Finite Group Databasebeta

← Group #13017993

Character table — Group #13017993

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size111122444444444488888888888888888816161616161616162020202020202020404040408080808080808080
order12222244510101010101010444444202020202020202020202020202020202020202022444444224444448888
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1ii−i−iii−i−i
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−iii−i−iii
χ5111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1
χ6111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ7111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111ii−i−i−i−iii
χ8111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−iiiii−i−i
χ91111111111111111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-1-11-11-11-11-1
χ101111111111111111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-11-11-11-11
χ111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111i−i−iii−i−ii
χ121111111111111111-1-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111−iii−i−iii−i
χ131111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1111-11-1-11-11
χ141111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-111-11-111-11-1
χ151111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-111-1-1i−i−ii−iii−i
χ161111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-111-1-1−iii−ii−i−ii
χ17222222-2-2222222222-20000-2-2-2-22222-2-2-2-20000000022-2-222-2-2000000000000
χ18222222-2-2222222222-20000-2-2-2-22222-2-2-2-200000000-2-222-2-222000000000000
χ19222222-2-222222222-220000-2-2-2-2-2-2-2-22222000000002222-2-2-2-2000000000000
χ20222222-2-222222222-220000-2-2-2-2-2-2-2-2222200000000-2-2-2-22222000000000000
χ212222-2-22-22-2-2-2-222200002-222-2-200000000000022-2-22-200002-2002-200000000
χ222222-2-22-22-2-2-2-222200002-222-2-200000000000022-2-2-220000-2200-2200000000
χ232222-2-22-22-2-2-2-22220000-2222-2-2000000000000-2-2222-200002-200-2200000000
χ242222-2-22-22-2-2-2-22220000-2222-2-2000000000000-2-222-220000-22002-200000000
χ252222-2-2-222-2-2-2-2222002-200-2-2220000000022-2-200002-20000-222-20000000000
χ262222-2-2-222-2-2-2-2222002-200-2-2220000000022-2-20000-2200002-2-220000000000
χ272222-2-2-222-2-2-2-222200-2200-2-22200000000-2-22200002-20000-22-220000000000
χ282222-2-2-222-2-2-2-222200-2200-2-22200000000-2-2220000-2200002-22-20000000000
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
χ3044444444-1-1-1-1-1-1-1-144-4-4-4-4-1-1-1-1-1-1-1-1-1-1-1-11111111100000000000000000000
χ3144444444-1-1-1-1-1-1-1-1-4-444-4-4-1-1-1-111111111-1-1-1-1111100000000000000000000
χ3244444444-1-1-1-1-1-1-1-1-4-4-4-444-1-1-1-1111111111111-1-1-1-100000000000000000000
χ33444444-4-4-1-1-1-1-1-1-1-14-400001111-1-1-1-111115−55−55−55−500000000000000000000
χ34444444-4-4-1-1-1-1-1-1-1-14-400001111-1-1-1-11111−55−55−55−5500000000000000000000
χ35444444-4-4-1-1-1-1-1-1-1-1-44000011111111-1-1-1-15−55−5−55−5500000000000000000000
χ36444444-4-4-1-1-1-1-1-1-1-1-44000011111111-1-1-1-1−55−555−55−500000000000000000000
χ374444-4-44-4-11111-1-1-100004-4-1-11155−5−555−5−55−5−55-1-11100000000000000000000
χ384444-4-44-4-11111-1-1-100004-4-1-111−5−555−5−555−555−5-1-11100000000000000000000
χ394444-4-44-4-11111-1-1-10000-44-1-11155−5−555−5−5−555−511-1-100000000000000000000
χ404444-4-44-4-11111-1-1-10000-44-1-111−5−555−5−5555−5−5511-1-100000000000000000000
χ414444-4-4-44-11111-1-1-1004-40011-1-155−5−5−5−555-1-1115−5−5500000000000000000000
χ424444-4-4-44-11111-1-1-1004-40011-1-1−5−55555−5−5-1-111−555−500000000000000000000
χ434444-4-4-44-11111-1-1-100-440011-1-155−5−5−5−55511-1-1−555−500000000000000000000
χ444444-4-4-44-11111-1-1-100-440011-1-1−5−55555−5−511-1-15−5−5500000000000000000000
χ454-4-444-400444-4-44-4-40000000000000000000000000000004i−4i00000000000000
χ464-4-444-400444-4-44-4-4000000000000000000000000000000−4i4i00000000000000
χ474-4-44-44004-4-4444-4-400000000000000000000000000004i−4i0000000000000000
χ484-4-44-44004-4-4444-4-40000000000000000000000000000−4i4i0000000000000000
χ4988-8-8000080000-88-80000000000000000000000000000000000000000000000
χ5088-8-80000-225−2525−252-220000000000−2ζ2+2ζ6−2ζ14+2ζ182ζ2−2ζ6+2ζ14−2ζ18−2ζ2−2ζ6+2ζ14+2ζ182ζ2+2ζ6−2ζ14−2ζ1800000000000000000000000000000000
χ5188-8-80000-225−2525−252-2200000000002ζ2−2ζ6+2ζ14−2ζ18−2ζ2+2ζ6−2ζ14+2ζ182ζ2+2ζ6−2ζ14−2ζ18−2ζ2−2ζ6+2ζ14+2ζ1800000000000000000000000000000000
χ5288-8-80000-2−2525−25252-220000000000−2ζ2−2ζ6+2ζ14+2ζ182ζ2+2ζ6−2ζ14−2ζ182ζ2−2ζ6+2ζ14−2ζ18−2ζ2+2ζ6−2ζ14+2ζ1800000000000000000000000000000000
χ5388-8-80000-2−2525−25252-2200000000002ζ2+2ζ6−2ζ14−2ζ18−2ζ2−2ζ6+2ζ14+2ζ18−2ζ2+2ζ6−2ζ14+2ζ182ζ2−2ζ6+2ζ14−2ζ1800000000000000000000000000000000
χ548-88-8000080000-8-880000000000000000000000000000000000000000000000
χ558-88-80000-225−25−252522-200000000000000−2ζ2+2ζ6−2ζ14+2ζ182ζ2−2ζ6+2ζ14−2ζ18−2ζ2−2ζ6+2ζ14+2ζ182ζ2+2ζ6−2ζ14−2ζ180000000000000000000000000000
χ568-88-80000-225−25−252522-2000000000000002ζ2−2ζ6+2ζ14−2ζ18−2ζ2+2ζ6−2ζ14+2ζ182ζ2+2ζ6−2ζ14−2ζ18−2ζ2−2ζ6+2ζ14+2ζ180000000000000000000000000000
χ578-88-80000-2−252525−2522-200000000000000−2ζ2−2ζ6+2ζ14+2ζ182ζ2+2ζ6−2ζ14−2ζ182ζ2−2ζ6+2ζ14−2ζ18−2ζ2+2ζ6−2ζ14+2ζ180000000000000000000000000000
χ588-88-80000-2−252525−2522-2000000000000002ζ2+2ζ6−2ζ14−2ζ18−2ζ2−2ζ6+2ζ14+2ζ18−2ζ2+2ζ6−2ζ14+2ζ182ζ2−2ζ6+2ζ14−2ζ180000000000000000000000000000
χ598-8-888-800-2-2-222-22200000025−2525−25000000000000000000000000000000000000
χ608-8-888-800-2-2-222-222000000−2525−2525000000000000000000000000000000000000
χ618-8-88-8800-222-2-2-22200000025−25−2525000000000000000000000000000000000000
χ628-8-88-8800-222-2-2-222000000−252525−25000000000000000000000000000000000000

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