Finite Group Databasebeta

← Group #10604949

Character table — Group #10604949

Order 640.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64
size11111111444444444444445555555588888888888820202020202020202020202020202020202020202020
order12222222222244510101010101010444444441010101010101010202020204444448888888888888888
χ11111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i
χ41111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii
χ51111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-111-1-111-1-1
χ61111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-111-1-111-1-111
χ71111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111ii−i−i−i−iiiii−i−i−i−iii
χ81111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111−i−iiiii−i−i−i−iiiii−i−i
χ911111111-1-111-1-11111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111-1-1-1-111-1-111
χ1011111111-1-111-1-11111111111111111-1-1-1-11111-1-1-1-1-1-1-1-111-1-111-1-11111-1-111-1-1
χ1111111111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1ii−i−i−i−iii−i−iiiii−i−i
χ1211111111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1−i−iiiii−i−iii−i−i−i−iii
χ1311111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ1411111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111111
χ1511111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111iiii−i−i−i−i−i−i−i−iiiii
χ1611111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111−i−i−i−iiiiiiiii−i−i−i−i
χ17222-2-22-2-2002-200222-2-2-2-222i−2i2i2i−2i−2i2i−2i000022-2-2000000002i−2i0000000000000000
χ18222-2-22-2-2002-200222-2-2-2-22−2i2i−2i−2i2i2i−2i2i000022-2-200000000−2i2i0000000000000000
χ19222-2-22-2-200-2200222-2-2-2-222i−2i2i2i−2i−2i2i−2i0000-2-22200000000−2i2i0000000000000000
χ20222-2-22-2-200-2200222-2-2-2-22−2i2i−2i−2i2i2i−2i2i0000-2-222000000002i−2i0000000000000000
χ2122-22-2-22-200000022-222-2-2-22i−2i2i−2i2i−2i−2i2i00000000000000000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900
χ2222-22-2-22-200000022-222-2-2-22i−2i2i−2i2i−2i−2i2i000000000000000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ3900
χ2322-22-2-22-200000022-222-2-2-2−2i2i−2i2i−2i2i2i−2i00000000000000000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700
χ2422-22-2-22-200000022-222-2-2-2−2i2i−2i2i−2i2i2i−2i000000000000000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ3700
χ2522-2-22-2-2200000022-2-2-222-2222-2-22-2-2000000000000000000002i−2i002i−2i00000000
χ2622-2-22-2-2200000022-2-2-222-2222-2-22-2-200000000000000000000−2i2i00−2i2i00000000
χ2722-2-22-2-2200000022-2-2-222-2-2-2-222-222000000000000000000002-200-2200000000
χ2822-2-22-2-2200000022-2-2-222-2-2-2-222-22200000000000000000000-22002-200000000
χ292-222-2-2-220000002-222-22-2-222-222-2-2-20000000000000000002i−2i002i−2i0000000000
χ302-222-2-2-220000002-222-22-2-222-222-2-2-2000000000000000000−2i2i00−2i2i0000000000
χ312-222-2-2-220000002-222-22-2-2-2-22-2-22220000000000000000002-200-220000000000
χ322-222-2-2-220000002-222-22-2-2-2-22-2-2222000000000000000000-22002-20000000000
χ332-22-22-22-20000002-22-22-22-22i−2i−2i2i−2i2i−2i2i0000000000000000000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37
χ342-22-22-22-20000002-22-22-22-22i−2i−2i2i−2i2i−2i2i00000000000000000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37
χ352-22-22-22-20000002-22-22-22-2−2i2i2i−2i2i−2i2i−2i0000000000000000000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39
χ362-22-22-22-20000002-22-22-22-2−2i2i2i−2i2i−2i2i−2i00000000000000000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39
χ372-2-2222-2-22-200002-2-22-2-2222i−2i−2i−2i2i2i2i−2i22-2-200000000002i−2i000000000000000000
χ382-2-2222-2-22-200002-2-22-2-222−2i2i2i2i−2i−2i−2i2i22-2-20000000000−2i2i000000000000000000
χ392-2-2222-2-2-2200002-2-22-2-2222i−2i−2i−2i2i2i2i−2i-2-2220000000000−2i2i000000000000000000
χ402-2-2222-2-2-2200002-2-22-2-222−2i2i2i2i−2i−2i−2i2i-2-22200000000002i−2i000000000000000000
χ412-2-2-2-222200002-22-2-2-222-2222-2-2-2-2220000000022-2-22-200000000000000000000
χ422-2-2-2-222200002-22-2-2-222-22-2-22222-2-20000000022-2-2-2200000000000000000000
χ432-2-2-2-22220000-222-2-2-222-2222-2-2-2-22200000000-2-222-2200000000000000000000
χ442-2-2-2-22220000-222-2-2-222-22-2-22222-2-200000000-2-2222-200000000000000000000
χ4544444444444444-1-1-1-1-1-1-1-100000000-1-1-1-1-1-1-1-1-1-1-1-10000000000000000000000
χ464444444444-4-4-4-4-1-1-1-1-1-1-1-100000000-1-1-1-1111111110000000000000000000000
χ4744444444-4-444-4-4-1-1-1-1-1-1-1-1000000001111-1-1-1-111110000000000000000000000
χ4844444444-4-4-4-444-1-1-1-1-1-1-1-10000000011111111-1-1-1-10000000000000000000000
χ49444-4-44-4-4004-400-1-1-11111-1000000005−55−5-1-1115−55−50000000000000000000000
χ50444-4-44-4-4004-400-1-1-11111-100000000−55−55-1-111−55−550000000000000000000000
χ51444-4-44-4-400-4400-1-1-11111-1000000005−55−511-1-1−55−550000000000000000000000
χ52444-4-44-4-400-4400-1-1-11111-100000000−55−5511-1-15−55−50000000000000000000000
χ534-4-4444-4-44-40000-111-111-1-100000000-1-1115−55−55−5−550000000000000000000000
χ544-4-4444-4-44-40000-111-111-1-100000000-1-111−55−55−555−50000000000000000000000
χ554-4-4444-4-4-440000-111-111-1-10000000011-1-15−55−5−555−50000000000000000000000
χ564-4-4444-4-4-440000-111-111-1-10000000011-1-1−55−555−5−550000000000000000000000
χ574-4-4-4-444400004-4-1111-1-11-1000000005−5−555−5−55-1-1110000000000000000000000
χ584-4-4-4-444400004-4-1111-1-11-100000000−555−5−555−5-1-1110000000000000000000000
χ594-4-4-4-44440000-44-1111-1-11-1000000005−5−55−555−511-1-10000000000000000000000
χ604-4-4-4-44440000-44-1111-1-11-100000000−555−55−5−5511-1-10000000000000000000000
χ6188-88-8-88-8000000-2-22-2-2222000000000000000000000000000000000000000000
χ6288-8-88-8-88000000-2-2222-2-22000000000000000000000000000000000000000000
χ638-888-8-8-88000000-22-2-22-222000000000000000000000000000000000000000000
χ648-88-88-88-8000000-22-22-22-22000000000000000000000000000000000000000000

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