Finite Group Databasebeta

← Group #13020513

Character table — Group #13020513

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size11112244444444448888101010101010161616161616161616161616161616204040404040404040404040408080808080
order12222244510101010101010224444444441010101020202020202020202020424448888888848888
χ111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1
χ311111111111111111111-1-1-1-1-1-1111111111111111-1-1-1-1-1iiii−i−i−i−i-1ii−i−i
χ411111111111111111111-1-1-1-1-1-1111111111111111-1-1-1-1-1−i−i−i−iiiii-1−i−iii
χ5111111111111111111-1-1111111-11111-1-1-1-1-1-111-1-11-111-111-1-111-1-1-11-11-1
χ6111111111111111111-1-1111111-11111-1-1-1-1-1-111-1-11-111-1-1-111-1-111-1-11-11
χ7111111111111111111-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-11-1-11ii−i−i−i−iii1i−i−ii
χ8111111111111111111-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-11-1-11−i−iiiii−i−i1−iii−i
χ91111111111111111-1-111111111-1-1-1-1-111-1-1-1-1111111-1-1111111111-1-1-1-1-1
χ101111111111111111-1-111111111-1-1-1-1-111-1-1-1-1111111-1-11-1-1-1-1-1-1-1-1-11111
χ111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-1iiii−i−i−i−i1−i−iii
χ121111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-111-1−i−i−i−iiiii1ii−i−i
χ131111111111111111-1-1-1-11111111-1-1-1-1-1-1111111-1-11-1-1-1-111-1-111-1-11-11-11
χ141111111111111111-1-1-1-11111111-1-1-1-1-1-1111111-1-11-1-1-1-1-1-111-1-11111-11-1
χ151111111111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1111111-1-1-11111ii−i−i−i−iii-1−iii−i
χ161111111111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-1111111-1-1-11111−i−iiiii−i−i-1i−i−ii
χ17222222-2-222222222002-22222-2-200000-2-20000-2-222-2200-20000000000000
χ18222222-2-222222222002-2-2-2-2-22200000-2-20000-2-2222-20020000000000000
χ19222222-2-22222222200-222222-2-200000220000-2-2-2-2-2-20020000000000000
χ20222222-2-22222222200-22-2-2-2-22200000220000-2-2-2-22200-20000000000000
χ212222-2-22-222-2-22-2-22000022-2-222000000000002-200-20000002-2002-200000
χ222222-2-22-222-2-22-2-22000022-2-222000000000002-200-2000000-2200-2200000
χ232222-2-22-222-2-22-2-220000-2-222-2-2000000000002-20020000002i−2i00−2i2i00000
χ242222-2-22-222-2-22-2-220000-2-222-2-2000000000002-2002000000−2i2i002i−2i00000
χ252222-2-2-2222-2-22-2-22000022-2-2-2-200000000000-2200200002i−2i002i−2i0000000
χ262222-2-2-2222-2-22-2-22000022-2-2-2-200000000000-220020000−2i2i00−2i2i0000000
χ272222-2-2-2222-2-22-2-220000-2-2222200000000000-2200-200002-200-220000000
χ282222-2-2-2222-2-22-2-220000-2-2222200000000000-2200-20000-22002-20000000
χ2944444444-1-1-1-1-1-1-1-144440000004-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000
χ3044444444-1-1-1-1-1-1-1-144-4-4000000-4-1-1-1-1111111-1-111000000000000000000
χ3144444444-1-1-1-1-1-1-1-1-4-444000000-41111-1-11111-1-1-1-1000000000000000000
χ3244444444-1-1-1-1-1-1-1-1-4-4-4-40000004111111-1-1-1-1-1-111000000000000000000
χ33444444-4-4-1-1-1-1-1-1-1-1004-4000000055−5−51155−5−511-1-1000000000000000000
χ34444444-4-4-1-1-1-1-1-1-1-1004-40000000−5−55511−5−55511-1-1000000000000000000
χ35444444-4-4-1-1-1-1-1-1-1-100-44000000055−5−5-1-1−5−5551111000000000000000000
χ36444444-4-4-1-1-1-1-1-1-1-100-440000000−5−555-1-155−5−51111000000000000000000
χ3744-4-400004-400-40042-20000004i−4i02-22-20000000000002i−2i00000000000000
χ3844-4-400004-400-40042-2000000−4i4i02-22-2000000000000−2i2i00000000000000
χ3944-4-400004-400-4004-220000004i−4i0-22-22000000000000−2i2i00000000000000
χ4044-4-400004-400-4004-22000000−4i4i0-22-220000000000002i−2i00000000000000
χ414-44-44-4004-4-4-4444-400004i−4i4i−4i00000000000000000000000000000000000
χ424-44-44-4004-4-4-4444-40000−4i4i−4i4i00000000000000000000000000000000000
χ434-44-4-44004-4444-4-4-400004i−4i−4i4i00000000000000000000000000000000000
χ444-44-4-44004-4444-4-4-40000−4i4i4i−4i00000000000000000000000000000000000
χ458888-8-88-8-2-222-222-2000000000000000000000-2200000000000000000000
χ468888-8-8-88-2-222-222-20000000000000000000002-200000000000000000000
χ4788-8-80000-2225−25225−25-24-4000000000−1+51−5−1−51+50000000000000000000000000000
χ4888-8-80000-2225−25225−25-2-440000000001−5−1+51+5−1−50000000000000000000000000000
χ4988-8-80000-22−25252−2525-24-4000000000−1−51+5−1+51−50000000000000000000000000000
χ5088-8-80000-22−25252−2525-2-440000000001+5−1−51−5−1+50000000000000000000000000000
χ518-88-88-800-2222-2-2-2200000000000000025−2500000000000000000000000000
χ528-88-88-800-2222-2-2-22000000000000000−252500000000000000000000000000
χ538-88-8-8800-22-2-2-2222000000000000000000000002i5−2i5000000000000000000
χ548-88-8-8800-22-2-2-222200000000000000000000000−2i52i5000000000000000000
χ558-8-8800008800-800-80000000000000000000000000000000000000000000
χ568-8-880000-2-225−252−2525200000000000000000−2ζ11+2ζ192ζ11−2ζ192ζ3−2ζ7−2ζ3+2ζ70000000000000000000000
χ578-8-880000-2-225−252−25252000000000000000002ζ11−2ζ19−2ζ11+2ζ19−2ζ3+2ζ72ζ3−2ζ70000000000000000000000
χ588-8-880000-2-2−2525225−252000000000000000002ζ3−2ζ7−2ζ3+2ζ72ζ11−2ζ19−2ζ11+2ζ190000000000000000000000
χ598-8-880000-2-2−2525225−25200000000000000000−2ζ3+2ζ72ζ3−2ζ7−2ζ11+2ζ192ζ11−2ζ190000000000000000000000

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