Finite Group Databasebeta

← Group #13026141

Character table — Group #13026141

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size112224444444444448888888888888888816161616161616162020202020202020404040408080808080808080
order12222222251010101010101022444101010101010101010101010101020202020202022224444244444448888
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
χ91111111-1-111111111-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-111-1-1i−ii−ii−ii−i
χ101111111-1-111111111-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111-1-111-1-1−ii−ii−ii−ii
χ111111111-1-111111111-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111-1-1111-1-111-1-11
χ121111111-1-111111111-111-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111-1-111-111-1-111-1
χ131111111-1-111111111-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-111i−ii−i−ii−ii
χ141111111-1-111111111-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-111-1-1-1-111−ii−iii−ii−i
χ151111111-1-111111111-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-11111-1-11-1-11-111-1
χ161111111-1-111111111-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-11111-1-1-111-11-1-11
χ1722222-2-2222-2-2-2-2222-2000022-2-22222-2-2-2-2000000002222-2-2-2-2000000000000
χ1822222-2-2222-2-2-2-2222-2000022-2-22222-2-2-2-200000000-2-2-2-22222000000000000
χ1922222-2-2-2-22-2-2-2-22222000022-2-2-2-2-2-222220000000022-2-2-2-222000000000000
χ2022222-2-2-2-22-2-2-2-22222000022-2-2-2-2-2-2222200000000-2-22222-2-2000000000000
χ2122-2-222-2002222222202-200-2-2-2-20000000022-2-20000002-2002-2002-200000000
χ2222-2-222-2002222222202-200-2-2-2-20000000022-2-2000000-2200-2200-2200000000
χ2322-2-222-200222222220-2200-2-2-2-200000000-2-2220000002-2002-200-2200000000
χ2422-2-222-200222222220-2200-2-2-2-200000000-2-222000000-2200-22002-200000000
χ2522-2-22-22002-2-2-2-22220002-2-2-22200000000000022-2-2002-200-222-20000000000
χ2622-2-22-22002-2-2-2-22220002-2-2-22200000000000022-2-200-22002-2-220000000000
χ2722-2-22-22002-2-2-2-2222000-22-2-222000000000000-2-222002-200-22-220000000000
χ2822-2-22-22002-2-2-2-2222000-22-2-222000000000000-2-22200-22002-22-20000000000
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
χ30444444444-1-1-1-1-1-1-1-14-4-4-4-4-1-1-1-1-1-1-1-1-1-1-1-11111111100000000000000000000
χ314444444-4-4-1-1-1-1-1-1-1-1-444-4-4-1-1-1-111111111-1-1-1-1111100000000000000000000
χ324444444-4-4-1-1-1-1-1-1-1-1-4-4-444-1-1-1-1111111111111-1-1-1-100000000000000000000
χ3344444-4-444-11111-1-1-1-40000-1-111-1-1-1-111115−55−55−55−500000000000000000000
χ3444444-4-444-11111-1-1-1-40000-1-111-1-1-1-11111−55−55−55−5500000000000000000000
χ3544444-4-4-4-4-11111-1-1-140000-1-1111111-1-1-1-15−55−5−55−5500000000000000000000
χ3644444-4-4-4-4-11111-1-1-140000-1-1111111-1-1-1-1−55−555−55−500000000000000000000
χ37444-4-40000400004-4-4000004-400000000000000000000004-400000000000000
