Finite Group Databasebeta

← Group #13022598

Character table — Group #13022598

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80
size1111222222444444444444555588888888888888881010101010101616161616161616202020204040404040404040404040404040404040404040
order12442224445888810101020202020224424881010202040404040404040402224441010202040404040888824444444448888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-1-1-11111
χ51111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1ii−i−iii−i−i-1-1ii−i−iii−i−i
χ61111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1−i−iii−i−iii-1-1−i−iii−i−iii
χ71111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111ii−i−i−i−iii11ii−i−i−i−iii
χ81111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111−i−iiiii−i−i11−i−iiiii−i−i
χ911111111111-1-1-1-11111111111111-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111
χ1011111111111-1-1-1-11111111111111-1-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-11111-1-1-1-1
χ1111111111111-1-1-1-111111111111-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1
χ1211111111111-1-1-1-111111111111-1-1111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111
χ1311111111111-1-1-1-11111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1ii−i−i−i−iii11−i−iiiii−i−i
χ1411111111111-1-1-1-11111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1−i−iiiii−i−i11ii−i−i−i−iii
χ1511111111111-1-1-1-11111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111ii−i−iii−i−i-1-1−i−iii−i−iii
χ1611111111111-1-1-1-11111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111−i−iii−i−iii-1-1ii−i−iii−i−i
χ1722222-2-22-2-220000-2-2222-2-2222200002-22-2000000002-2-2-22-200000000000000000000000000002-22-2
χ1822222-2-22-2-220000-2-2222-2-2222200002-22-2000000002-2-2-22-20000000000000000000000000000-22-22
χ1922222-2-22-2-220000-2-2222-2-2-2-2-2-200002-22-200000000-2222-2200000000000000000000000000002i−2i−2i2i
χ2022222-2-22-2-220000-2-2222-2-2-2-2-2-200002-22-200000000-2222-220000000000000000000000000000−2i2i2i−2i
χ212222-22-2-22-220000-2-2222-2-222220000-22-2200000000-22-2-2-220000000000000000000000002-22-20000
χ222222-22-2-22-220000-2-2222-2-222220000-22-2200000000-22-2-2-22000000000000000000000000-22-220000
χ232222-22-2-22-220000-2-2222-2-2-2-2-2-20000-22-22000000002-2222-20000000000000000000000002i−2i−2i2i0000
χ242222-22-2-22-220000-2-2222-2-2-2-2-2-20000-22-22000000002-2222-2000000000000000000000000−2i2i2i−2i0000
χ252222-2-22-2-222000022222222222002-2-2-2-2-200000000-2-222-2-2000022-2-2000000000000002-200000000
χ262222-2-22-2-22200002222222222200-22-2-2-2-200000000-2-222-2-20000-2-22200000000000000-2200000000
χ272222-2-22-2-22200002222222-2-2-2-2002-2-2-2-2-20000000022-2-222000022-2-200000000000000-2200000000
χ282222-2-22-2-22200002222222-2-2-2-200-22-2-2-2-20000000022-2-2220000-2-222000000000000002-200000000
χ2922-2-2222-2-2-222i2i−2i−2i222-2-2-2-222-2-2000022-2-22i2i2i2i−2i−2i−2i−2i222-2-2-2000000002i2i−2i−2i00000000000000000000
χ3022-2-2222-2-2-222i2i−2i−2i222-2-2-2-2-2-222000022-2-22i2i2i2i−2i−2i−2i−2i-2-2-222200000000−2i−2i2i2i00000000000000000000
χ3122-2-2222-2-2-22−2i−2i2i2i222-2-2-2-222-2-2000022-2-2−2i−2i−2i−2i2i2i2i2i222-2-2-200000000−2i−2i2i2i00000000000000000000
χ3222-2-2222-2-2-22−2i−2i2i2i222-2-2-2-2-2-222000022-2-2−2i−2i−2i−2i2i2i2i2i-2-2-2222000000002i2i−2i−2i00000000000000000000
