Finite Group Databasebeta

← Group #13020124

Character table — Group #13020124

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11112244444444448888101010101010161616161616161616161620202020202020202020202020202020202020202032324040404080808080
order12224422444451010102020202022444448101020202040404040224444444444444444444202088884888
χ111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1
χ311111111111111111111111111-1-111111-1-1-1-1111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111-1-111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ511111111111111111111-1-1-1-1-1-111111111111-1-1-1-1-1ii−i−iiiiiii−i−i−i−i−i−i11ii−i−i-1-1i−i
χ611111111111111111111-1-1-1-1-1-111111111111-1-1-1-1-1−i−iii−i−i−i−i−i−iiiiiii11−i−iii-1-1−ii
χ711111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1ii−i−iiiiiii−i−i−i−i−i−i-1-1−i−iii11−ii
χ811111111111111111111-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1-1-1−i−iii−i−i−i−i−i−iiiiiii-1-1ii−i−i11i−i
χ9111111-1-111-1-1111111111111111-1-1-11-1-1-1-1-1-1-1-1-1-11111111-1-1-1-111-1-1-1-111-1-1-1-11-111
χ10111111-1-111-1-1111111111111111-1-1-11-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-11111-1-111111111111-1-1-1
χ11111111-1-111-1-111111111111111-11-1-11-1-11111-1-1-1-11111111-1-1-1-111-1-1-1-1-1-11111-11-1-1
χ12111111-1-111-1-111111111111111-11-1-11-1-11111-1-1-1-11-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1111
χ13111111-1-111-1-111111111-1-1-1-1-1-11-1-1-11-1-1-1-1-1-11111-1ii−i−iii−i−i−i−i−i−iiiii11−i−iii-11i−i
χ14111111-1-111-1-111111111-1-1-1-1-1-11-1-1-11-1-1-1-1-1-11111-1−i−iii−i−iiiiiii−i−i−i−i11ii−i−i-11−ii
χ15111111-1-111-1-111111111-1-1-1-1-1-1-11-1-11-1-111111111-1ii−i−iii−i−i−i−i−i−iiiii-1-1ii−i−i1-1−ii
χ16111111-1-111-1-111111111-1-1-1-1-1-1-11-1-11-1-111111111-1−i−iii−i−iiiiiii−i−i−i−i-1-1−i−iii1-1i−i
χ1722222222-2-2-2-222222-2-2222-2-2-2-20022-2-2-2000022-2-2200000000000000000000000000
χ1822222222-2-2-2-222222-2-22-2-222220022-2-2-20000-2-222-200000000000000000000000000
χ19222222-2-2-2-22222222-2-2222-2-2-2-200-2-2-2220000-2-222200000000000000000000000000
χ20222222-2-2-2-22222222-2-22-2-2222200-2-2-222000022-2-2-200000000000000000000000000
χ212222-2-2002-2002222-2-2-2-22222-2-2000020000000000-200000022-2-20022-2-20000000000
χ222222-2-2002-2002222-2-2-2-22222-2-2000020000000000-2000000-2-22200-2-2220000000000
χ232222-2-2002-2002222-2-2-2-2-2-2-2-22200002000000000020000002i2i−2i−2i00−2i−2i2i2i0000000000
χ242222-2-2002-2002222-2-2-2-2-2-2-2-2220000200000000002000000−2i−2i2i2i002i2i−2i−2i0000000000
