Finite Group Databasebeta

← Group #10603981

Character table — Group #10603981

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
χ91111111-1-111111111-111-1-1-1-111-1-111-1-11111-1-1-1-1-111-11-1
χ101111111-1-111111111-111-1-1-1-111-1-111-1-1-1-1-1-11111-11-11-11
χ111111111-1-11111111-1111-1-1-1-11111-1-1-1-11111-1-1-1-11-1-11-11
χ121111111-1-11111111-1111-1-1-1-11111-1-1-1-1-1-1-1-111111-11-11-1
χ131111111-1-1111-1-1-1-11-111-1-1-1-1-1-1-1-11111i−ii−i−i−iii1-1i−i−ii
χ141111111-1-1111-1-1-1-11-111-1-1-1-1-1-1-1-11111−ii−iiii−i−i1-1−iii−i
χ151111111-1-1111-1-1-1-1-1111-1-1-1-1-1-111-1-111i−ii−i−i−iii-11−iii−i
χ161111111-1-1111-1-1-1-1-1111-1-1-1-1-1-111-1-111−ii−iiii−i−i-11i−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
χ2122-2-22-2200-2-222i−2i2i−2i00-2200002i−2i0000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39000000
χ2222-2-22-2200-2-222i−2i2i−2i00-2200002i−2i00000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39000000
χ2322-2-22-2200-2-22−2i2i−2i2i00-220000−2i2i0000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37000000
χ2422-2-22-2200-2-22−2i2i−2i2i00-220000−2i2i00000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37000000
χ2522-2-2-2222i−2i-2-222i−2i2i−2i002-22i2i−2i−2i−2i2i00002-200000000000000
χ2622-2-2-2222i−2i-2-22−2i2i−2i2i002-22i2i−2i−2i2i−2i0000-2200000000000000
χ2722-2-2-222−2i2i-2-222i−2i2i−2i002-2−2i−2i2i2i−2i2i0000-2200000000000000
χ2822-2-2-222−2i2i-2-22−2i2i−2i2i002-2−2i−2i2i2i2i−2i00002-200000000000000
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
χ31444444-1-4-4-1-1-100004-4-1-111110011-1-10000000000000000
χ32444444-1-4-4-1-1-10000-44-1-1111100-1-1110000000000000000
χ3344-4-4-44-14i−4i11-1000000-11−i−iii00i5−i55−50000000000000000
χ3444-4-4-44-14i−4i11-1000000-11−i−iii00−i5i5−550000000000000000
χ3544-4-4-44-1−4i4i11-1000000-11ii−i−i00i5−i5−550000000000000000
χ3644-4-4-44-1−4i4i11-1000000-11ii−i−i00−i5i55−50000000000000000
χ374-44-400400-44-444-4-4000000000000000000000000000000
χ384-44-400400-44-4-4-444000000000000000000000000000000
χ394-4-44004004-4-44i−4i−4i4i000000000000000000000000000000
χ404-4-44004004-4-4−4i4i4i−4i000000000000000000000000000000
χ418888-8-8-200-2-2-20000002200000000000000000000000000
χ4288-8-88-8-20022-20000002-200000000000000000000000000
χ438-88-800-2002-2200000000i10−i10i10−i100000000000000000000000
χ448-88-800-2002-2200000000−i10i10−i10i100000000000000000000000
χ458-8-8800-200-2220000000010−10−10100000000000000000000000
χ468-8-8800-200-22200000000−101010−100000000000000000000000

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