2i00−2i2i−2i2i000000000-22000000−1+i1−i−1−i1+i00001+i−1−i1−i−1+i00
χ332-22-22-200−2i2i2-22-20000000002-200−2i−2i2i2i002i−2i2i−2i000000000-220000001+i−1−i1−i−1+i0000−1+i1−i−1−i1+i00
χ342-22-22-200−2i2i2-22-20000000002-200−2i−2i2i2i002i−2i2i−2i000000000-22000000−1−i1+i−1+i1−i00001−i−1+i1+i−1−i00
χ352-22-22-200−2i2i2-22-20000000002-200−2i−2i2i2i00−2i2i−2i2i0000000002-20000001−i−1+i1+i−1−i00001+i−1−i1−i−1+i00
χ362-22-22-200−2i2i2-22-20000000002-200−2i−2i2i2i00−2i2i−2i2i0000000002-2000000−1+i1−i−1−i1+i0000−1−i1+i−1+i1−i00
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
χ384444444444-1-1-1-14-4-4-4-41111-1-1-1-1-1-1-1-1000000-1-1-11111110000000000000000000000
χ3944444444-4-4-1-1-1-1-44-4-44-1-1-1-1-1-1-1-1111100000011-1-1-111110000000000000000000000
χ4044444444-4-4-1-1-1-1-4-444-41111-1-1-1-1111100000011-111-1-1-1-10000000000000000000000
χ41444444-4-444-1-1-1-1-4000055−5−5-1-111-1-1-1-10000001115−55−55−50000000000000000000000
χ42444444-4-444-1-1-1-1-40000−5−555-1-111-1-1-1-1000000111−55−55−550000000000000000000000
χ43444444-4-4-4-4-1-1-1-14000055−5−5-1-1111111000000-1-115−5−55−550000000000000000000000
χ44444444-4-4-4-4-1-1-1-140000−5−555-1-1111111000000-1-11−555−55−50000000000000000000000
χ454444-4-44-400-1-1-1-1004-4055−5−511115−55−50000005−5-1−55-1-1110000000000000000000000
χ464444-4-44-400-1-1-1-1004-40−5−5551111−55−55000000−55-15−5-1-1110000000000000000000000
χ474444-4-44-400-1-1-1-100-44055−5−51111−55−55000000−55-1−5511-1-10000000000000000000000
χ484444-4-44-400-1-1-1-100-440−5−55511115−55−50000005−5-15−511-1-10000000000000000000000
χ494444-4-4-4400-1-1-1-10400-4-1-1-1-111-1-15−55−5000000−551115−5−550000000000000000000000
χ504444-4-4-4400-1-1-1-10400-4-1-1-1-111-1-1−55−550000005−5111−555−50000000000000000000000
χ514444-4-4-4400-1-1-1-10-4004111111-1-15−55−5000000−551-1-1−555−50000000000000000000000
χ524444-4-4-4400-1-1-1-10-4004111111-1-1−55−550000005−51-1-15−5−550000000000000000000000
χ5344-4-400000044-4-4000000000000000004-400000000000000000000000002-22-2000000
χ5444-4-400000044-4-4000000000000000004-40000000000000000000000000-22-22000000
χ5544-4-400000044-4-400000000000000000-4400000000000000000000000002i−2i−2i2i000000
χ5644-4-400000044-4-400000000000000000-440000000000000000000000000−2i2i2i−2i000000
χ574-44-4-4400004-44-4000000000-44000000004i−4i−4i4i0000000000000000000000000000000
χ584-44-4-4400004-44-4000000000-4400000000−4i4i4i−4i0000000000000000000000000000000
χ598-88-88-8008i−8i-22-22000000000-2200−2i−2i2i2i0000000000000000000000000000000000000
χ608-88-88-800−8i8i-22-22000000000-22002i2i−2i−2i0000000000000000000000000000000000000
χ618-88-8-880000-22-220000000002-2002i5−2i5−2i52i50000000000000000000000000000000000000
χ628-88-8-880000-22-220000000002-200−2i52i52i5−2i50000000000000000000000000000000000000
χ638-8-880000008-8-88000000000000000000000000000000000000000000000000000000
χ648-8-88000000-222-200000−2ζ3+2ζ7−2ζ11+2ζ192ζ3−2ζ7+2ζ11−2ζ192ζ3−2ζ7−2ζ11+2ζ19−2ζ3+2ζ7+2ζ11−2ζ190025−2500000000000000000000000000000000000000000
χ658-8-88000000-222-2000002ζ3−2ζ7−2ζ11+2ζ19−2ζ3+2ζ7+2ζ11−2ζ192ζ3−2ζ7+2ζ11−2ζ19−2ζ3+2ζ7−2ζ11+2ζ1900−252500000000000000000000000000000000000000000
χ668-8-88000000-222-2000002ζ3−2ζ7+2ζ11−2ζ19−2ζ3+2ζ7−2ζ11+2ζ19−2ζ3+2ζ7+2ζ11−2ζ192ζ3−2ζ7−2ζ11+2ζ190025−2500000000000000000000000000000000000000000
χ678-8-88000000-222-200000−2ζ3+2ζ7+2ζ11−2ζ192ζ3−2ζ7−2ζ11+2ζ19−2ζ3+2ζ7−2ζ11+2ζ192ζ3−2ζ7+2ζ11−2ζ1900−252500000000000000000000000000000000000000000
χ681616-16-16000000-4-444000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 20 (ζ20 = 1); i = ζ5.