Finite Group Databasebeta

← Group #10604554

Character table — Group #10604554

Order 640.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58
size111122222244445555888888881010101010101010101010101010101010101010101016161616404040404040
order12224444445101010444424202020202020224444888888888888888810102020448888
χ11111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1
χ3111111111111111111-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111111111-1-1-1-111111111-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i1111-1-1ii−i−i
χ611111111111111-1-1-1-111111111-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii1111-1-1−i−iii
χ711111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-111−i−iii
χ811111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-111ii−i−i
χ9111111-1-1-1-1111111111-1-1-1-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-111-1-11-11-11-1
χ10111111-1-1-1-1111111111-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-1111111-1-11-1-11-11
χ11111111-1-1-1-111111111-11-1-1-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-111-11-11-11
χ12111111-1-1-1-111111111-11-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-111-111-11-1
χ13111111-1-1-1-11111-1-1-1-11-1-1-1-1-1111111-1-1iiii−i−i−i−i−i−i−i−iiiii11-1-1-11i−i−ii
χ14111111-1-1-1-11111-1-1-1-11-1-1-1-1-1111111-1-1−i−i−i−iiiiiiiii−i−i−i−i11-1-1-11−iii−i
χ15111111-1-1-1-11111-1-1-1-1-11-1-1-1-1111111-1-1iiii−i−i−i−i−i−i−i−iiiii-1-1111-1−iii−i
χ16111111-1-1-1-11111-1-1-1-1-11-1-1-1-1111111-1-1−i−i−i−iiiiiiiii−i−i−i−i-1-1111-1i−i−ii
χ172222-2-222-2-2222222220022-2-2-2-222-2-2-2-200000000000000000000000000
χ182222-2-222-2-22222-2-2-2-20022-2-2-2-2-2-2222200000000000000000000000000
χ192222-2-2-2-2222222222200-2-222-2-2-2-222-2-200000000000000000000000000
χ202222-2-2-2-2222222-2-2-2-200-2-222-2-222-2-22200000000000000000000000000
χ2122-2-22-200002-2-222i2i−2i−2i0000002-200002i−2i0000−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ390000−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ370000000000
χ2222-2-22-200002-2-222i2i−2i−2i0000002-200002i−2i00002ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ3900002ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ370000000000
χ2322-2-22-200002-2-22−2i−2i2i2i0000002-20000−2i2i0000−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ370000−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ390000000000
χ2422-2-22-200002-2-22−2i−2i2i2i0000002-20000−2i2i00002ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ3700002ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ390000000000
χ2522-2-2-2200002-2-222i2i−2i−2i000000-220000−2i2i−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ390000−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ3700000000000000
χ2622-2-2-2200002-2-222i2i−2i−2i000000-220000−2i2i2ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ3900002ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ3700000000000000
χ2722-2-2-2200002-2-22−2i−2i2i2i000000-2200002i−2i−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ370000−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ3900000000000000
