Finite Group Databasebeta

← Group #13020331

Character table — Group #13020331

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size11112244444444448888101010101010161616161616161616161616161616204040404040404040404040408080808080
order12222244510101010101010444422444421010101020202020202020202020244444444444448888
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
χ5111111111111111111-1-1111111-1-1-1-1-111-1-1-1-11111111-1-111111111-1-1-1-1-1
χ6111111111111111111-1-1111111-1-1-1-1-111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-11111
χ7111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-111iiii−i−i−i−i1−i−iii
χ8111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-111−i−i−i−iiiii1ii−i−i
χ91111111111111111-1-111111111-1-1-1-1-1-1-1111111-1-11-1-11111-1-111-1-1-11-11-1
χ101111111111111111-1-111111111-1-1-1-1-1-1-1111111-1-11-1-111-1-111-1-111-1-11-11
χ111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-111-1-1ii−i−i−i−iii1i−i−ii
χ121111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-111-1-1−i−iiiii−i−i1−iii−i
χ131111111111111111-1-1-1-111111111111-1-1-1-1-1-111-1-11-1-1-1-111-1-111-1-11-11-11
χ141111111111111111-1-1-1-111111111111-1-1-1-1-1-111-1-11-1-1-1-1-1-111-1-11111-11-1
χ151111111111111111-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-111-1-1-11111ii−i−i−i−iii-1−iii−i
χ161111111111111111-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-111-1-1-11111−i−iiiii−i−i-1i−i−ii
χ17222222-2-2222222222-20022-2-2-2-200000220000-2-2-2-222-2000000000000000
χ18222222-2-2222222222-200-2-2222200000220000-2-2-2-2-2-22000000000000000
χ19222222-2-222222222-220022-2-2-2-200000-2-20000-2-2222-22000000000000000
χ20222222-2-222222222-2200-2-2222200000-2-20000-2-222-22-2000000000000000
χ212222-2-22-222-2-22-2-2200002222-2-2000000000002-200-20000002-2002-200000
χ222222-2-22-222-2-22-2-2200002222-2-2000000000002-200-2000000-2200-2200000
χ232222-2-22-222-2-22-2-220000-2-2-2-222000000000002-20020000002i−2i00−2i2i00000
χ242222-2-22-222-2-22-2-220000-2-2-2-222000000000002-2002000000−2i2i002i−2i00000
χ252222-2-2-2222-2-22-2-22000022-2-22200000000000-2200-200002-2002-20000000
χ262222-2-2-2222-2-22-2-22000022-2-22200000000000-2200-20000-2200-220000000
χ272222-2-2-2222-2-22-2-220000-2-222-2-200000000000-2200200002i−2i00−2i2i0000000
χ282222-2-2-2222-2-22-2-220000-2-222-2-200000000000-220020000−2i2i002i−2i0000000
χ2944444444-1-1-1-1-1-1-1-144440000004-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000
χ3044444444-1-1-1-1-1-1-1-144-4-4000000-41111-1-11111-1-1-1-1000000000000000000
χ3144444444-1-1-1-1-1-1-1-1-4-444000000-4111111-1-1-1-1-1-111000000000000000000
χ3244444444-1-1-1-1-1-1-1-1-4-4-4-40000004-1-1-1-1111111-1-111000000000000000000
χ33444444-4-4-1-1-1-1-1-1-1-14-400000000055−5−5-1-155−5−51111000000000000000000
χ34444444-4-4-1-1-1-1-1-1-1-14-4000000000−5−555-1-1−5−5551111000000000000000000
χ35444444-4-4-1-1-1-1-1-1-1-1-4400000000055−5−511−5−55511-1-1000000000000000000
χ36444444-4-4-1-1-1-1-1-1-1-1-44000000000−5−5551155−5−511-1-1000000000000000000
χ3744-4-44-4004-4-4-4444-40000004i−4i4i−4i000000000000000000000000000000000
χ3844-4-44-4004-4-4-4444-4000000−4i4i−4i4i000000000000000000000000000000000
χ3944-4-4-44004-4444-4-4-40000004i−4i−4i4i000000000000000000000000000000000
χ4044-4-4-44004-4444-4-4-4000000−4i4i4i−4i000000000000000000000000000000000
χ414-44-400004400-400-4002i−2i4-4000000000002i−2i2i−2i00000002i−2i0000000000000
χ424-44-400004400-400-4002i−2i-44000000000002i−2i2i−2i0000000−2i2i0000000000000
χ434-44-400004400-400-400−2i2i4-400000000000−2i2i−2i2i0000000−2i2i0000000000000
χ444-44-400004400-400-400−2i2i-4400000000000−2i2i−2i2i00000002i−2i0000000000000
χ458888-8-88-8-2-222-222-2000000000000000000000-2200000000000000000000
χ468888-8-8-88-2-222-222-20000000000000000000002-200000000000000000000
χ4788-8-88-800-2222-2-2-2200000000000000025−2500000000000000000000000000
χ4888-8-88-800-2222-2-2-22000000000000000−252500000000000000000000000000
χ4988-8-8-8800-22-2-2-2222000000000000000000000002i5−2i5000000000000000000
χ5088-8-8-8800-22-2-2-222200000000000000000000000−2i52i5000000000000000000
χ518-88-80000-2-225−25225−252004i−4i0000000000000−2ζ3−2ζ72ζ3+2ζ7−2ζ11−2ζ192ζ11+2ζ190000000000000000000000
χ528-88-80000-2-225−25225−25200−4i4i00000000000002ζ3+2ζ7−2ζ3−2ζ72ζ11+2ζ19−2ζ11−2ζ190000000000000000000000
χ538-88-80000-2-2−25252−25252004i−4i0000000000000−2ζ11−2ζ192ζ11+2ζ19−2ζ3−2ζ72ζ3+2ζ70000000000000000000000
χ548-88-80000-2-2−25252−2525200−4i4i00000000000002ζ11+2ζ19−2ζ11−2ζ192ζ3+2ζ7−2ζ3−2ζ70000000000000000000000
χ558-8-8800008-800-80080000000000000000000000000000000000000000000
χ568-8-880000-2225−252−2525-2000000000002ζ6−2ζ14−2ζ6+2ζ14−2ζ2+2ζ182ζ2−2ζ180000000000000000000000000000
χ578-8-880000-2225−252−2525-200000000000−2ζ6+2ζ142ζ6−2ζ142ζ2−2ζ18−2ζ2+2ζ180000000000000000000000000000
χ588-8-880000-22−2525225−25-200000000000−2ζ2+2ζ182ζ2−2ζ18−2ζ6+2ζ142ζ6−2ζ140000000000000000000000000000
χ598-8-880000-22−2525225−25-2000000000002ζ2−2ζ18−2ζ2+2ζ182ζ6−2ζ14−2ζ6+2ζ140000000000000000000000000000

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