Finite Group Databasebeta

← Group #10604607

Character table — Group #10604607

Order 640.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46
size11112244444455558888888810101616161620202020202020202020404040404040
order12224444510101044442220202020202044101010102488888888448888
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
χ5111111111111-1-1-1-111111111-1-11111-1-1iiii−i−i−i−i-1-1ii−i−i
χ6111111111111-1-1-1-111111111-1-11111-1-1−i−i−i−iiiii-1-1−i−iii
χ7111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1iiii−i−i−i−i11−i−iii
χ8111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1−i−i−i−iiiii11ii−i−i
χ9111111-1-1111111111-111-1-1-1-11111-1-1-1-111-1-111-1-11-11-11-1
χ10111111-1-1111111111-111-1-1-1-11111-1-1-1-1-1-111-1-1111-1-11-11
χ11111111-1-111111111-1111-1-1-1-111-1-111-1-111-1-111-1-1-11-11-11
χ12111111-1-111111111-1111-1-1-1-111-1-111-1-1-1-111-1-111-111-11-1
χ13111111-1-11111-1-1-1-11-111-1-1-1-1-1-111-1-111ii−i−i−i−iii-11i−i−ii
χ14111111-1-11111-1-1-1-11-111-1-1-1-1-1-111-1-111−i−iiiii−i−i-11−iii−i
χ15111111-1-11111-1-1-1-1-1111-1-1-1-1-1-1-1-11111ii−i−i−i−iii1-1−iii−i
χ16111111-1-11111-1-1-1-1-1111-1-1-1-1-1-1-1-11111−i−iiiii−i−i1-1i−i−ii
χ172222-2-22-22222222200-2-222-2-2-2-20000-2200000000000000
χ182222-2-22-22222-2-2-2-200-2-222-2-22200002-200000000000000
χ192222-2-2-222222222200-2-2-2-222-2-200002-200000000000000
χ202222-2-2-222222-2-2-2-200-2-2-2-222220000-2200000000000000
χ2122-2-22-20022-2-22i2i−2i−2i002-200002i−2i00000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37000000
χ2222-2-22-20022-2-22i2i−2i−2i002-200002i−2i000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37000000
χ2322-2-22-20022-2-2−2i−2i2i2i002-20000−2i2i00000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39000000
χ2422-2-22-20022-2-2−2i−2i2i2i002-20000−2i2i000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39000000
χ2522-2-2-220022-2-22i2i−2i−2i00-220000−2i2i000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700000000
χ2622-2-2-220022-2-22i2i−2i−2i00-220000−2i2i0000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ3700000000
χ2722-2-2-220022-2-2−2i−2i2i2i00-2200002i−2i000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900000000
χ2822-2-2-220022-2-2−2i−2i2i2i00-2200002i−2i0000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ3900000000
χ2944444444-1-1-1-1000044-1-1-1-1-1-100-1-1-1-10000000000000000
χ3044444444-1-1-1-10000-4-4-1-1-1-1-1-10011110000000000000000
χ31444444-4-4-1-1-1-100004-4-1-1111100-1-1110000000000000000
χ32444444-4-4-1-1-1-10000-44-1-111110011-1-10000000000000000
χ334444-4-44-4-1-1-1-100000011-1-111005−55−50000000000000000
χ344444-4-44-4-1-1-1-100000011-1-11100−55−550000000000000000
χ354444-4-4-44-1-1-1-10000001111-1-1005−5−550000000000000000
χ364444-4-4-44-1-1-1-10000001111-1-100−555−50000000000000000
χ374-44-400004-44-44i−4i4i−4i000000000000000000000000000000
χ384-44-400004-44-4−4i4i−4i4i000000000000000000000000000000
χ394-4-4400004-4-444-4-44000000000000000000000000000000
χ404-4-4400004-4-44-444-4000000000000000000000000000000
χ4188-8-88-800-2-222000000-2200000000000000000000000000
χ4288-8-8-8800-2-2220000002-200000000000000000000000000
χ438-88-80000-22-220000000025−25000000000000000000000000
χ448-88-80000-22-2200000000−2525000000000000000000000000
χ458-8-880000-222-2000000000025−250000000000000000000000
χ468-8-880000-222-20000000000−25250000000000000000000000

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