Finite Group Databasebeta

← Group #10604516

Character table — Group #10604516

Order 640.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46
size11112244444455558888888810101616161620202020202020202020404040404040
order12224424510101044444410102020202044202020204488888888448888
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
χ9111111-1-1111111111-1-1-111-1-111-1-111-1-111-1-111-1-1-111-11-1
χ10111111-1-1111111111-1-1-111-1-111-1-111-1-1-1-111-1-111-11-11-11
χ11111111-1-111111111-11-1-111-1-11111-1-1-1-111-1-111-1-11-1-11-11
χ12111111-1-111111111-11-1-111-1-11111-1-1-1-1-1-111-1-1111-11-11-1
χ13111111-1-11111-1-1-1-11-1-1-111-1-1-1-1-1-11111ii−i−i−i−iii1-1i−i−ii
χ14111111-1-11111-1-1-1-11-1-1-111-1-1-1-1-1-11111−i−iiiii−i−i1-1−iii−i
χ15111111-1-11111-1-1-1-1-11-1-111-1-1-1-111-1-111ii−i−i−i−iii-11−iii−i
χ16111111-1-11111-1-1-1-1-11-1-111-1-1-1-111-1-111−i−iiiii−i−i-11i−i−ii
χ172222-2-22-2222222220022-2-2-2-2-2-200002-200000000000000
χ182222-2-22-22222-2-2-2-20022-2-2-2-2220000-2200000000000000
χ192222-2-2-222222222200-2-2-2-222-2-20000-2200000000000000
χ202222-2-2-222222-2-2-2-200-2-2-2-2222200002-200000000000000
χ212-22-22-2002-2-222i2i−2i−2i00002-2002i−2i00000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39000000
χ222-22-22-2002-2-222i2i−2i−2i00002-2002i−2i000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39000000
χ232-22-22-2002-2-22−2i−2i2i2i00002-200−2i2i00000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37000000
χ242-22-22-2002-2-22−2i−2i2i2i00002-200−2i2i000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37000000
χ252-22-2-22002-2-222i2i−2i−2i0000-2200−2i2i000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700000000
χ262-22-2-22002-2-222i2i−2i−2i0000-2200−2i2i0000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ3700000000
χ272-22-2-22002-2-22−2i−2i2i2i0000-22002i−2i000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900000000
χ282-22-2-22002-2-22−2i−2i2i2i0000-22002i−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
χ31444444-4-4-1-1-1-100004-411-1-1110011-1-10000000000000000
χ32444444-4-4-1-1-1-10000-4411-1-11100-1-1110000000000000000
χ334444-4-44-4-1-1-1-1000000-1-11111005−55−50000000000000000
χ344444-4-44-4-1-1-1-1000000-1-1111100−55−550000000000000000
χ354444-4-4-44-1-1-1-10000001111-1-1005−5−550000000000000000
χ364444-4-4-44-1-1-1-10000001111-1-100−555−50000000000000000
χ3744-4-4000044-4-44-44-4000000000000000000000000000000
χ3844-4-4000044-4-4-44-44000000000000000000000000000000
χ394-4-4400004-44-44i−4i−4i4i000000000000000000000000000000
χ404-4-4400004-44-4−4i4i4i−4i000000000000000000000000000000
χ4188-8-80000-2-22200000025−2500000000000000000000000000
χ4288-8-80000-2-222000000−252500000000000000000000000000
χ438-88-88-800-222-200000000-22000000000000000000000000
χ448-88-8-8800-222-2000000002-2000000000000000000000000
χ458-8-880000-22-2200000000002i5−2i50000000000000000000000
χ468-8-880000-22-220000000000−2i52i50000000000000000000000

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