Finite Group Databasebeta

← Group #13026185

Character table — Group #13026185

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size112224444444444448888888888888888816161616161616162020202020202020404040408080808080808080
order12244244451010101010101044444202020202020202020202020202020202020202022224444244444448888
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
χ511111111111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-111ii−i−i−i−iii
χ611111111111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-111−i−iiiii−i−i
χ711111111111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-11111-1-1-1-1
χ811111111111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-11111
χ91111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-11-11-11-11-1
χ101111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-11-11-11-11
χ111111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111i−i−iii−i−ii
χ121111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111−iii−i−iii−i
χ131111111-1-111111111-1-111-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-111-1-1i−i−ii−iii−i
χ141111111-1-111111111-1-111-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-111-1-1−iii−ii−i−ii
χ151111111-1-111111111-1-111-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-111-1-1111-11-1-11-11
χ161111111-1-111111111-1-111-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-111-1-111-11-111-11-1
χ1722222-2-2002-2-2-2-22222-20000000000022-2-222-2-20000222-2-2-22-2000000000000
χ1822222-2-2002-2-2-2-22222-20000000000022-2-222-2-20000-2-2-2222-22000000000000
χ1922222-2-2002-2-2-2-2222-220000000000022-2-2-2-222000022-22-2-2-22000000000000
χ2022222-2-2002-2-2-2-2222-220000000000022-2-2-2-2220000-2-22-2222-2000000000000
χ21222-2-22-20022222222002-2000000000-2-2-2-2000022-2-2002-200-22002-200000000
χ22222-2-22-20022222222002-2000000000-2-2-2-2000022-2-200-22002-200-2200000000
χ23222-2-22-2002222222200-22000000000-2-2-2-20000-2-222002-200-2200-2200000000
χ24222-2-22-2002222222200-22000000000-2-2-2-20000-2-22200-22002-2002-200000000
χ25222-2-2-22222-2-2-2-22220000-22222-2-2-2-2-2-22200000000002200-2-22-20000000000
χ26222-2-2-22222-2-2-2-22220000-22222-2-2-2-2-2-2220000000000-2-20022-220000000000
χ27222-2-2-22-2-22-2-2-2-222200002-2-2-2-22222-2-22200000000002200-2-2-220000000000
χ28222-2-2-22-2-22-2-2-2-222200002-2-2-2-22222-2-2220000000000-2-200222-20000000000
χ29444444444-1-1-1-1-1-1-1-144444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000
χ30444444444-1-1-1-1-1-1-1-1-4-4-4-44-1-1-1-1-1-1-1-1-1-1-1-11111111100000000000000000000
χ314444444-4-4-1-1-1-1-1-1-1-144-4-4-411111111-1-1-1-1-1-1-1-1111100000000000000000000
χ324444444-4-4-1-1-1-1-1-1-1-1-4-444-411111111-1-1-1-11111-1-1-1-100000000000000000000
χ3344444-4-400-11111-1-1-14-400055−5−555−5−5-1-111-1-1115−55−500000000000000000000
χ3444444-4-400-11111-1-1-14-4000−5−555−5−555-1-111-1-111−55−5500000000000000000000
χ3544444-4-400-11111-1-1-1-4400055−5−555−5−5-1-11111-1-1−55−5500000000000000000000
