Finite Group Databasebeta

← Group #13020497

Character table — Group #13020497

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size11112244444444448888101010101010161616161616161616161616161616204040404040404040404040408080808080
order12222244510101010101010244444444441010202020202020202020202020422248888888848888
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
χ511111111111111111-1-11111111-1111111-1-1-1-1-1-1-1-111-1-1111111111-1-1-1-1-1
χ611111111111111111-1-11111111-1111111-1-1-1-1-1-1-1-111-1-11-1-1-1-1-1-1-1-1-11111
χ711111111111111111-1-11-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1iiii−i−i−i−i1−i−iii
χ811111111111111111-1-11-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1−i−i−i−iiiii1ii−i−i
χ91111111111111111-111-1111111-1-1-111-1-1-1-1-1-111111-111-111-1-111-1-1-11-11-1
χ101111111111111111-111-1111111-1-1-111-1-1-1-1-1-111111-111-1-1-111-1-111-1-11-11
χ111111111111111111-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-11-1-11ii−i−i−i−iii1i−i−ii
χ121111111111111111-111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-11-1-11−i−iiiii−i−i1−iii−i
χ131111111111111111-1-1-1-11111111-1-111-1-11111-1-1-1-11-1-1-1-111-1-111-1-11-11-11
χ141111111111111111-1-1-1-11111111-1-111-1-11111-1-1-1-11-1-1-1-1-1-111-1-11111-11-1
χ151111111111111111-1-1-1-1-1-1-1-1-1-11-1-111-1-11111-1-1-1-1-11111ii−i−i−i−iii-1−iii−i
χ161111111111111111-1-1-1-1-1-1-1-1-1-11-1-111-1-11111-1-1-1-1-11111−i−iiiii−i−i-1i−i−ii
χ17222222-2-222222222200-22222-2-2022-2-2-2-200000000-2200-20000000000000
χ18222222-2-222222222200-2-2-2-2-222022-2-2-2-2000000002-20020000000000000
χ19222222-2-222222222-20022222-2-20-2-2-2-22200000000-2-20020000000000000
χ20222222-2-222222222-2002-2-2-2-2220-2-2-2-222000000002200-20000000000000
χ212222-2-22-22-2-222-2-2200002-22-2220002-20000000000-20000002-2002-200000
χ222222-2-22-22-2-222-2-2200002-22-2220002-20000000000-2000000-2200-2200000
χ232222-2-22-22-2-222-2-220000-22-22-2-20002-2000000000020000002i−2i00−2i2i00000
χ242222-2-22-22-2-222-2-220000-22-22-2-20002-200000000002000000−2i2i002i−2i00000
χ252222-2-2-222-2-222-2-2200002-22-2-2-2000-220000000000200002i−2i002i−2i0000000
χ262222-2-2-222-2-222-2-2200002-22-2-2-2000-22000000000020000−2i2i00−2i2i0000000
χ272222-2-2-222-2-222-2-220000-22-2222000-220000000000-200002-200-220000000
χ282222-2-2-222-2-222-2-220000-22-2222000-220000000000-20000-22002-20000000
χ2944444444-1-1-1-1-1-1-1-144440000004-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000
χ3044444444-1-1-1-1-1-1-1-14-4-44000000-4-1-1-1-1-1-111111111000000000000000000
χ3144444444-1-1-1-1-1-1-1-1-444-4000000-411-1-1111111-1-1-1-1000000000000000000
χ3244444444-1-1-1-1-1-1-1-1-4-4-4-4000000411-1-111-1-1-1-11111000000000000000000
χ33444444-4-4-1-1-1-1-1-1-1-1400-40000000-1-1111155−5−555−5−5000000000000000000
χ34444444-4-4-1-1-1-1-1-1-1-1400-40000000-1-11111−5−555−5−555000000000000000000
χ35444444-4-4-1-1-1-1-1-1-1-1-400400000001111-1-155−5−5−5−555000000000000000000
χ36444444-4-4-1-1-1-1-1-1-1-1-400400000001111-1-1−5−55555−5−5000000000000000000
χ3744-4-400004004-400-402i−2i000004i−4i000000000002i−2i2i−2i002-200000000000000
χ3844-4-400004004-400-402i−2i00000−4i4i000000000002i−2i2i−2i00-2200000000000000
χ3944-4-400004004-400-40−2i2i000004i−4i00000000000−2i2i−2i2i00-2200000000000000
χ4044-4-400004004-400-40−2i2i00000−4i4i00000000000−2i2i−2i2i002-200000000000000
χ414-44-44-400444-4-4-4-44000044-4-400000000000000000000000000000000000
χ424-44-44-400444-4-4-4-440000-4-44400000000000000000000000000000000000
χ434-44-4-44004-4-4-4-444400004-4-4400000000000000000000000000000000000
χ444-44-4-44004-4-4-4-44440000-444-400000000000000000000000000000000000
χ458888-8-88-8-222-2-222-20000000000000-220000000000000000000000000000
χ468888-8-8-88-222-2-222-200000000000002-20000000000000000000000000000
χ4788-8-80000-225−25-2225−25204i−4i000000000000000000−2ζ11−2ζ192ζ11+2ζ19−2ζ3−2ζ72ζ3+2ζ7000000000000000000
χ4888-8-80000-225−25-2225−2520−4i4i0000000000000000002ζ11+2ζ19−2ζ11−2ζ192ζ3+2ζ7−2ζ3−2ζ7000000000000000000
χ4988-8-80000-2−2525-22−2525204i−4i000000000000000000−2ζ3−2ζ72ζ3+2ζ7−2ζ11−2ζ192ζ11+2ζ19000000000000000000
χ5088-8-80000-2−2525-22−252520−4i4i0000000000000000002ζ3+2ζ7−2ζ3−2ζ72ζ11+2ζ19−2ζ11−2ζ19000000000000000000
χ518-88-88-800-2-2-22222-20000000000000002i5−2i500000000000000000000000000
χ528-88-88-800-2-2-22222-2000000000000000−2i52i500000000000000000000000000
χ538-88-8-8800-22222-2-2-20000000000025−25000000000000000000000000000000
χ548-88-8-8800-22222-2-2-200000000000−2525000000000000000000000000000000
χ558-8-880000800-8800-80000000000000000000000000000000000000000000
χ568-8-880000-225−252-2−25252000000000000000002ζ3−2ζ7−2ζ3+2ζ7−2ζ11+2ζ192ζ11−2ζ190000000000000000000000
χ578-8-880000-225−252-2−2525200000000000000000−2ζ3+2ζ72ζ3−2ζ72ζ11−2ζ19−2ζ11+2ζ190000000000000000000000
χ588-8-880000-2−25252-225−25200000000000000000−2ζ11+2ζ192ζ11−2ζ19−2ζ3+2ζ72ζ3−2ζ70000000000000000000000
χ598-8-880000-2−25252-225−252000000000000000002ζ11−2ζ19−2ζ11+2ζ192ζ3−2ζ7−2ζ3+2ζ70000000000000000000000

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