Finite Group Databasebeta

← Group #10604512

Character table — Group #10604512

Order 640.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52
size1111222244444555588888888101010101616161620202020202020202020202020202020204040
order12224444251010104444441010202020204444202020204888888888888888844
χ11111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111
χ311111111111111111-1-11111111111-1-1-1-1111111111-1-1-1-1-1-1-1-1-1-1
χ411111111111111111-1-11111111111-1-1-1-11-1-1-1-1-1-1-1-111111111-1-1
χ51111111111111-1-1-1-111111111-1-1-1-11111-1iiii−i−i−i−iiiii−i−i−i−i-1-1
χ61111111111111-1-1-1-111111111-1-1-1-11111-1−i−i−i−iiiii−i−i−i−iiiii-1-1
χ71111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii11
χ81111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i11
χ9111111-1-1-1111111111-1-1-111-1-1-1-111-1-111-111-1-111-1-111-1-111-1-1-11
χ10111111-1-1-1111111111-1-1-111-1-1-1-111-1-111-1-1-111-1-111-1-111-1-111-11
χ11111111-1-1-111111111-11-1-111-1-1-1-11111-1-1-111-1-111-1-1-1-111-1-1111-1
χ12111111-1-1-111111111-11-1-111-1-1-1-11111-1-1-1-1-111-1-11111-1-111-1-11-1
χ13111111-1-1-11111-1-1-1-11-1-1-111-1-111-1-1-1-1111ii−i−i−i−iiiii−i−i−i−iii1-1
χ14111111-1-1-11111-1-1-1-11-1-1-111-1-111-1-1-1-1111−i−iiiii−i−i−i−iiiii−i−i1-1
χ15111111-1-1-11111-1-1-1-1-11-1-111-1-111-1-111-1-11ii−i−i−i−iii−i−iiiii−i−i-11
χ16111111-1-1-11111-1-1-1-1-11-1-111-1-111-1-111-1-11−i−iiiii−i−iii−i−i−i−iii-11
χ172222-2-222-22222222200-2-2-2-22222-2-20000-2000000000000000000
χ182222-2-222-22222-2-2-2-200-2-2-2-222-2-22200002000000000000000000
χ192222-2-2-2-22222222220022-2-2-2-2-2-2-2-200002000000000000000000
χ202222-2-2-2-222222-2-2-2-20022-2-2-2-222220000-2000000000000000000
χ212-22-22-20002-2-222i2i−2i−2i00002-200002i−2i0000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ390000000000
χ222-22-22-20002-2-222i2i−2i−2i00002-200002i−2i00000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ390000000000
χ232-22-22-20002-2-22−2i−2i2i2i00002-20000−2i2i0000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ370000000000
χ242-22-22-20002-2-22−2i−2i2i2i00002-20000−2i2i00000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ370000000000
χ252-22-2-220002-2-222i2i−2i−2i0000-220000−2i2i00000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39000000000000
χ262-22-2-220002-2-222i2i−2i−2i0000-220000−2i2i000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39000000000000
χ272-22-2-220002-2-22−2i−2i2i2i0000-2200002i−2i00000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37000000000000
χ282-22-2-220002-2-22−2i−2i2i2i0000-2200002i−2i000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37000000000000
χ292-2-22002i−2i02-22-22i−2i2i−2i0000002i−2i2-20000000000000001−i−1+i1+i−1−i1+i−1−i1−i−1+i00
χ302-2-22002i−2i02-22-22i−2i2i−2i0000002i−2i2-2000000000000000−1+i1−i−1−i1+i−1−i1+i−1+i1−i00
χ312-2-22002i−2i02-22-2−2i2i−2i2i0000002i−2i-220000000000000001+i−1−i−1+i1−i1−i−1+i−1−i1+i00
χ322-2-22002i−2i02-22-2−2i2i−2i2i0000002i−2i-22000000000000000−1−i1+i1−i−1+i−1+i1−i1+i−1−i00
χ332-2-2200−2i2i02-22-22i−2i2i−2i000000−2i2i-220000000000000001−i−1+i−1−i1+i1+i−1−i−1+i1−i00
χ342-2-2200−2i2i02-22-22i−2i2i−2i000000−2i2i-22000000000000000−1+i1−i1+i−1−i−1−i1+i1−i−1+i00
χ352-2-2200−2i2i02-22-2−2i2i−2i2i000000−2i2i2-20000000000000001+i−1−i1−i−1+i1−i−1+i1+i−1−i00
χ362-2-2200−2i2i02-22-2−2i2i−2i2i000000−2i2i2-2000000000000000−1−i1+i−1+i1−i−1+i1−i−1−i1+i00
χ37444444444-1-1-1-1000044-1-1-1-1-1-10000-1-1-1-10000000000000000000
χ38444444444-1-1-1-10000-4-4-1-1-1-1-1-1000011110000000000000000000
χ39444444-4-4-4-1-1-1-100004-411-1-111000011-1-10000000000000000000
χ40444444-4-4-4-1-1-1-10000-4411-1-1110000-1-1110000000000000000000
χ414444-4-444-4-1-1-1-10000001111-1-100005−55−50000000000000000000
χ424444-4-444-4-1-1-1-10000001111-1-10000−55−550000000000000000000
χ434444-4-4-4-44-1-1-1-1000000-1-1111100005−5−550000000000000000000
χ444444-4-4-4-44-1-1-1-1000000-1-111110000−555−50000000000000000000
χ4544-4-40000044-4-44-4-4400000000000000000000000000000000000
χ4644-4-40000044-4-4-444-400000000000000000000000000000000000
χ4788-8-800000-2-22200000025−250000000000000000000000000000000
χ4888-8-800000-2-222000000−25250000000000000000000000000000000
χ498-88-88-8000-222-200000000-2200000000000000000000000000000
χ508-88-8-88000-222-2000000002-200000000000000000000000000000
χ518-8-88008i−8i0-22-220000000000−2i2i000000000000000000000000000
χ528-8-8800−8i8i0-22-2200000000002i−2i000000000000000000000000000

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