Finite Group Databasebeta

← Group #13018007

Character table — Group #13018007

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size111122444444444488888888888888888816161616161616162020202020202020404040408080808080808080
order12222244510101010101010222444101010102020202020202020101010102020202044444444444488888888
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii
χ5111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111ii−i−iii−i−i
χ6111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-111−i−iii−i−iii
χ7111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-111
χ8111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1
χ91111111111111111-1-111-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11-11-11-11-1
χ101111111111111111-1-111-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-11-11-11-11
χ111111111111111111-1-111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111i−ii−i−ii−ii
χ121111111111111111-1-111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−ii−iii−ii−i
χ131111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1i−i−iii−i−ii
χ141111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-111-1-1−iii−i−iii−i
χ151111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1111-1-11-111-1
χ161111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-111-11-1-11
χ17222222-2-222222222002-2002222-2-2-2-2-2-2-2-20000000022-2-2-2-222000000000000
χ18222222-2-222222222002-2002222-2-2-2-2-2-2-2-200000000-2-22222-2-2000000000000
χ19222222-2-22222222200-2200-2-2-2-2-2-2-2-222220000000022-2-222-2-2000000000000
χ20222222-2-22222222200-2200-2-2-2-2-2-2-2-2222200000000-2-222-2-222000000000000
χ212222-2-22-222-2-2-2-22200002-2000022-2-20000000022-2-200002-22-2002-200000000
χ222222-2-22-222-2-2-2-22200002-2000022-2-20000000022-2-20000-22-2200-2200000000
χ232222-2-22-222-2-2-2-2220000-22000022-2-200000000-2-22200002-22-200-2200000000
χ242222-2-22-222-2-2-2-2220000-22000022-2-200000000-2-2220000-22-22002-200000000
χ252222-2-2-2222-2-2-2-2222-200000000-2-222000022-2-2000000002-2-222-20000000000
χ262222-2-2-2222-2-2-2-2222-200000000-2-222000022-2-200000000-222-2-220000000000
χ272222-2-2-2222-2-2-2-222-2200000000-2-2220000-2-222000000002-2-22-220000000000
χ282222-2-2-2222-2-2-2-222-2200000000-2-2220000-2-22200000000-222-22-20000000000
χ2944444444-1-1-1-1-1-1-1-1444444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000
χ3044444444-1-1-1-1-1-1-1-144-4-4-4-41111-1-1-1-11111-1-1-1-1111100000000000000000000
χ3144444444-1-1-1-1-1-1-1-1-4-444-4-4-1-1-1-1-1-1-1-1-1-1-1-11111111100000000000000000000
χ3244444444-1-1-1-1-1-1-1-1-4-4-4-4441111-1-1-1-111111111-1-1-1-100000000000000000000
χ33444444-4-4-1-1-1-1-1-1-1-1004-400-1-1-1-1111111115−55−55−55−500000000000000000000
χ34444444-4-4-1-1-1-1-1-1-1-1004-400-1-1-1-111111111−55−55−55−5500000000000000000000
