Finite Group Databasebeta

← Group #10604043

Character table — Group #10604043

Order 640.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52
size1111224444444455558888888101010101010161616162020202020202020202020202020404040
order12224444588101010444442020404040404488882020202022888888888888488
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−i1111-1-1-1-1i−iii−i−iii−i−i-1i−i
χ411111111111111-1-1-1-11111111-1-1−i−iii1111-1-1-1-1−ii−i−iii−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−i11-1-1-1-111i−iii−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−ii−i−iiiii−i−i1i−i
χ9111111-1-11111111111-1111111111111-1-1-1-1-1-11111-1-1-1-11111-1-1-1
χ10111111-1-11111111111-111111111-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-111
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
χ13111111-1-11-1-11111111111-1-1-1-1111111-1-111-1-1-1-111-1-1-1-1-1-1-1-1111
χ14111111-1-11-1-11111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1111111111-1-1
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
χ172222-2-20020022222220-2-20000-2-2222200000000-2-200000000000
χ182222-2-20020022222220-2-20000-2-2-2-2-2-2000000002200000000000
χ192222-2-200200222-2-2-2-20-2-20000222i2i−2i−2i00000000−2i2i00000000000
χ202222-2-200200222-2-2-2-20-2-2000022−2i−2i2i2i000000002i−2i00000000000
χ2122-2-200002i2−i2-22-22i−2i2i−2i000i2i2−i2−i200−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ390000002−20000001−i−1+i1+i−1−i000
χ2222-2-200002i2−i2-22-22i−2i2i−2i000i2i2−i2−i2002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ390000002−2000000−1+i1−i−1−i1+i000
χ2322-2-200002i2−i2-22-2−2i2i−2i2i000i2i2−i2−i200−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37000000−220000001+i−1−i1−i−1+i000
χ2422-2-200002i2−i2-22-2−2i2i−2i2i000i2i2−i2−i2002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37000000−22000000−1−i1+i−1+i1−i000
χ2522-2-200002−i2i2-22-22i−2i2i−2i000−i2−i2i2i200−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39000000−22000000−1+i1−i−1−i1+i000
χ2622-2-200002−i2i2-22-22i−2i2i−2i000−i2−i2i2i2002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39000000−220000001−i−1+i1+i−1−i000
χ2722-2-200002−i2i2-22-2−2i2i−2i2i000−i2−i2i2i200−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ370000002−2000000−1−i1+i−1+i1−i000
χ2822-2-200002−i2i2-22-2−2i2i−2i2i000−i2−i2i2i2002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ370000002−20000001+i−1−i1−i−1+i000
χ292-2-222-22i−2i2002-2-22i−2i−2i2i0-2200002i−2i00002i−2i002-2000000000000000
χ302-2-222-22i−2i2002-2-2−2i2i2i−2i0-220000−2i2i00002i−2i00-22000000000000000
χ312-2-222-2−2i2i2002-2-22i−2i−2i2i0-2200002i−2i0000−2i2i00-22000000000000000
χ322-2-222-2−2i2i2002-2-2−2i2i2i−2i0-220000−2i2i0000−2i2i002-2000000000000000
χ332-2-22-22002002-2-22i−2i−2i2i02-20000−2i2i00000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ390000000
χ342-2-22-22002002-2-22i−2i−2i2i02-20000−2i2i000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ390000000
χ352-2-22-22002002-2-2−2i2i2i−2i02-200002i−2i00000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ370000000
χ362-2-22-22002002-2-2−2i2i2i−2i02-200002i−2i000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+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
χ414-44-40000400-4-4444-4-40000000000000000000000000000000000
χ424-44-40000400-4-44-4-4440000000000000000000000000000000000
χ434-4-444-44i−4i-100-111000001-15−55−5000000−iii5−i500000000000000000
χ444-4-444-44i−4i-100-111000001-1−55−55000000−ii−i5i500000000000000000
χ454-4-444-4−4i4i-100-111000001-15−55−5000000i−i−i5i500000000000000000
χ464-4-444-4−4i4i-100-111000001-1−55−55000000i−ii5−i500000000000000000
χ478888-8-800-200-2-2-200000220000000000000000000000000000000
χ4888-8-80000-24i2−4i22-220000000−i2−i2i2i2000000000000000000000000000
χ4988-8-80000-2−4i24i22-220000000i2i2−i2−i2000000000000000000000000000
χ508-88-80000-20022-20000000i10−i10−i10i10000000000000000000000000000
χ518-88-80000-20022-20000000−i10i10i10−i10000000000000000000000000000
χ528-8-88-8800-200-22200000-220000000000000000000000000000000

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