χ2822-2-2-2200002-2-22−2i−2i2i2i000000-2200002i−2i2ζ13+2ζ21+2ζ29+2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ13−2ζ21−2ζ29−2ζ3700002ζ7+2ζ23+2ζ31+2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ7−2ζ23−2ζ31−2ζ3900000000000000
χ292-22-200002i−2i22-2-22-22-200002i−2i00002i−2i00i2−i2i2−i22−22−2i2−i2i2−i22−22−20000000000
χ302-22-200002i−2i22-2-22-22-200002i−2i00002i−2i00−i2i2−i2i2−22−22−i2i2−i2i2−22−220000000000
χ312-22-200002i−2i22-2-2-22-2200002i−2i0000−2i2i002−22−2−i2i2−i2i2−22−22i2−i2i2−i20000000000
χ322-22-200002i−2i22-2-2-22-2200002i−2i0000−2i2i00−22−22i2−i2i2−i22−22−2−i2i2−i2i20000000000
χ332-22-20000−2i2i22-2-22-22-20000−2i2i0000−2i2i00i2−i2i2−i2−22−22i2−i2i2−i2−22−220000000000
χ342-22-20000−2i2i22-2-22-22-20000−2i2i0000−2i2i00−i2i2−i2i22−22−2−i2i2−i2i22−22−20000000000
χ352-22-20000−2i2i22-2-2-22-220000−2i2i00002i−2i002−22−2i2−i2i2−i2−22−22−i2i2−i2i20000000000
χ362-22-20000−2i2i22-2-2-22-220000−2i2i00002i−2i00−22−22−i2i2−i2i22−22−2i2−i2i2−i20000000000
χ372-2-22002i−2i002-22-22i−2i−2i2i002i−2i00002-200001+i−1−i−1−i1+i1−i−1+i−1+i1−i1−i−1+i−1+i1−i−1−i1+i1+i−1−i0000000000
χ382-2-22002i−2i002-22-22i−2i−2i2i002i−2i00002-20000−1−i1+i1+i−1−i−1+i1−i1−i−1+i−1+i1−i1−i−1+i1+i−1−i−1−i1+i0000000000
χ392-2-22002i−2i002-22-2−2i2i2i−2i002i−2i0000-2200001−i−1+i−1+i1−i−1−i1+i1+i−1−i1+i−1−i−1−i1+i1−i−1+i−1+i1−i0000000000
χ402-2-22002i−2i002-22-2−2i2i2i−2i002i−2i0000-220000−1+i1−i1−i−1+i1+i−1−i−1−i1+i−1−i1+i1+i−1−i−1+i1−i1−i−1+i0000000000
χ412-2-2200−2i2i002-22-22i−2i−2i2i00−2i2i0000-2200001+i−1−i−1−i1+i−1+i1−i1−i−1+i1−i−1+i−1+i1−i1+i−1−i−1−i1+i0000000000
χ422-2-2200−2i2i002-22-22i−2i−2i2i00−2i2i0000-220000−1−i1+i1+i−1−i1−i−1+i−1+i1−i−1+i1−i1−i−1+i−1−i1+i1+i−1−i0000000000
χ432-2-2200−2i2i002-22-2−2i2i2i−2i00−2i2i00002-200001−i−1+i−1+i1−i1+i−1−i−1−i1+i1+i−1−i−1−i1+i−1+i1−i1−i−1+i0000000000
χ442-2-2200−2i2i002-22-2−2i2i2i−2i00−2i2i00002-20000−1+i1−i1−i−1+i−1−i1+i1+i−1−i−1−i1+i1+i−1−i1−i−1+i−1+i1−i0000000000
χ454444444444-1-1-1-1000044-1-1-1-1-1-10000000000000000000000-1-1-1-1000000
χ464444444444-1-1-1-10000-4-4-1-1-1-1-1-100000000000000000000001111000000
χ47444444-4-4-4-4-1-1-1-100004-41111-1-10000000000000000000000-1-111000000
χ48444444-4-4-4-4-1-1-1-10000-441111-1-1000000000000000000000011-1-1000000
χ494444-4-444-4-4-1-1-1-1000000-1-1111100000000000000000000005−55−5000000
χ504444-4-444-4-4-1-1-1-1000000-1-111110000000000000000000000−55−55000000
χ514444-4-4-4-444-1-1-1-100000011-1-11100000000000000000000005−5−55000000
χ524444-4-4-4-444-1-1-1-100000011-1-1110000000000000000000000−555−5000000
χ5388-8-88-80000-222-20000000000-2200000000000000000000000000000000
χ5488-8-8-880000-222-200000000002-200000000000000000000000000000000
χ558-88-800008i−8i-2-22200000000−2i2i0000000000000000000000000000000000
χ568-88-80000−8i8i-2-222000000002i−2i0000000000000000000000000000000000
χ578-8-88008i−8i00-22-22000000−2i2i000000000000000000000000000000000000
χ588-8-8800−8i8i00-22-220000002i−2i000000000000000000000000000000000000

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