Finite Group Databasebeta

← Group #13017751

Character table — Group #13017751

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111122444444448888888888888888810101010101016161616161616161620202040404040404040404040404040404040408080
order12224444445101010222442020202020202020202020202244441010101010102020204444444444448888888888
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
χ511111111111111-1-1-1-1111111111-1-1-1-1111111-1-1-1-1-1-1111111-11-1-1-11111-1-1-1-11111-1-1
χ611111111111111-1-1-1-1111111111-1-1-1-1111111-1-1-1-1-1-1111111-11-1-1-1-1-1-1-11111-1-1-1-111
χ711111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-11-1111ii−i−i−i−iiiii−i−i−ii
χ811111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-11-1111−i−iiiii−i−i−i−iiii−i
χ91111111-1-11111111-1-1-11111-1-1-1-1-1-1-1-11111111111-1-11-1-1-1-11-1-111-111111111-1-1-1-1-1-1
χ101111111-1-11111111-1-1-11111-1-1-1-1-1-1-1-11111111111-1-11-1-1-1-11-1-111-1-1-1-1-1-1-1-1-1111111
χ111111111-1-11111111-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11-1-111-111-1-11ii−i−iii−i−i−i−iii−ii
χ121111111-1-11111111-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11-1-111-111-1-11−i−iii−i−iiiii−i−ii−i
χ131111111-1-111111-1-111-11111-1-1-1-11111111111-1-1-1-1111-1-1-1-111-1-1-111111-1-1-1-1-1-1-1-111
χ141111111-1-111111-1-111-11111-1-1-1-11111111111-1-1-1-1111-1-1-1-111-1-1-11-1-1-1-111111111-1-1
χ151111111-1-111111-1-111-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111-1-111-1-1111-1ii−i−i−i−iii−i−iiii−i
χ161111111-1-111111-1-111-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1111-1-111-1-1111-1−i−iiiii−i−iii−i−i−ii
χ17222222-222-222220000-2-2-2222222000022-2-2-2-2000000-2-2-2-2-220200000000000000000
χ18222222-222-222220000-2-2-22222220000-2-22222000000-2-2-222-20-200000000000000000
χ19222222-2-2-2-2222200002-2-222-2-2-2-2000022-2-2-2-2000000-2222220-200000000000000000
χ20222222-2-2-2-2222200002-2-222-2-2-2-20000-2-22222000000-222-2-2-20200000000000000000
χ212222-2-2200-22222002-2022-2-20000-2-2-2-22222-2-2000022-20000-2-2000200000000000000
χ222222-2-2200-22222002-2022-2-20000-2-2-2-2-2-2-2-222000022-2000022000-200000000000000
χ232222-2-2200-2222200-22022-2-2000022222222-2-20000-2-2-20000-22000-200000000000000
χ242222-2-2200-2222200-22022-2-200002222-2-2-2-2220000-2-2-200002-2000200000000000000
χ252222-2-2-200222222-2000-2-2-2-20000000022-2-22222-2-20020000-2002-2000000000000000
χ262222-2-2-200222222-2000-2-2-2-200000000-2-222-2-222-2-20020000200-22000000000000000
χ272222-2-2-20022222-22000-2-2-2-20000000022-2-222-2-2220020000-200-22000000000000000
χ282222-2-2-20022222-22000-2-2-2-200000000-2-222-2-2-2-22200200002002-2000000000000000
χ292-22-22-202-202-2-2200000002-222-2-20000002i−2i2i−2i0000000002i−2i0000001+i−1−i1−i−1+i00001+i−1−i1−i−1+i00
χ302-22-22-202-202-2-2200000002-222-2-20000002i−2i2i−2i0000000002i−2i000000−1−i1+i−1+i1−i0000−1−i1+i−1+i1−i00
χ312-22-22-202-202-2-2200000002-222-2-2000000−2i2i−2i2i000000000−2i2i0000001−i−1+i1+i−1−i00001−i−1+i1+i−1−i00
χ322-22-22-202-202-2-2200000002-222-2-2000000−2i2i−2i2i000000000−2i2i000000−1+i1−i−1−i1+i0000−1+i1−i−1−i1+i00
χ332-22-22-20-2202-2-2200000002-2-2-2220000002i−2i2i−2i000000000−2i2i0000001+i−1−i1−i−1+i0000−1−i1+i−1+i1−i00
χ342-22-22-20-2202-2-2200000002-2-2-2220000002i−2i2i−2i000000000−2i2i000000−1−i1+i−1+i1−i00001+i−1−i1−i−1+i00
