Finite Group Databasebeta

← Group #13026744

Character table — Group #13026744

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53
size11244444445588101616161616161620202020202020202020202020323232323240404040404040404080808080
order12222224510444104481010101020244448888888820202040404888888884888
χ111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1
χ3111111111111111-1-11111111111111111111-1-1-1-1111-1-1-1-111-1-1-1-1
χ4111111111111111-1-11111111111-1-1-1-1-1-1-1-11-1-1-1-11-1-11111-1-1-1-111
χ51111111111-1-111-11111111-1-1-1-1-1ii−i−iii−i−i11111-1i−iii−i−ii−i-1-1i−i
χ61111111111-1-111-11111111-1-1-1-1-1−i−iii−i−iii11111-1−ii−i−iii−ii-1-1−ii
χ71111111111-1-111-1-1-111111-1-1-1-1-1ii−i−iii−i−i1-1-1-1-1-1i−i−i−iiii−i11−ii
χ81111111111-1-111-1-1-111111-1-1-1-1-1−i−iii−i−iii1-1-1-1-1-1−iiii−i−i−ii11i−i
χ91111-1-1111111-1111-11-1-11111-1-111111-1-1-1-1-111-1-1-1-1-11111111-1-1-1
χ101111-1-1111111-1111-11-1-11111-1-11-1-1-1-11111-111-1-1-111-1-1-1-1-1-11-111
χ111111-1-1111111-111-111-1-11111-1-111111-1-1-1-1-1-1-111-1-1-1-1-1-1-111-1111
χ121111-1-1111111-111-111-1-11111-1-11-1-1-1-11111-1-1-111-1111111-1-1-11-1-1
χ131111-1-11111-1-1-11-11-11-1-111-1-111-1ii−i−i−i−iii-111-1-11−iiii−i−ii−i-11−ii
χ141111-1-11111-1-1-11-11-11-1-111-1-111-1−i−iiiii−i−i-111-1-11i−i−i−iii−ii-11i−i
χ151111-1-11111-1-1-11-1-111-1-111-1-111-1ii−i−i−i−iii-1-1-1111−ii−i−iiii−i1-1i−i
χ161111-1-11111-1-1-11-1-111-1-111-1-111-1−i−iiiii−i−i-1-1-1111i−iii−i−i−ii1-1−ii
χ17222222-2-22222-22200222-2-2-2-222200000000-20000-2000000000000
χ18222222-2-222-2-2-22-200222-2-222-2-2-200000000-200002000000000000
χ192222-2-2-2-22222222002-2-2-2-2-2-2-2-2200000000200002000000000000
χ202222-2-2-2-222-2-222-2002-2-2-2-22222-20000000020000-2000000000000
χ21222-2002-2222202200-2002-2-2200-222220000000000000000-2-20000
χ22222-2002-2222202200-2002-2-2200-2-2-2-2-20000000000000000220000
χ23222-2002-222-2-202-200-2002-22-20022i2i−2i−2i0000000000000000−2i2i0000
χ24222-2002-222-2-202-200-2002-22-2002−2i−2i2i2i00000000000000002i−2i0000
χ25222-200-22222202200-200-222-200-200002222000000-2-20000000000
χ26222-200-22222202200-200-222-200-20000-2-2-2-2000000220000000000
χ27222-200-2222-2-202-200-200-22-2200200002i2i−2i−2i000000−2i2i0000000000
χ28222-200-2222-2-202-200-200-22-220020000−2i−2i2i2i0000002i−2i0000000000
χ2944444444-1-1004-1044-1-1-1-1-10000000000000-1-1-1-1-10000000000000
χ3044444444-1-1004-10-4-4-1-1-1-1-10000000000000-111110000000000000
χ31444444-4-4-1-100-4-1000-1-1-11100000000000001i5−i5i5−i50000000000000
χ32444444-4-4-1-100-4-1000-1-1-11100000000000001−i5i5−i5i50000000000000
χ334444-4-444-1-100-4-104-4-111-1-100000000000001-1-1110000000000000
χ344444-4-444-1-100-4-10-44-111-1-10000000000000111-1-10000000000000
χ354444-4-4-4-4-1-1004-1000-111110000000000000-1i5−i5−i5i50000000000000
χ364444-4-4-4-4-1-1004-1000-111110000000000000-1−i5i5i5−i50000000000000
χ3744-40000044440-4-400000000000000000000000000002-22-2000000
χ3844-40000044440-4-40000000000000000000000000000-22-22000000
χ3944-40000044-4-40-4400000000000000000000000000002i−2i−2i2i000000
χ4044-40000044-4-40-440000000000000000000000000000−2i2i2i−2i000000
χ414-4002-2004-44i−4i0000002-200002i−2i0−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39000000000000000000
χ424-4002-2004-44i−4i0000002-200002i−2i02ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39000000000000000000
χ434-4002-2004-4−4i4i0000002-20000−2i2i0−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37000000000000000000
χ444-4002-2004-4−4i4i0000002-20000−2i2i02ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37000000000000000000
χ454-400-22004-44i−4i000000-220000−2i2i0−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39000000000000000000
χ464-400-22004-44i−4i000000-220000−2i2i02ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39000000000000000000
χ474-400-22004-4−4i4i000000-2200002i−2i0−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37000000000000000000
χ484-400-22004-4−4i4i000000-2200002i−2i02ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37000000000000000000
χ49888-8008-8-2-2000-2000200-220000000000000000000000000000000
χ50888-800-88-2-2000-20002002-20000000000000000000000000000000
χ511616-1600000-4-40004000000000000000000000000000000000000000
χ5216-16008-800-4400000000-22000000000000000000000000000000000
χ5316-1600-8800-44000000002-2000000000000000000000000000000000

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