χ252222-2-200-22002222-222-222-2-2220000-20000000000-22222-2-20000-2-200000000000000
χ262222-2-200-22002222-222-222-2-2220000-20000000000-2-2-2-2-22200002200000000000000
χ272222-2-200-22002222-222-2-2-222-2-20000-2000000000022i2i−2i−2i−2i−2i00002i2i00000000000000
χ282222-2-200-22002222-222-2-2-222-2-20000-200000000002−2i−2i2i2i2i2i0000−2i−2i00000000000000
χ292-2-222-200002i−2i22-2-2-2002002i−2i2i−2i000002i−2i00002-20001+i−1−i1−i−1+i1+i−1−i1−i−1+i1−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000
χ302-2-222-200002i−2i22-2-2-2002002i−2i2i−2i000002i−2i00002-2000−1−i1+i−1+i1−i−1−i1+i−1+i1−i−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000
χ312-2-222-200002i−2i22-2-2-200200−2i2i−2i2i000002i−2i0000-220001−i−1+i1+i−1−i1−i−1+i−1−i1+i−1−i1+i1+i−1−i−1+i1−i−1+i1−i0000000000
χ322-2-222-200002i−2i22-2-2-200200−2i2i−2i2i000002i−2i0000-22000−1+i1−i−1−i1+i−1+i1−i1+i−1−i1+i−1−i−1−i1+i1−i−1+i1−i−1+i0000000000
χ332-2-222-20000−2i2i22-2-2-2002002i−2i2i−2i00000−2i2i0000-220001+i−1−i1−i−1+i1+i−1−i−1+i1−i−1+i1−i1−i−1+i−1−i1+i−1−i1+i0000000000
χ342-2-222-20000−2i2i22-2-2-2002002i−2i2i−2i00000−2i2i0000-22000−1−i1+i−1+i1−i−1−i1+i1−i−1+i1−i−1+i−1+i1−i1+i−1−i1+i−1−i0000000000
χ352-2-222-20000−2i2i22-2-2-200200−2i2i−2i2i00000−2i2i00002-20001−i−1+i1+i−1−i1−i−1+i1+i−1−i1+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000
χ362-2-222-20000−2i2i22-2-2-200200−2i2i−2i2i00000−2i2i00002-2000−1+i1−i−1−i1+i−1+i1−i−1−i1+i−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000
χ372-2-22-222-2000022-2-2200-2002i−2i−2i2i002-20000000002i−2i01−i−1+i1+i−1−i−1+i1−i1−i−1+i−1+i1−i−1−i1+i1+i−1−i−1−i1+i0000000000
χ382-2-22-222-2000022-2-2200-2002i−2i−2i2i002-20000000002i−2i0−1+i1−i−1−i1+i1−i−1+i−1+i1−i1−i−1+i1+i−1−i−1−i1+i1+i−1−i0000000000
χ392-2-22-222-2000022-2-2200-200−2i2i2i−2i002-2000000000−2i2i01+i−1−i1−i−1+i−1−i1+i1+i−1−i−1−i1+i−1+i1−i1−i−1+i−1+i1−i0000000000
χ402-2-22-222-2000022-2-2200-200−2i2i2i−2i002-2000000000−2i2i0−1−i1+i−1+i1−i1+i−1−i−1−i1+i1+i−1−i1−i−1+i−1+i1−i1−i−1+i0000000000
χ412-2-22-22-22000022-2-2200-2002i−2i−2i2i00-22000000000−2i2i01−i−1+i1+i−1−i−1+i1−i−1+i1−i1−i−1+i−1−i1+i−1−i1+i1+i−1−i0000000000
χ422-2-22-22-22000022-2-2200-2002i−2i−2i2i00-22000000000−2i2i0−1+i1−i−1−i1+i1−i−1+i1−i−1+i−1+i1−i1+i−1−i1+i−1−i−1−i1+i0000000000
χ432-2-22-22-22000022-2-2200-200−2i2i2i−2i00-220000000002i−2i01+i−1−i1−i−1+i−1−i1+i−1−i1+i1+i−1−i−1+i1−i−1+i1−i1−i−1+i0000000000
χ442-2-22-22-22000022-2-2200-200−2i2i2i−2i00-220000000002i−2i0−1−i1+i−1+i1−i1+i−1−i1+i−1−i−1−i1+i1−i−1+i1−i−1+i−1+i1−i0000000000
