Finite Group Databasebeta

← Group #13017745

Character table — Group #13017745

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size111122444444448888888888888888810101010101016161616161616161620202040404040404040404040404040404040408080
order12224444445101010444442020202020202020202020202244442020202020202020204442444444448888888888
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
χ511111111111111-1-11-1-111-1-1-1-11111111111111-1-111-1-1-1-1111-11-1-1-11111-1-1-1-11111-1-1
χ611111111111111-1-11-1-111-1-1-1-11111111111111-1-111-1-1-1-1111-11-1-1-1-1-1-1-11111-1-1-1-111
χ711111111111111-1-11-1-111-1-1-1-1111111-1-1-1-1-1-11-1-111-1-1-1-1-1-1-11-1111ii−i−i−i−iiiii−i−i−ii
χ811111111111111-1-11-1-111-1-1-1-1111111-1-1-1-1-1-11-1-111-1-1-1-1-1-1-11-1111−i−iiiii−i−i−i−iiii−i
χ91111111-1-11111111-1-1-1111111-1-1-1-111111111111-1-1-1-1-1-1-1-111-1-1-111111-1-1-1-1-1-1-1-111
χ101111111-1-11111111-1-1-1111111-1-1-1-111111111111-1-1-1-1-1-1-1-111-1-1-11-1-1-1-111111111-1-1
χ111111111-1-11111111-1-1-1111111-1-1-1-111-1-1-1-1-1-1111-1-1-1-1-1-111-1-1111-1ii−i−i−i−iii−i−iiii−i
χ121111111-1-11111111-1-1-1111111-1-1-1-111-1-1-1-1-1-1111-1-1-1-1-1-111-1-1111-1−i−iiiii−i−iii−i−i−ii
χ131111111-1-111111-1-1-11111-1-1-1-1-1-1-1-1111111111-1-1-1-11111-1-11-1-111-111111111-1-1-1-1-1-1
χ141111111-1-111111-1-1-11111-1-1-1-1-1-1-1-1111111111-1-1-1-11111-1-11-1-111-1-1-1-1-1-1-1-1-1111111
χ151111111-1-111111-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-11-1-1-1-1111111-111-1-11ii−i−iii−i−i−i−iii−ii
χ161111111-1-111111-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-11-1-1-1-1111111-111-1-11−i−iii−i−iiiii−i−ii−i
χ17222222-222-2222200-200-2-2000022222222-2-2-2-2-200-2-20000-2-220200000000000000000
χ18222222-222-2222200-200-2-20000222222-2-22222-200-2-2000022-20-200000000000000000
χ19222222-2-2-2-2222200200-2-20000-2-2-2-22222-2-2-2-2-2002200002220-200000000000000000
χ20222222-2-2-2-2222200200-2-20000-2-2-2-222-2-22222-200220000-2-2-20200000000000000000
χ212222-2-2200-222220002-2-2-200000000-2-22222-2-22000022-2-200-2002-2000000000000000
χ222222-2-2200-222220002-2-2-200000000-2-2-2-2-2-2222000022-2-200200-22000000000000000
χ232222-2-2200-22222000-22-2-200000000-2-22222-2-220000-2-22200-200-22000000000000000
χ242222-2-2200-22222000-22-2-200000000-2-2-2-2-2-22220000-2-222002002-2000000000000000
χ252222-2-2-200222222-200022-2-2-2-20000-2-222-2-222-22200000000-22000-200000000000000
χ262222-2-2-200222222-200022-2-2-2-20000-2-2-2-222-2-2-222000000002-2000200000000000000
χ272222-2-2-20022222-220002222220000-2-222-2-222-2-2-200000000-2-2000200000000000000
χ282222-2-2-20022222-220002222220000-2-2-2-222-2-2-2-2-20000000022000-200000000000000
χ292-2-222-202i−2i02-2-22000000000002i2i−2i−2i2-2002i−2i2i−2i0000000002-20000001+i−1−i1−i−1+i00001−i−1+i1+i−1−i00
χ302-2-222-202i−2i02-2-22000000000002i2i−2i−2i2-2002i−2i2i−2i0000000002-2000000−1−i1+i−1+i1−i0000−1+i1−i−1−i1+i00
χ312-2-222-202i−2i02-2-22000000000002i2i−2i−2i2-200−2i2i−2i2i000000000-220000001−i−1+i1+i−1−i0000−1−i1+i−1+i1−i00
χ322-2-222-202i−2i02-2-22000000000002i2i−2i−2i2-200−2i2i−2i2i000000000-22000000−1+i1−i−1−i1+i00001+i−1−i1−i−1+i00
χ332-2-222-20−2i2i02-2-2200000000000−2i−2i2i2i2-2002i−2i2i−2i000000000-220000001+i−1−i1−i−1+i0000−1+i1−i−1−i1+i00