χ38444-4-40000400004-4-4000004-40000000000000000000000-4400000000000000
χ3944-44-40000400004-4-400000-440000000000000000004-4000000000000000000
χ4044-44-40000400004-4-400000-44000000000000000000-44000000000000000000
χ4144-4-444-400-1-1-1-1-1-1-1-104-400111155−5−555−5−5-1-1115−5−5500000000000000000000
χ4244-4-444-400-1-1-1-1-1-1-1-104-4001111−5−555−5−555-1-111−555−500000000000000000000
χ4344-4-444-400-1-1-1-1-1-1-1-10-4400111155−5−555−5−511-1-1−555−500000000000000000000
χ4444-4-444-400-1-1-1-1-1-1-1-10-44001111−5−555−5−55511-1-15−5−5500000000000000000000
χ4544-4-44-4400-11111-1-1-10004-411-1-155−5−5−5−5555−5−55-1-11100000000000000000000
χ4644-4-44-4400-11111-1-1-10004-411-1-1−5−55555−5−5−555−5-1-11100000000000000000000
χ4744-4-44-4400-11111-1-1-1000-4411-1-155−5−5−5−555−555−511-1-100000000000000000000
χ4844-4-44-4400-11111-1-1-1000-4411-1-1−5−55555−5−55−5−5511-1-100000000000000000000
χ49888-8-80000-22525−25−25-22200000-2225−25000000000000000000000000000000000000
χ50888-8-80000-2−25−252525-22200000-22−2525000000000000000000000000000000000000
χ5188-88-80000-22525−25−25-222000002-2−2525000000000000000000000000000000000000
χ5288-88-80000-2−25−252525-222000002-225−25000000000000000000000000000000000000
χ538-8000004-480000-8000000000004-44-400000000000000000000000000000000
χ548-8000004-4-2−2ζ2+2ζ6−2ζ14+2ζ182ζ2−2ζ6+2ζ14−2ζ18−2ζ2−2ζ6+2ζ14+2ζ182ζ2+2ζ6−2ζ14−2ζ18225−25000000000−1+51−5−1−51+52ζ6−2ζ14−2ζ6+2ζ14−2ζ2+2ζ182ζ2−2ζ180000000000000000000000000000
χ558-8000004-4-2−2ζ2−2ζ6+2ζ14+2ζ182ζ2+2ζ6−2ζ14−2ζ182ζ2−2ζ6+2ζ14−2ζ18−2ζ2+2ζ6−2ζ14+2ζ182−2525000000000−1−51+5−1+51−5−2ζ2+2ζ182ζ2−2ζ18−2ζ6+2ζ142ζ6−2ζ140000000000000000000000000000
χ568-8000004-4-22ζ2−2ζ6+2ζ14−2ζ18−2ζ2+2ζ6−2ζ14+2ζ182ζ2+2ζ6−2ζ14−2ζ18−2ζ2−2ζ6+2ζ14+2ζ18225−25000000000−1+51−5−1−51+5−2ζ6+2ζ142ζ6−2ζ142ζ2−2ζ18−2ζ2+2ζ180000000000000000000000000000
χ578-8000004-4-22ζ2+2ζ6−2ζ14−2ζ18−2ζ2−2ζ6+2ζ14+2ζ18−2ζ2+2ζ6−2ζ14+2ζ182ζ2−2ζ6+2ζ14−2ζ182−2525000000000−1−51+5−1+51−52ζ2−2ζ18−2ζ2+2ζ182ζ6−2ζ14−2ζ6+2ζ140000000000000000000000000000
χ588-800000-4480000-800000000000-44-4400000000000000000000000000000000
χ598-800000-44-2−2ζ2+2ζ6−2ζ14+2ζ182ζ2−2ζ6+2ζ14−2ζ18−2ζ2−2ζ6+2ζ14+2ζ182ζ2+2ζ6−2ζ14−2ζ18225−250000000001−5−1+51+5−1−5−2ζ6+2ζ142ζ6−2ζ142ζ2−2ζ18−2ζ2+2ζ180000000000000000000000000000
χ608-800000-44-2−2ζ2−2ζ6+2ζ14+2ζ182ζ2+2ζ6−2ζ14−2ζ182ζ2−2ζ6+2ζ14−2ζ18−2ζ2+2ζ6−2ζ14+2ζ182−25250000000001+5−1−51−5−1+52ζ2−2ζ18−2ζ2+2ζ182ζ6−2ζ14−2ζ6+2ζ140000000000000000000000000000
χ618-800000-44-22ζ2−2ζ6+2ζ14−2ζ18−2ζ2+2ζ6−2ζ14+2ζ182ζ2+2ζ6−2ζ14−2ζ18−2ζ2−2ζ6+2ζ14+2ζ18225−250000000001−5−1+51+5−1−52ζ6−2ζ14−2ζ6+2ζ14−2ζ2+2ζ182ζ2−2ζ180000000000000000000000000000
χ628-800000-44-22ζ2+2ζ6−2ζ14−2ζ18−2ζ2−2ζ6+2ζ14+2ζ18−2ζ2+2ζ6−2ζ14+2ζ182ζ2−2ζ6+2ζ14−2ζ182−25250000000001+5−1−51−5−1+5−2ζ2+2ζ182ζ2−2ζ18−2ζ6+2ζ142ζ6−2ζ140000000000000000000000000000

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