Finite Group Databasebeta

← Group #13020114

Character table — Group #13020114

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11112244444444448888101010101010161616161616161616161620202020202020202020202020202020202020202032324040404080808080
order12224422444451010102020202022444428101020202040404040444448888888888888888101044442888
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
χ9111111-1-11-1-11111111111111111-1-1-11-1-1-1-1-1-11-1-1-1-1111111-1-1-1-111-1-1-1-111-1-1-1-11-111
χ10111111-1-11-1-11111111111111111-1-1-11-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-11111-1-111111111111-1-1-1
χ11111111-1-11-1-1111111111111111-11-1-11-1-111111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-11111-11-1-1
χ12111111-1-11-1-1111111111111111-11-1-11-1-111111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1111
χ13111111-1-11-1-1111111111-1-1-1-1-1-11-1-1-11-1-1-1-1-1-1-11111ii−i−iii−i−i−i−i−i−iiiii11−i−iii-11i−i
χ14111111-1-11-1-1111111111-1-1-1-1-1-11-1-1-11-1-1-1-1-1-1-11111−i−iii−i−iiiiiii−i−i−i−i11ii−i−i-11−ii
χ15111111-1-11-1-1111111111-1-1-1-1-1-1-11-1-11-1-11111-11111ii−i−iii−i−i−i−i−i−iiiii-1-1ii−i−i1-1−ii
χ16111111-1-11-1-1111111111-1-1-1-1-1-1-11-1-11-1-11111-11111−i−iii−i−iiiiiii−i−i−i−i-1-1−i−iii1-1i−i
χ1722222222-2-2-2-222222-2-22222-22-20022-2-2-20000-222-2-200000000000000000000000000
χ1822222222-2-2-2-222222-2-22-2-2-22-220022-2-2-200002-2-22200000000000000000000000000
χ19222222-2-2-222-222222-2-22222-22-200-2-2-2220000-2-2-22200000000000000000000000000
χ20222222-2-2-222-222222-2-22-2-2-22-2200-2-2-2220000222-2-200000000000000000000000000
χ212222-2-200200-22222-222-222-2-2-2-20000-2000000200002i2i−2i−2i−2i−2i00002i2i00000000000000
χ222222-2-200200-22222-222-222-2-2-2-20000-200000020000−2i−2i2i2i2i2i0000−2i−2i00000000000000
χ232222-2-200200-22222-222-2-2-222220000-2000000-200002222-2-20000-2-200000000000000
χ242222-2-200200-22222-222-2-2-222220000-2000000-20000-2-2-2-22200002200000000000000
χ252222-2-200-20022222-2-2-2-222-22-2200002000000-2000000000022-2-20022-2-20000000000
χ262222-2-200-20022222-2-2-2-222-22-2200002000000-20000000000-2-22200-2-2220000000000
χ272222-2-200-20022222-2-2-2-2-2-22-22-200002000000200000000002i2i−2i−2i00−2i−2i2i2i0000000000
χ282222-2-200-20022222-2-2-2-2-2-22-22-20000200000020000000000−2i−2i2i2i002i2i−2i−2i0000000000
χ292-22-22-20002i−2i022-2-2200-22-2-2020000002i−2i00000002i−2i2−22−22−2i2−i2i2−i22−2i2−i2i2−i20000000000
χ302-22-22-20002i−2i022-2-2200-22-2-2020000002i−2i00000002i−2i−22−22−22−i2i2−i2i2−22−i2i2−i2i20000000000
χ312-22-22-20002i−2i022-2-2200-2-2220-20000002i−2i0000000−2i2ii2−i2−i2i2i2−i2−22−22−i2i22−22−20000000000
χ322-22-22-20002i−2i022-2-2200-2-2220-20000002i−2i0000000−2i2i−i2i2i2−i2−i2i22−22−2i2−i2−22−220000000000
χ332-22-22-2000−2i2i022-2-2200-22-2-202000000−2i2i0000000−2i2i2−22−22−2−i2i2−i2i22−2−i2i2−i2i20000000000
χ342-22-22-2000−2i2i022-2-2200-22-2-202000000−2i2i0000000−2i2i−22−22−22i2−i2i2−i2−22i2−i2i2−i20000000000
χ352-22-22-2000−2i2i022-2-2200-2-2220-2000000−2i2i00000002i−2ii2−i2−i2i2i2−i22−22−2−i2i2−22−220000000000
χ362-22-22-2000−2i2i022-2-2200-2-2220-2000000−2i2i00000002i−2i−i2i2i2−i2−i2i2−22−22i2−i22−22−20000000000
χ372-22-2-222-2000022-2-2-20022-220-20002-2000000002-200i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2i2−i2−i2i20000000000
χ382-22-2-222-2000022-2-2-20022-220-20002-2000000002-200−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2−i2i2i2−i20000000000
χ392-22-2-222-2000022-2-2-2002-22-2020002-200000000-22002−22−2−222−2−22−22−222−20000000000
χ402-22-2-222-2000022-2-2-2002-22-2020002-200000000-2200−22−222−2−222−22−22−2−220000000000
χ412-22-2-22-22000022-2-2-20022-220-2000-2200000000-2200i2−i2−i2i2−i2i2−i2i2i2−i2i2−i2−i2i2i2−i20000000000
χ422-22-2-22-22000022-2-2-20022-220-2000-2200000000-2200−i2i2i2−i2i2−i2i2−i2−i2i2−i2i2i2−i2−i2i20000000000
χ432-22-2-22-22000022-2-2-2002-22-202000-22000000002-2002−22−2−22−222−2−222−2−220000000000
χ442-22-2-22-22000022-2-2-2002-22-202000-22000000002-200−22−222−22−2−222−2−222−20000000000
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
χ49444444-4-44-4-44-1-1-1-1-1-1-1-10000004-411-1111111000000000000000000000-1-100000000
χ50444444-4-44-4-44-1-1-1-1-1-1-1-1000000-4411-111-1-1-1-10000000000000000000001100000000
χ51444444-4-4-444-4-1-1-1-1-111-100000000111-1-155−5−5000000000000000000000−5500000000
χ52444444-4-4-444-4-1-1-1-1-111-100000000111-1-1−5−5550000000000000000000005−500000000
χ534-4-44000000004-44-4000000040-400000000000000000000000000000000002i−2i2i−2i0000
χ544-4-44000000004-44-4000000040-40000000000000000000000000000000000−2i2i−2i2i0000
χ554-4-44000000004-44-40000000-40400000000000000000000000000000000002-2-220000
χ564-4-44000000004-44-40000000-4040000000000000000000000000000000000-222-20000
χ578888-8-800800-8-2-2-2-22-2-22000000000020000000000000000000000000000000000000
χ588888-8-800-8008-2-2-2-222220000000000-20000000000000000000000000000000000000
χ5988-8-8000000008-8-880000000000000000000000000000000000000000000000000000
χ6088-8-800000000-222-2025−2500000000000000−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
χ6188-8-800000000-222-2025−2500000000000000ζ7+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
χ6288-8-800000000-222-20−252500000000000000ζ7+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
χ6388-8-800000000-222-20−252500000000000000−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
χ648-88-88-80008i−8i0-2-222-200200000000000−2i2i00000000000000000000000000000000000
χ658-88-88-8000−8i8i0-2-222-2002000000000002i−2i00000000000000000000000000000000000
χ668-88-8-888-80000-2-222200-200000000-2200000000000000000000000000000000000000
χ678-88-8-88-880000-2-222200-2000000002-200000000000000000000000000000000000000
χ6816-16-161600000000-44-440000000000000000000000000000000000000000000000000000

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