χ342-2-222-20−2i2i02-2-2200000000000−2i−2i2i2i2-2002i−2i2i−2i000000000-22000000−1−i1+i−1+i1−i00001−i−1+i1+i−1−i00
χ352-2-222-20−2i2i02-2-2200000000000−2i−2i2i2i2-200−2i2i−2i2i0000000002-20000001−i−1+i1+i−1−i00001+i−1−i1−i−1+i00
χ362-2-222-20−2i2i02-2-2200000000000−2i−2i2i2i2-200−2i2i−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
χ384444444444-1-1-1-1-4-44-4-4-1-11111-1-1-1-1-1-1000000-111-1-111110000000000000000000000
χ394444444-4-44-1-1-1-144-4-4-4-1-1-1-1-1-11111-1-1000000-1-1-11111110000000000000000000000
χ404444444-4-44-1-1-1-1-4-4-444-1-111111111-1-1000000-11111-1-1-1-10000000000000000000000
χ41444444-444-4-1-1-1-100-4001155−5−5-1-1-1-1-1-100000015−5115−55−50000000000000000000000
χ42444444-444-4-1-1-1-100-40011−5−555-1-1-1-1-1-10000001−5511−55−550000000000000000000000
χ43444444-4-4-4-4-1-1-1-1004001155−5−51111-1-100000015−5-1-1−55−550000000000000000000000
χ44444444-4-4-4-4-1-1-1-10040011−5−5551111-1-10000001−55-1-15−55−50000000000000000000000
χ454444-4-4400-4-1-1-1-10004-41155−5−55−55−511000000-1−555−5-1-1110000000000000000000000
χ464444-4-4400-4-1-1-1-10004-411−5−555−55−5511000000-15−5−55-1-1110000000000000000000000
χ474444-4-4400-4-1-1-1-1000-441155−5−5−55−5511000000-1−55−5511-1-10000000000000000000000
χ484444-4-4400-4-1-1-1-1000-4411−5−5555−55−511000000-15−55−511-1-10000000000000000000000
χ494444-4-4-4004-1-1-1-14-4000-1-111115−55−5110000001-1-1−55−555−50000000000000000000000
χ504444-4-4-4004-1-1-1-14-4000-1-11111−55−55110000001-1-15−55−5−550000000000000000000000
χ514444-4-4-4004-1-1-1-1-44000-1-1-1-1-1-15−55−511000000111−555−5−550000000000000000000000
χ524444-4-4-4004-1-1-1-1-44000-1-1-1-1-1-1−55−55110000001115−5−555−50000000000000000000000
χ5344-4-40000004-44-4000000000000000004-400000000000000000000000002-22-2000000
χ5444-4-40000004-44-4000000000000000004-40000000000000000000000000-22-22000000
χ5544-4-40000004-44-400000000000000000-4400000000000000000000000002i−2i−2i2i000000
χ5644-4-40000004-44-400000000000000000-440000000000000000000000000−2i2i2i−2i000000
χ574-4-44-4400004-4-44000000000000000-44004i−4i−4i4i0000000000000000000000000000000
χ584-4-44-4400004-4-44000000000000000-4400−4i4i4i−4i0000000000000000000000000000000
χ598-88-800000088-8-8000000000000000000000000000000000000000000000000000000
χ608-88-8000000-2-2220000025−25−2ζ2+2ζ6−2ζ14+2ζ182ζ2−2ζ6+2ζ14−2ζ18−2ζ2−2ζ6+2ζ14+2ζ182ζ2+2ζ6−2ζ14−2ζ180000000000000000000000000000000000000000000
χ618-88-8000000-2-2220000025−252ζ2−2ζ6+2ζ14−2ζ18−2ζ2+2ζ6−2ζ14+2ζ182ζ2+2ζ6−2ζ14−2ζ18−2ζ2−2ζ6+2ζ14+2ζ180000000000000000000000000000000000000000000
χ628-88-8000000-2-22200000−2525−2ζ2−2ζ6+2ζ14+2ζ182ζ2+2ζ6−2ζ14−2ζ182ζ2−2ζ6+2ζ14−2ζ18−2ζ2+2ζ6−2ζ14+2ζ180000000000000000000000000000000000000000000
χ638-88-8000000-2-22200000−25252ζ2+2ζ6−2ζ14−2ζ18−2ζ2−2ζ6+2ζ14+2ζ18−2ζ2+2ζ6−2ζ14+2ζ182ζ2−2ζ6+2ζ14−2ζ180000000000000000000000000000000000000000000
χ648-8-888-808i−8i0-222-200000000000−2i−2i2i2i-220000000000000000000000000000000000000
χ658-8-888-80−8i8i0-222-2000000000002i2i−2i−2i-220000000000000000000000000000000000000
χ668-8-88-880000-222-2000000000002i5−2i5−2i52i52-20000000000000000000000000000000000000
χ678-8-88-880000-222-200000000000−2i52i52i5−2i52-20000000000000000000000000000000000000
χ681616-16-16000000-44-44000000000000000000000000000000000000000000000000000000

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