χ3644444-4-400-11111-1-1-1-44000−5−555−5−555-1-11111-1-15−55−500000000000000000000
χ37444-4-44-400-1-1-1-1-1-1-1-1004-4055−5−5−5−55511115−55−5-1-11100000000000000000000
χ38444-4-44-400-1-1-1-1-1-1-1-1004-40−5−55555−5−51111−55−55-1-11100000000000000000000
χ39444-4-44-400-1-1-1-1-1-1-1-100-44055−5−5−5−5551111−55−5511-1-100000000000000000000
χ40444-4-44-400-1-1-1-1-1-1-1-100-440−5−55555−5−511115−55−511-1-100000000000000000000
χ41444-4-4-4444-11111-1-1-10000-4-1-1-1-1111111-1-15−5−555−5−5500000000000000000000
χ42444-4-4-4444-11111-1-1-10000-4-1-1-1-1111111-1-1−555−5−555−500000000000000000000
χ43444-4-4-44-4-4-11111-1-1-1000041111-1-1-1-111-1-15−5−55−555−500000000000000000000
χ44444-4-4-44-4-4-11111-1-1-1000041111-1-1-1-111-1-1−555−55−5−5500000000000000000000
χ4544-44-4000040000-4-4400000000000004-4000000000000004-400000000000000
χ4644-44-4000040000-4-4400000000000004-400000000000000-4400000000000000
χ4744-4-44000040000-4-440000000000000-4400000000004-4000000000000000000
χ4844-4-44000040000-4-440000000000000-440000000000-44000000000000000000
χ4988-88-80000-22525−25−2522-20000000000000-2225−250000000000000000000000000000
χ5088-88-80000-2−25−25252522-20000000000000-22−25250000000000000000000000000000
χ5188-8-880000-22525−25−2522-200000000000002-2−25250000000000000000000000000000
χ5288-8-880000-2−25−25252522-200000000000002-225−250000000000000000000000000000
χ538-8000004-48000000-8000004-44-4000000000000000000000000000000000000
χ548-8000004-4-2−2ζ2+2ζ6−2ζ14+2ζ182ζ2−2ζ6+2ζ14−2ζ18−2ζ2−2ζ6+2ζ14+2ζ182ζ2+2ζ6−2ζ14−2ζ1825−25200000−1+51−5−1−51+5−2ζ2+2ζ182ζ2−2ζ182ζ6−2ζ14−2ζ6+2ζ1400000000000000000000000000000000
χ558-8000004-4-2−2ζ2−2ζ6+2ζ14+2ζ182ζ2+2ζ6−2ζ14−2ζ182ζ2−2ζ6+2ζ14−2ζ18−2ζ2+2ζ6−2ζ14+2ζ18−2525200000−1−51+5−1+51−5−2ζ6+2ζ142ζ6−2ζ14−2ζ2+2ζ182ζ2−2ζ1800000000000000000000000000000000
χ568-8000004-4-22ζ2−2ζ6+2ζ14−2ζ18−2ζ2+2ζ6−2ζ14+2ζ182ζ2+2ζ6−2ζ14−2ζ18−2ζ2−2ζ6+2ζ14+2ζ1825−25200000−1+51−5−1−51+52ζ2−2ζ18−2ζ2+2ζ18−2ζ6+2ζ142ζ6−2ζ1400000000000000000000000000000000
χ578-8000004-4-22ζ2+2ζ6−2ζ14−2ζ18−2ζ2−2ζ6+2ζ14+2ζ18−2ζ2+2ζ6−2ζ14+2ζ182ζ2−2ζ6+2ζ14−2ζ18−2525200000−1−51+5−1+51−52ζ6−2ζ14−2ζ6+2ζ142ζ2−2ζ18−2ζ2+2ζ1800000000000000000000000000000000
χ588-800000-448000000-800000-44-44000000000000000000000000000000000000
χ598-800000-44-2−2ζ2+2ζ6−2ζ14+2ζ182ζ2−2ζ6+2ζ14−2ζ18−2ζ2−2ζ6+2ζ14+2ζ182ζ2+2ζ6−2ζ14−2ζ1825−252000001−5−1+51+5−1−52ζ2−2ζ18−2ζ2+2ζ18−2ζ6+2ζ142ζ6−2ζ1400000000000000000000000000000000
χ608-800000-44-2−2ζ2−2ζ6+2ζ14+2ζ182ζ2+2ζ6−2ζ14−2ζ182ζ2−2ζ6+2ζ14−2ζ18−2ζ2+2ζ6−2ζ14+2ζ18−25252000001+5−1−51−5−1+52ζ6−2ζ14−2ζ6+2ζ142ζ2−2ζ18−2ζ2+2ζ1800000000000000000000000000000000
χ618-800000-44-22ζ2−2ζ6+2ζ14−2ζ18−2ζ2+2ζ6−2ζ14+2ζ182ζ2+2ζ6−2ζ14−2ζ18−2ζ2−2ζ6+2ζ14+2ζ1825−252000001−5−1+51+5−1−5−2ζ2+2ζ182ζ2−2ζ182ζ6−2ζ14−2ζ6+2ζ1400000000000000000000000000000000
χ628-800000-44-22ζ2+2ζ6−2ζ14−2ζ18−2ζ2−2ζ6+2ζ14+2ζ18−2ζ2+2ζ6−2ζ14+2ζ182ζ2−2ζ6+2ζ14−2ζ18−25252000001+5−1−51−5−1+5−2ζ6+2ζ142ζ6−2ζ14−2ζ2+2ζ182ζ2−2ζ1800000000000000000000000000000000

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