χ3322-2-22-2-2-22220000-2-22-2-22222-2-200002-2-22000000002-2-22-220000000000000000002-22-20000000000
χ3422-2-22-2-2-22220000-2-22-2-22222-2-200002-2-22000000002-2-22-22000000000000000000-22-220000000000
χ3522-2-22-2-2-22220000-2-22-2-222-2-22200002-2-2200000000-222-22-20000000000000000002i−2i−2i2i0000000000
χ3622-2-22-2-2-22220000-2-22-2-222-2-22200002-2-2200000000-222-22-2000000000000000000−2i2i2i−2i0000000000
χ3722-2-2-22-22-2220000-2-22-2-22222-2-20000-222-200000000-22-222-2000000000000002-22-200000000000000
χ3822-2-2-22-22-2220000-2-22-2-22222-2-20000-222-200000000-22-222-200000000000000-22-2200000000000000
χ3922-2-2-22-22-2220000-2-22-2-222-2-2220000-222-2000000002-22-2-22000000000000002i−2i−2i2i00000000000000
χ4022-2-2-22-22-2220000-2-22-2-222-2-2220000-222-2000000002-22-2-2200000000000000−2i2i2i−2i00000000000000
χ4122-2-2-2-2222-220000222-2-2-2-222-2-22-200-2-22200000000-2-22-22222-2-2000000002-2000000000000000000
χ4222-2-2-2-2222-220000222-2-2-2-222-2-2-2200-2-22200000000-2-22-222-2-22200000000-22000000000000000000
χ4322-2-2-2-2222-220000222-2-2-2-2-2-2222-200-2-2220000000022-22-2-222-2-200000000-22000000000000000000
χ4422-2-2-2-2222-220000222-2-2-2-2-2-222-2200-2-2220000000022-22-2-2-2-222000000002-2000000000000000000
χ454444444444-14444-1-1-1-1-1-1-100004444-1-1-1-1-1-1-1-1-1-1-1-1000000-1-1-1-1-1-1-1-1000000000000000000000000
χ464444444444-14444-1-1-1-1-1-1-10000-4-4-4-4-1-1-1-1-1-1-1-1-1-1-1-100000011111111000000000000000000000000
χ474444444444-1-4-4-4-4-1-1-1-1-1-1-1000044-4-4-1-1-1-111111111000000-1-1-1-11111000000000000000000000000
χ484444444444-1-4-4-4-4-1-1-1-1-1-1-10000-4-444-1-1-1-1111111110000001111-1-1-1-1000000000000000000000000
χ494444-4-44-4-44-10000-1-1-1-1-1-1-10000004-4111155−5−555−5−50000005−55−5-1-111000000000000000000000000
χ504444-4-44-4-44-10000-1-1-1-1-1-1-10000004-41111−5−555−5−555000000−55−55-1-111000000000000000000000000
χ514444-4-44-4-44-10000-1-1-1-1-1-1-1000000-44111155−5−555−5−5000000−55−5511-1-1000000000000000000000000
χ524444-4-44-4-44-10000-1-1-1-1-1-1-1000000-441111−5−555−5−5550000005−55−511-1-1000000000000000000000000
χ5344-4-4444-4-4-4-14i4i−4i−4i-1-1-1111100000000-1-111−i−i−i−iiiii0000005−5−55i5−i5i5−i5000000000000000000000000
χ5444-4-4444-4-4-4-14i4i−4i−4i-1-1-1111100000000-1-111−i−i−i−iiiii000000−555−5−i5i5−i5i5000000000000000000000000
χ5544-4-4444-4-4-4-1−4i−4i4i4i-1-1-1111100000000-1-111iiii−i−i−i−i0000005−5−55−i5i5−i5i5000000000000000000000000
χ5644-4-4444-4-4-4-1−4i−4i4i4i-1-1-1111100000000-1-111iiii−i−i−i−i000000−555−5i5−i5i5−i5000000000000000000000000
χ5744-4-4-4-4444-4-10000-1-1-1111100004-40011-1-1i5i5−i5−i5−i5−i5i5i5000000-1-111i5−i5−i5i5000000000000000000000000
χ5844-4-4-4-4444-4-10000-1-1-1111100004-40011-1-1−i5−i5i5i5i5i5−i5−i5000000-1-111−i5i5i5−i5000000000000000000000000
χ5944-4-4-4-4444-4-10000-1-1-111110000-440011-1-1i5i5−i5−i5−i5−i5i5i500000011-1-1−i5i5i5−i5000000000000000000000000
χ6044-4-4-4-4444-4-10000-1-1-111110000-440011-1-1−i5−i5i5i5i5i5−i5−i500000011-1-1i5−i5−i5i5000000000000000000000000
χ614-44i−4i0000004−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900-44i−4i004-44i−4i00000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900000000000000000000
χ624-44i−4i0000004−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900-44i−4i00-44−4i4i00000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ3900000000000000000000
