Finite Group Databasebeta

← Group #10604327

Character table — Group #10604327

Order 640.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64
size11111111444444444444445555555588888888888820202020202020202020202020202020202020202020
order12222222444444510101010101010444444442020202020202020202020204444448888888888888888
χ11111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1ii−i−iiiiiii−i−i−i−i−i−i
χ41111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1−i−iii−i−i−i−i−i−iiiiiii
χ51111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-111-1-1-1-1
χ61111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-11111
χ71111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111ii−i−iii−i−i−i−i−i−iiiii
χ81111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111−i−iii−i−iiiiiii−i−i−i−i
χ911111111-1-111-1-11111111111111111-1-1-1-11111-1-1-1-1-1-111-1-11111-1-111-1-1-1-111-1-1
χ1011111111-1-111-1-11111111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-111-1-11111-1-111
χ1111111111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111ii−i−i−i−iii−i−iii−i−iii
χ1211111111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111−i−iiiii−i−iii−i−iii−i−i
χ1311111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-1-1-111
χ1411111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-1-11111-1-1
χ1511111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1ii−i−i−i−i−i−iiiiiii−i−i
χ1611111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1−i−iiiiiii−i−i−i−i−i−iii
χ17222-2-22-2-20000002222-2-2-2-222-2-222-2-20000000000000000002-22-2000000000000
χ18222-2-22-2-20000002222-2-2-2-222-2-222-2-2000000000000000000-22-22000000000000
χ19222-2-22-2-20000002222-2-2-2-2-2-222-2-2220000000000000000002i−2i−2i2i000000000000
χ20222-2-22-2-20000002222-2-2-2-2-2-222-2-222000000000000000000−2i2i2i−2i000000000000
χ2122-222-2-2-200002-222-2-2-2-2222i−2i2i−2i2i−2i2i−2i0000000022-2-200002i−2i0000000000000000
χ2222-222-2-2-200002-222-2-2-2-222−2i2i−2i2i−2i2i−2i2i0000000022-2-20000−2i2i0000000000000000
χ2322-222-2-2-20000-2222-2-2-2-2222i−2i2i−2i2i−2i2i−2i00000000-2-2220000−2i2i0000000000000000
χ2422-222-2-2-20000-2222-2-2-2-222−2i2i−2i2i−2i2i−2i2i00000000-2-22200002i−2i0000000000000000
χ2522-2-2-2-22200000022-2-222-2-22i−2i−2i2i2i−2i−2i2i00000000000000000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ390000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37
χ2622-2-2-2-22200000022-2-222-2-22i−2i−2i2i2i−2i−2i2i000000000000000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ3900002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37
χ2722-2-2-2-22200000022-2-222-2-2−2i2i2i−2i−2i2i2i−2i00000000000000000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ370000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39
χ2822-2-2-2-22200000022-2-222-2-2−2i2i2i−2i−2i2i2i−2i000000000000000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ3700002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39
χ292-222-2-2-22002i−2i002-22-22-22-22i−2i2i−2i−2i2i−2i2i00002i2i−2i−2i0000002-2000000000000000000
χ302-222-2-2-22002i−2i002-22-22-22-2−2i2i−2i2i2i−2i2i−2i00002i2i−2i−2i000000-22000000000000000000
χ312-222-2-2-2200−2i2i002-22-22-22-22i−2i2i−2i−2i2i−2i2i0000−2i−2i2i2i000000-22000000000000000000
χ322-222-2-2-2200−2i2i002-22-22-22-2−2i2i−2i2i2i−2i2i−2i0000−2i−2i2i2i0000002-2000000000000000000
χ332-22-22-22-20000002-22-2-22-222i−2i−2i2i−2i2i2i−2i000000000000000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ390000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700
χ342-22-22-22-20000002-22-2-22-222i−2i−2i2i−2i2i2i−2i0000000000000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ3900002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ3700
χ352-22-22-22-20000002-22-2-22-22−2i2i2i−2i2i−2i−2i2i000000000000000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ370000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900
χ362-22-22-22-20000002-22-2-22-22−2i2i2i−2i2i−2i−2i2i0000000000000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ3700002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ3900
χ372-2-22-222-22-200002-2-22-222-22222-2-2-2-222-2-2000000002-200000000000000000000
χ382-2-22-222-22-200002-2-22-222-2-2-2-2-2222222-2-200000000-2200000000000000000000
χ392-2-22-222-2-2200002-2-22-222-22222-2-2-2-2-2-22200000000-2200000000000000000000
χ402-2-22-222-2-2200002-2-22-222-2-2-2-2-22222-2-222000000002-200000000000000000000
χ412-2-2-222-220000002-2-222-2-2222-2-2-2-22200000000000000000000002-200002-20000
χ422-2-2-222-220000002-2-222-2-2222-2-2-2-2220000000000000000000000-220000-220000
χ432-2-2-222-220000002-2-222-2-22-2-22222-2-200000000000000000000002i−2i0000−2i2i0000
χ442-2-2-222-220000002-2-222-2-22-2-22222-2-20000000000000000000000−2i2i00002i−2i0000
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
χ4944-444-4-4-400004-4-1-11111-1-1000000005−55−55−55−5-1-1110000000000000000000000
χ5044-444-4-4-400004-4-1-11111-1-100000000−55−55−55−55-1-1110000000000000000000000
χ5144-444-4-4-40000-44-1-11111-1-1000000005−55−5−55−5511-1-10000000000000000000000
χ5244-444-4-4-40000-44-1-11111-1-100000000−55−555−55−511-1-10000000000000000000000
χ534-444-4-4-44004i−4i00-11-11-11-11000000005−5−55−i−iiii5−i5i5−i50000000000000000000000
χ544-444-4-4-44004i−4i00-11-11-11-1100000000−555−5−i−iii−i5i5−i5i50000000000000000000000
χ554-444-4-4-4400−4i4i00-11-11-11-11000000005−5−55ii−i−i−i5i5−i5i50000000000000000000000
χ564-444-4-4-4400−4i4i00-11-11-11-1100000000−555−5ii−i−ii5−i5i5−i50000000000000000000000
χ574-4-44-444-44-40000-111-11-1-1100000000-1-111i5−i5−i5i5i5−i5−i5i50000000000000000000000
χ584-4-44-444-44-40000-111-11-1-1100000000-1-111−i5i5i5−i5−i5i5i5−i50000000000000000000000
χ594-4-44-444-4-440000-111-11-1-110000000011-1-1i5−i5−i5i5−i5i5i5−i50000000000000000000000
χ604-4-44-444-4-440000-111-11-1-110000000011-1-1−i5i5i5−i5i5−i5−i5i50000000000000000000000
χ61888-8-88-8-8000000-2-2-2-22222000000000000000000000000000000000000000000
χ6288-8-8-8-888000000-2-222-2-222000000000000000000000000000000000000000000
χ638-88-88-88-8000000-22-222-22-2000000000000000000000000000000000000000000
χ648-8-8-888-88000000-222-2-222-2000000000000000000000000000000000000000000

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