Finite Group Databasebeta

← Group #10604839

Character table — Group #10604839

Order 640.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52
size1111224444444455558888888101010101010161616162020202020202020202020202020404040
order12224444588101010444442020404040404488882020202044888888888888488
χ11111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11-1-1
χ311111111111111-1-1-1-11111111-1-1ii−i−i1111-1-1-1-1iii−i−i−iii−i−i-1i−i
χ411111111111111-1-1-1-11111111-1-1−i−iii1111-1-1-1-1−i−i−iiii−i−iii-1−ii
χ5111111111-1-11111111-111-1-1-1-111111111-1-111-1-1111111-1-1-1-1-1-1-1
χ6111111111-1-11111111-111-1-1-1-111-1-1-1-111-1-111-1-1-1-1-1-1-1-11111-111
χ7111111111-1-1111-1-1-1-1-111-1-1-1-1-1-1ii−i−i11-1-1-1-111iii−i−i−i−i−iii1−ii
χ8111111111-1-1111-1-1-1-1-111-1-1-1-1-1-1−i−iii11-1-1-1-111−i−i−iiiiii−i−i1i−i
χ9111111-1-11111111111-1111111111111-1-1-1-1-1-1111-1-11-1-11111-1-1-1
χ10111111-1-11111111111-111111111-1-1-1-1-1-1-1-1-1-111-111-111-1-1-1-1-111
χ11111111-1-1111111-1-1-1-1-1111111-1-1ii−i−i-1-1-1-111-1-1i−i−i−iiiii−i−i1−ii
χ12111111-1-1111111-1-1-1-1-1111111-1-1−i−iii-1-1-1-111-1-1−iiii−i−i−i−iii1i−i
χ13111111-1-11-1-11111111111-1-1-1-1111111-1-111-1-1-1-11-1-11-1-1-1-1-1-1111
χ14111111-1-11-1-11111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-111-11111111-1-1
χ15111111-1-11-1-1111-1-1-1-1111-1-1-1-1-1-1ii−i−i-1-1111111i−i−i−iii−i−iii-1i−i
χ16111111-1-11-1-1111-1-1-1-1111-1-1-1-1-1-1−i−iii-1-1111111−iiii−i−iii−i−i-1−ii
χ172222-2-20020022222220-2-20000-2-2222200000000-200-2000000000
χ182222-2-20020022222220-2-20000-2-2-2-2-2-2000000002002000000000
χ192222-2-200200222-2-2-2-20-2-20000222i2i−2i−2i00000000−2i002i000000000
χ202222-2-200200222-2-2-2-20-2-2000022−2i−2i2i2i000000002i00−2i000000000
χ2122-2-2000022−22-2-222-2-200022−2−2002-22-20000002−20000002−22−2000
χ2222-2-2000022−22-2-222-2-200022−2−200-22-220000002−2000000−22−22000
χ2322-2-2000022−22-2-2-2-22200022−2−2002i−2i−2i2i000000−22000000i2−i2−i2i2000
χ2422-2-2000022−22-2-2-2-22200022−2−200−2i2i2i−2i000000−22000000−i2i2i2−i2000
χ2522-2-200002−222-2-222-2-2000−2−222002-22-2000000−22000000−22−22000
χ2622-2-200002−222-2-222-2-2000−2−22200-22-22000000−220000002−22−2000
χ2722-2-200002−222-2-2-2-222000−2−222002i−2i−2i2i0000002−2000000−i2i2i2−i2000
χ2822-2-200002−222-2-2-2-222000−2−22200−2i2i2i−2i0000002−2000000i2−i2−i2i2000
χ292-22-22-22-2200-2-222i−2i2i−2i0-2200002i−2i00002-2002i−2i000000000000000
χ302-22-22-22-2200-2-22−2i2i−2i2i0-220000−2i2i00002-200−2i2i000000000000000
χ312-22-22-2-22200-2-222i−2i2i−2i0-2200002i−2i0000-2200−2i2i000000000000000
χ322-22-22-2-22200-2-22−2i2i−2i2i0-220000−2i2i0000-22002i−2i000000000000000
χ332-22-2-2200200-2-222i−2i2i−2i02-20000−2i2i0000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ370−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ390000000
χ342-22-2-2200200-2-222i−2i2i−2i02-20000−2i2i00000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ3702ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ390000000
χ352-22-2-2200200-2-22−2i2i−2i2i02-200002i−2i0000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ390−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ370000000
χ362-22-2-2200200-2-22−2i2i−2i2i02-200002i−2i00000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ3902ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ370000000
χ3744444444-144-1-1-100004-1-1-1-1-1-1000000-1-1-1-100000000000000000
χ3844444444-1-4-4-1-1-10000-4-1-11111000000-1-11100000000000000000
χ39444444-4-4-144-1-1-10000-4-1-1-1-1-1-1000000111100000000000000000
χ40444444-4-4-1-4-4-1-1-100004-1-1111100000011-1-100000000000000000
χ414-44-44-44-4-10011-1000001-15−55−5000000-115−500000000000000000
χ424-44-44-44-4-10011-1000001-1−55−55000000-11−5500000000000000000
χ434-44-44-4-44-10011-1000001-15−55−50000001-1−5500000000000000000
χ444-44-44-4-44-10011-1000001-1−55−550000001-15−500000000000000000
χ454-4-440000400-44-44i−4i−4i4i0000000000000000000000000000000000
χ464-4-440000400-44-4−4i4i4i−4i0000000000000000000000000000000000
χ478888-8-800-200-2-2-200000220000000000000000000000000000000
χ4888-8-80000-242−42-2220000000−2−222000000000000000000000000000
χ4988-8-80000-2−4242-222000000022−2−2000000000000000000000000000
χ508-88-8-8800-20022-200000-220000000000000000000000000000000
χ518-8-880000-2002-22000000010−10−1010000000000000000000000000000
χ528-8-880000-2002-220000000−101010−10000000000000000000000000000

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