Finite Group Databasebeta

← Group #10604580

Character table — Group #10604580

Order 640.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52
size1111222244444555588888888101010101616161620202020202020202020202020202020204040
order12224444451010104444442020202020204444202020202888888888888888824
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
χ91111-1-111-1111111111-111-1-1-1-1-1-11111-1-1-111-1-111-1-111-1-111-1-11-1
χ101111-1-111-1111111111-111-1-1-1-1-1-11111-1-1-1-1-111-1-111-1-111-1-1111-1
χ111111-1-111-111111111-1111-1-1-1-1-1-111-1-111-111-1-111-1-1-1-111-1-111-11
χ121111-1-111-111111111-1111-1-1-1-1-1-111-1-111-1-1-111-1-11111-1-111-1-1-11
χ131111-1-111-11111-1-1-1-11-111-1-1-1-111-1-111-1-11ii−i−i−i−iiiii−i−i−i−iii-11
χ141111-1-111-11111-1-1-1-11-111-1-1-1-111-1-111-1-11−i−iiiii−i−i−i−iiiii−i−i-11
χ151111-1-111-11111-1-1-1-1-1111-1-1-1-111-1-1-1-1111ii−i−i−i−iii−i−iiiii−i−i1-1
χ161111-1-111-11111-1-1-1-1-1111-1-1-1-111-1-1-1-1111−i−iiiii−i−iii−i−i−i−iii1-1
χ17222222-2-2-22222222200-2-222-2-222-2-20000-2000000000000000000
χ18222222-2-2-22222-2-2-2-200-2-222-2-2-2-22200002000000000000000000
χ192222-2-2-2-222222222200-2-2-2-222-2-2-2-200002000000000000000000
χ202222-2-2-2-222222-2-2-2-200-2-2-2-22222220000-2000000000000000000
χ2122-2-22i−2i0002-22-222-2-200002i−2i002i−2i0000000000000002−2i2−i22−2i2−i200
χ2222-2-22i−2i0002-22-222-2-200002i−2i002i−2i000000000000000−22−i2i2−22−i2i200
χ2322-2-22i−2i0002-22-2-2-22200002i−2i00−2i2i000000000000000i2−i2−22−i2i22−200
χ2422-2-22i−2i0002-22-2-2-22200002i−2i00−2i2i000000000000000−i2i22−2i2−i2−2200
χ2522-2-2−2i2i0002-22-222-2-20000−2i2i00−2i2i0000000000000002−2−i2i22−2−i2i200
χ2622-2-2−2i2i0002-22-222-2-20000−2i2i00−2i2i000000000000000−22i2−i2−22i2−i200
χ2722-2-2−2i2i0002-22-2-2-2220000−2i2i002i−2i000000000000000i2−i22−2−i2i2−2200
χ2822-2-2−2i2i0002-22-2-2-2220000−2i2i002i−2i000000000000000−i2i2−22i2−i22−200
χ292-2-22002-2022-2-22i−2i2i−2i002-20000002i−2i0000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ370000000000
χ302-2-22002-2022-2-22i−2i2i−2i002-20000002i−2i00000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ370000000000
χ312-2-22002-2022-2-2−2i2i−2i2i002-2000000−2i2i0000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ390000000000
χ322-2-22002-2022-2-2−2i2i−2i2i002-2000000−2i2i00000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ390000000000
χ332-2-2200-22022-2-22i−2i2i−2i00-22000000−2i2i00000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39000000000000
χ342-2-2200-22022-2-22i−2i2i−2i00-22000000−2i2i000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39000000000000
χ352-2-2200-22022-2-2−2i2i−2i2i00-220000002i−2i00000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37000000000000
χ362-2-2200-22022-2-2−2i2i−2i2i00-220000002i−2i000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37000000000000
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
χ39444444-4-4-4-1-1-1-100000011-1-11100005−55−50000000000000000000
χ40444444-4-4-4-1-1-1-100000011-1-1110000−55−550000000000000000000
χ414444-4-444-4-1-1-1-100004-4-1-111110000-1-1110000000000000000000
χ424444-4-444-4-1-1-1-10000-44-1-11111000011-1-10000000000000000000
χ434444-4-4-4-44-1-1-1-10000001111-1-100005−5−550000000000000000000
χ444444-4-4-4-44-1-1-1-10000001111-1-10000−555−50000000000000000000
χ454-44-4000004-4-444i−4i−4i4i00000000000000000000000000000000000
χ464-44-4000004-4-44−4i4i4i−4i00000000000000000000000000000000000
χ4788-8-88i−8i000-22-2200000000−2i2i00000000000000000000000000000
χ4888-8-8−8i8i000-22-22000000002i−2i00000000000000000000000000000
χ498-88-800000-222-200000000002i5−2i5000000000000000000000000000
χ508-88-800000-222-20000000000−2i52i5000000000000000000000000000
χ518-8-88008-80-2-222000000-220000000000000000000000000000000
χ528-8-8800-880-2-2220000002-20000000000000000000000000000000

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