Finite Group Databasebeta

← Group #10604046

Character table — Group #10604046

Order 640.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46
size11112244444455558888888810101616161620202020202020202020404040404040
order12224458810101044444420204040404044202020208888888888248888
χ11111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1
χ31111111111111111-1-111111111-1-1-1-11111111111-1-1-1-1-1-1
χ41111111111111111-1-111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111
χ5111111111111-1-1-1-111111111-1-11111-1-1i−ii−iii−i−i-1-1ii−i−i
χ6111111111111-1-1-1-111111111-1-11111-1-1−ii−ii−i−iii-1-1−i−iii
χ7111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1i−ii−iii−i−i11−i−iii
χ8111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1−ii−ii−i−iii11ii−i−i
χ91111111-1-111111111-111-1-1-1-11111-1-1-1-11111-1-1-1-11-11-11-1
χ101111111-1-111111111-111-1-1-1-11111-1-1-1-1-1-1-1-111111-1-11-11
χ111111111-1-11111111-1111-1-1-1-111-1-111-1-11111-1-1-1-1-11-11-11
χ121111111-1-11111111-1111-1-1-1-111-1-111-1-1-1-1-1-11111-111-11-1
χ131111111-1-1111-1-1-1-11-111-1-1-1-1-1-111-1-111i−ii−i−i−iii-11i−i−ii
χ141111111-1-1111-1-1-1-11-111-1-1-1-1-1-111-1-111−ii−iiii−i−i-11−iii−i
χ151111111-1-1111-1-1-1-1-1111-1-1-1-1-1-1-1-11111i−ii−i−i−iii1-1−iii−i
χ161111111-1-1111-1-1-1-1-1111-1-1-1-1-1-1-1-11111−ii−iiii−i−i1-1i−i−ii
χ172222-2-2200222222200-2-20000-2-200000022-2-20000000000
χ182222-2-2200222222200-2-20000-2-2000000-2-2220000000000
χ192222-2-2200222-2-2-2-200-2-20000220000002i−2i−2i2i0000000000
χ202222-2-2200222-2-2-2-200-2-2000022000000−2i2i2i−2i0000000000
χ212-2-222-222-22-2-22i−2i2i−2i00-2222-2-22i−2i00002i−2i00000000000000
χ222-2-222-222-22-2-2−2i2i−2i2i00-2222-2-2−2i2i0000−2i2i00000000000000
χ232-2-222-22-222-2-22i−2i2i−2i00-22-2-2222i−2i0000−2i2i00000000000000
χ242-2-222-22-222-2-2−2i2i−2i2i00-22-2-222−2i2i00002i−2i00000000000000
χ252-2-22-222002-2-22i−2i2i−2i002-20000−2i2i0000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37000000
χ262-2-22-222002-2-22i−2i2i−2i002-20000−2i2i00000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37000000
χ272-2-22-222002-2-2−2i2i−2i2i002-200002i−2i0000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39000000
χ282-2-22-222002-2-2−2i2i−2i2i002-200002i−2i00000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39000000
χ29444444-144-1-1-1000044-1-1-1-1-1-100-1-1-1-10000000000000000
χ30444444-144-1-1-10000-4-4-1-1-1-1-1-10011110000000000000000
χ31444444-1-4-4-1-1-100004-4-1-1111100-1-1110000000000000000
χ32444444-1-4-4-1-1-10000-44-1-111110011-1-10000000000000000
χ3344-4-400400-44-444-4-4000000000000000000000000000000
χ3444-4-400400-44-4-4-444000000000000000000000000000000
χ354-44-400400-4-444i−4i−4i4i000000000000000000000000000000
χ364-44-400400-4-44−4i4i4i−4i000000000000000000000000000000
χ374-4-444-4-14-4-1110000001-1-1-11100i5−i5i5−i50000000000000000
χ384-4-444-4-14-4-1110000001-1-1-11100−i5i5−i5i50000000000000000
χ394-4-444-4-1-44-1110000001-111-1-100i5−i5−i5i50000000000000000
χ404-4-444-4-1-44-1110000001-111-1-100−i5i5i5−i50000000000000000
χ418888-8-8-200-2-2-20000002200000000000000000000000000
χ4288-8-800-2002-2200000000i10−i10i10−i100000000000000000000000
χ4388-8-800-2002-2200000000−i10i10−i10i100000000000000000000000
χ448-88-800-20022-200000000i10−i10−i10i100000000000000000000000
χ458-88-800-20022-200000000−i10i10i10−i100000000000000000000000
χ468-8-88-88-200-222000000-2200000000000000000000000000

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