χ45444444444444-1-1-1-1-1-1-1-100000044-1-1-1-1-1-1-1-1-1000000000000000000000-1-100000000
χ46444444444444-1-1-1-1-1-1-1-1000000-4-4-1-1-1-1-111110000000000000000000001100000000
χ4744444444-4-4-4-4-1-1-1-1-111-100000000-1-111155−5−50000000000000000000005−500000000
χ4844444444-4-4-4-4-1-1-1-1-111-100000000-1-1111−5−555000000000000000000000−5500000000
χ49444444-4-444-4-4-1-1-1-1-1-1-1-10000004-411-1111111000000000000000000000-1-100000000
χ50444444-4-444-4-4-1-1-1-1-1-1-1-1000000-4411-111-1-1-1-10000000000000000000001100000000
χ51444444-4-4-4-444-1-1-1-1-111-100000000111-1-155−5−5000000000000000000000−5500000000
χ52444444-4-4-4-444-1-1-1-1-111-100000000111-1-1−5−5550000000000000000000005−500000000
χ5344-4-4000000004-44-400004-4000000000000000000000000000000000000002-22-20000
χ5444-4-4000000004-44-400004-400000000000000000000000000000000000000-22-220000
χ5544-4-4000000004-44-40000-44000000000000000000000000000000000000002i−2i−2i2i0000
χ5644-4-4000000004-44-40000-4400000000000000000000000000000000000000−2i2i2i−2i0000
χ578888-8-8008-800-2-2-2-222220000000000-20000000000000000000000000000000000000
χ588888-8-800-8800-2-2-2-22-2-22000000000020000000000000000000000000000000000000
χ598-88-8000000008-8-880000000000000000000000000000000000000000000000000000
χ608-88-800000000-222-2025−2500000000000000−ζ7−ζ13−ζ21+ζ23+ζ29+ζ31+ζ37−ζ39ζ7+ζ13+ζ21−ζ23−ζ29−ζ31−ζ37+ζ39ζ7+ζ13−ζ21−ζ23+ζ29+ζ31−ζ37−ζ39−ζ7−ζ13+ζ21+ζ23−ζ29−ζ31+ζ37+ζ390000000000000000000000000000000
χ618-88-800000000-222-2025−2500000000000000ζ7+ζ13+ζ21−ζ23−ζ29−ζ31−ζ37+ζ39−ζ7−ζ13−ζ21+ζ23+ζ29+ζ31+ζ37−ζ39−ζ7−ζ13+ζ21+ζ23−ζ29−ζ31+ζ37+ζ39ζ7+ζ13−ζ21−ζ23+ζ29+ζ31−ζ37−ζ390000000000000000000000000000000
χ628-88-800000000-222-20−252500000000000000ζ7+ζ13−ζ21−ζ23+ζ29+ζ31−ζ37−ζ39−ζ7−ζ13+ζ21+ζ23−ζ29−ζ31+ζ37+ζ39ζ7+ζ13+ζ21−ζ23−ζ29−ζ31−ζ37+ζ39−ζ7−ζ13−ζ21+ζ23+ζ29+ζ31+ζ37−ζ390000000000000000000000000000000
χ638-88-800000000-222-20−252500000000000000−ζ7−ζ13+ζ21+ζ23−ζ29−ζ31+ζ37+ζ39ζ7+ζ13−ζ21−ζ23+ζ29+ζ31−ζ37−ζ39−ζ7−ζ13−ζ21+ζ23+ζ29+ζ31+ζ37−ζ39ζ7+ζ13+ζ21−ζ23−ζ29−ζ31−ζ37+ζ390000000000000000000000000000000
χ648-8-888-800008i−8i-2-222200-200000000000−2i2i00000000000000000000000000000000000
χ658-8-888-80000−8i8i-2-222200-2000000000002i−2i00000000000000000000000000000000000
χ668-8-88-888-80000-2-222-200200000000-2200000000000000000000000000000000000000
χ678-8-88-88-880000-2-222-2002000000002-200000000000000000000000000000000000000
χ681616-16-1600000000-44-440000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 40 (ζ40 = 1); i = ζ10.