χ35444444-4-4-1-1-1-1-1-1-1-100-440011111111-1-1-1-15−55−5−55−5500000000000000000000
χ36444444-4-4-1-1-1-1-1-1-1-100-440011111111-1-1-1-1−55−555−55−500000000000000000000
χ374444-4-44-4-1-11111-1-100004-455−5−5-1-11155−5−55−5−55-1-11100000000000000000000
χ384444-4-44-4-1-11111-1-100004-4−5−555-1-111−5−555−555−5-1-11100000000000000000000
χ394444-4-44-4-1-11111-1-10000-4455−5−5-1-11155−5−5−555−511-1-100000000000000000000
χ404444-4-44-4-1-11111-1-10000-44−5−555-1-111−5−5555−5−5511-1-100000000000000000000
χ414444-4-4-44-1-11111-1-14-4000055−5−511-1-1−5−555-1-1115−5−5500000000000000000000
χ424444-4-4-44-1-11111-1-14-40000−5−55511-1-155−5−5-1-111−555−500000000000000000000
χ434444-4-4-44-1-11111-1-1-44000055−5−511-1-1−5−55511-1-1−555−500000000000000000000
χ444444-4-4-44-1-11111-1-1-440000−5−55511-1-155−5−511-1-15−5−5500000000000000000000
χ454-44-44-4004-444-4-44-400000000000000000000000000004i−4i0000000000000000
χ464-44-44-4004-444-4-44-40000000000000000000000000000−4i4i0000000000000000
χ474-44-4-44004-4-4-4444-4000000000000000000000000004i−4i000000000000000000
χ484-44-4-44004-4-4-4444-400000000000000000000000000−4i4i000000000000000000
χ4988-8-80000880000-8-80000000000000000000000000000000000000000000000
χ5088-8-80000-2-225−2525−252200000000000000−2ζ3+2ζ7−2ζ11+2ζ192ζ3−2ζ7+2ζ11−2ζ192ζ3−2ζ7−2ζ11+2ζ19−2ζ3+2ζ7+2ζ11−2ζ190000000000000000000000000000
χ5188-8-80000-2-225−2525−2522000000000000002ζ3−2ζ7+2ζ11−2ζ19−2ζ3+2ζ7−2ζ11+2ζ19−2ζ3+2ζ7+2ζ11−2ζ192ζ3−2ζ7−2ζ11+2ζ190000000000000000000000000000
χ5288-8-80000-2-2−2525−252522000000000000002ζ3−2ζ7−2ζ11+2ζ19−2ζ3+2ζ7+2ζ11−2ζ192ζ3−2ζ7+2ζ11−2ζ19−2ζ3+2ζ7−2ζ11+2ζ190000000000000000000000000000
χ5388-8-80000-2-2−2525−25252200000000000000−2ζ3+2ζ7+2ζ11−2ζ192ζ3−2ζ7−2ζ11+2ζ19−2ζ3+2ζ7−2ζ11+2ζ192ζ3−2ζ7+2ζ11−2ζ190000000000000000000000000000
χ548-88-88-800-22-2-222-22000000000025−2525−2500000000000000000000000000000000
χ558-88-88-800-22-2-222-220000000000−2525−252500000000000000000000000000000000
χ568-88-8-8800-2222-2-2-22000000000025−25−252500000000000000000000000000000000
χ578-88-8-8800-2222-2-2-220000000000−252525−2500000000000000000000000000000000
χ588-8-8800008-80000-880000000000000000000000000000000000000000000000
χ598-8-880000-2225−25−25252-2000000−2ζ2−2ζ6+2ζ14+2ζ182ζ2+2ζ6−2ζ14−2ζ18−2ζ2+2ζ6−2ζ14+2ζ182ζ2−2ζ6+2ζ14−2ζ18000000000000000000000000000000000000
χ608-8-880000-2225−25−25252-20000002ζ2+2ζ6−2ζ14−2ζ18−2ζ2−2ζ6+2ζ14+2ζ182ζ2−2ζ6+2ζ14−2ζ18−2ζ2+2ζ6−2ζ14+2ζ18000000000000000000000000000000000000
χ618-8-880000-22−252525−252-2000000−2ζ2+2ζ6−2ζ14+2ζ182ζ2−2ζ6+2ζ14−2ζ182ζ2+2ζ6−2ζ14−2ζ18−2ζ2−2ζ6+2ζ14+2ζ18000000000000000000000000000000000000
χ628-8-880000-22−252525−252-20000002ζ2−2ζ6+2ζ14−2ζ18−2ζ2+2ζ6−2ζ14+2ζ18−2ζ2−2ζ6+2ζ14+2ζ182ζ2+2ζ6−2ζ14−2ζ18000000000000000000000000000000000000

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