χ352-22-22-20-2202-2-2200000002-2-2-222000000−2i2i−2i2i0000000002i−2i0000001−i−1+i1+i−1−i0000−1+i1−i−1−i1+i00
χ362-22-22-20-2202-2-2200000002-2-2-222000000−2i2i−2i2i0000000002i−2i000000−1+i1−i−1−i1+i00001−i−1+i1+i−1−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
χ384444444444-1-1-1-1-4-4-4-44-1-1-1-1-1-1-1-11111000000111111-1-1-10000000000000000000000
χ394444444-4-44-1-1-1-144-4-4-4-1-1-1-111111111000000-1-1-1-111-1110000000000000000000000
χ404444444-4-44-1-1-1-1-4-444-4-1-1-1-11111-1-1-1-10000001111-1-1-1110000000000000000000000
χ41444444-444-4-1-1-1-10000-411-1-1-1-1-1-155−5−50000005−55−55−51110000000000000000000000
χ42444444-444-4-1-1-1-10000-411-1-1-1-1-1-1−5−555000000−55−55−551110000000000000000000000
χ43444444-4-4-4-4-1-1-1-10000411-1-1111155−5−5000000−55−555−51-1-10000000000000000000000
χ44444444-4-4-4-4-1-1-1-10000411-1-11111−5−5550000005−55−5−551-1-10000000000000000000000
χ454444-4-4400-4-1-1-1-1004-40-1-1115−55−511110000005−5−55-1-115−50000000000000000000000
χ464444-4-4400-4-1-1-1-1004-40-1-111−55−551111000000−555−5-1-11−550000000000000000000000
χ474444-4-4400-4-1-1-1-100-440-1-1115−55−5-1-1-1-1000000−555−51115−50000000000000000000000
χ484444-4-4400-4-1-1-1-100-440-1-111−55−55-1-1-1-10000005−5−55111−550000000000000000000000
χ494444-4-4-4004-1-1-1-14-400011115−55−5−5−555000000-1-1115−5-1−550000000000000000000000
χ504444-4-4-4004-1-1-1-14-40001111−55−5555−5−5000000-1-111−55-15−50000000000000000000000
χ514444-4-4-4004-1-1-1-1-4400011115−55−555−5−500000011-1-1−55-1−550000000000000000000000
χ524444-4-4-4004-1-1-1-1-440001111−55−55−5−55500000011-1-15−5-15−50000000000000000000000
χ534-44-4-4400004-4-440000000-4400000000004i−4i−4i4i0000000000000000000000000000000
χ544-44-4-4400004-4-440000000-440000000000−4i4i4i−4i0000000000000000000000000000000
χ554-4-440000004-44-4000000000000000004-400000000000000000000000002i−2i2i−2i000000
χ564-4-440000004-44-4000000000000000004-40000000000000000000000000−2i2i−2i2i000000
χ574-4-440000004-44-400000000000000000-4400000000000000000000000002-2-22000000
χ584-4-440000004-44-400000000000000000-440000000000000000000000000-222-2000000
χ5988-8-800000088-8-8000000000000000000000000000000000000000000000000000000
χ6088-8-8000000-2-2220000025−25000000−2ζ3+2ζ7−2ζ11+2ζ192ζ3−2ζ7+2ζ11−2ζ192ζ3−2ζ7−2ζ11+2ζ19−2ζ3+2ζ7+2ζ11−2ζ190000000000000000000000000000000000000
χ6188-8-8000000-2-2220000025−250000002ζ3−2ζ7+2ζ11−2ζ19−2ζ3+2ζ7−2ζ11+2ζ19−2ζ3+2ζ7+2ζ11−2ζ192ζ3−2ζ7−2ζ11+2ζ190000000000000000000000000000000000000
χ6288-8-8000000-2-22200000−25250000002ζ3−2ζ7−2ζ11+2ζ19−2ζ3+2ζ7+2ζ11−2ζ192ζ3−2ζ7+2ζ11−2ζ19−2ζ3+2ζ7−2ζ11+2ζ190000000000000000000000000000000000000
χ6388-8-8000000-2-22200000−2525000000−2ζ3+2ζ7+2ζ11−2ζ192ζ3−2ζ7−2ζ11+2ζ19−2ζ3+2ζ7−2ζ11+2ζ192ζ3−2ζ7+2ζ11−2ζ190000000000000000000000000000000000000
χ648-88-88-808-80-222-20000000-22-2-22200000000000000000000000000000000000000000
χ658-88-88-80-880-222-20000000-2222-2-200000000000000000000000000000000000000000
χ668-88-8-880000-222-200000002-225−25−252500000000000000000000000000000000000000000
χ678-88-8-880000-222-200000002-2−252525−2500000000000000000000000000000000000000000
χ6816-16-1616000000-44-44000000000000000000000000000000000000000000000000000000

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