χ634-44i−4i00000042ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ3900-44i−4i004-44i−4i000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ3900000000000000000000
χ644-44i−4i00000042ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ3900-44i−4i00-44−4i4i000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ3900000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900000000000000000000
χ654-4−4i4i0000004−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700-4−4i4i004-4−4i4i00000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700000000000000000000
χ664-4−4i4i0000004−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700-4−4i4i00-444i−4i00000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ3700000000000000000000
χ674-4−4i4i00000042ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ3700-4−4i4i004-4−4i4i000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ3700000000000000000000
χ684-4−4i4i00000042ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ3700-4−4i4i00-444i−4i000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ3700000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700000000000000000000
χ6988888-8-88-8-8-2000022-2-2-22200000000-22-220000000000000000000000000000000000000000000000
χ708888-88-8-88-8-2000022-2-2-222000000002-22-20000000000000000000000000000000000000000000000
χ7188-8-88-8-8-888-2000022-222-2-200000000-222-20000000000000000000000000000000000000000000000
χ7288-8-8-88-88-88-2000022-222-2-2000000002-2-220000000000000000000000000000000000000000000000
χ738-88i−8i000000-2−4ζ13−4ζ21−4ζ29−4ζ374ζ13+4ζ21+4ζ29+4ζ37−4ζ7−4ζ23−4ζ31−4ζ394ζ7+4ζ23+4ζ31+4ζ3925−252−2i2i2i5−2i50000000000002ζ21+2ζ29−2ζ21−2ζ292ζ13+2ζ37−2ζ13−2ζ372ζ31+2ζ39−2ζ31−2ζ392ζ7+2ζ23−2ζ7−2ζ2300000000000000000000000000000000000000
χ748-88i−8i000000-2−4ζ13−4ζ21−4ζ29−4ζ374ζ13+4ζ21+4ζ29+4ζ37−4ζ7−4ζ23−4ζ31−4ζ394ζ7+4ζ23+4ζ31+4ζ39−25252−2i2i−2i52i50000000000002ζ13+2ζ37−2ζ13−2ζ372ζ21+2ζ29−2ζ21−2ζ292ζ7+2ζ23−2ζ7−2ζ232ζ31+2ζ39−2ζ31−2ζ3900000000000000000000000000000000000000
χ758-88i−8i000000-24ζ13+4ζ21+4ζ29+4ζ37−4ζ13−4ζ21−4ζ29−4ζ374ζ7+4ζ23+4ζ31+4ζ39−4ζ7−4ζ23−4ζ31−4ζ3925−252−2i2i2i5−2i5000000000000−2ζ21−2ζ292ζ21+2ζ29−2ζ13−2ζ372ζ13+2ζ37−2ζ31−2ζ392ζ31+2ζ39−2ζ7−2ζ232ζ7+2ζ2300000000000000000000000000000000000000
χ768-88i−8i000000-24ζ13+4ζ21+4ζ29+4ζ37−4ζ13−4ζ21−4ζ29−4ζ374ζ7+4ζ23+4ζ31+4ζ39−4ζ7−4ζ23−4ζ31−4ζ39−25252−2i2i−2i52i5000000000000−2ζ13−2ζ372ζ13+2ζ37−2ζ21−2ζ292ζ21+2ζ29−2ζ7−2ζ232ζ7+2ζ23−2ζ31−2ζ392ζ31+2ζ3900000000000000000000000000000000000000
χ778-8−8i8i000000-2−4ζ7−4ζ23−4ζ31−4ζ394ζ7+4ζ23+4ζ31+4ζ39−4ζ13−4ζ21−4ζ29−4ζ374ζ13+4ζ21+4ζ29+4ζ3725−2522i−2i−2i52i50000000000002ζ31+2ζ39−2ζ31−2ζ392ζ7+2ζ23−2ζ7−2ζ232ζ21+2ζ29−2ζ21−2ζ292ζ13+2ζ37−2ζ13−2ζ3700000000000000000000000000000000000000
χ788-8−8i8i000000-2−4ζ7−4ζ23−4ζ31−4ζ394ζ7+4ζ23+4ζ31+4ζ39−4ζ13−4ζ21−4ζ29−4ζ374ζ13+4ζ21+4ζ29+4ζ37−252522i−2i2i5−2i50000000000002ζ7+2ζ23−2ζ7−2ζ232ζ31+2ζ39−2ζ31−2ζ392ζ13+2ζ37−2ζ13−2ζ372ζ21+2ζ29−2ζ21−2ζ2900000000000000000000000000000000000000
χ798-8−8i8i000000-24ζ7+4ζ23+4ζ31+4ζ39−4ζ7−4ζ23−4ζ31−4ζ394ζ13+4ζ21+4ζ29+4ζ37−4ζ13−4ζ21−4ζ29−4ζ3725−2522i−2i−2i52i5000000000000−2ζ31−2ζ392ζ31+2ζ39−2ζ7−2ζ232ζ7+2ζ23−2ζ21−2ζ292ζ21+2ζ29−2ζ13−2ζ372ζ13+2ζ3700000000000000000000000000000000000000
χ808-8−8i8i000000-24ζ7+4ζ23+4ζ31+4ζ39−4ζ7−4ζ23−4ζ31−4ζ394ζ13+4ζ21+4ζ29+4ζ37−4ζ13−4ζ21−4ζ29−4ζ37−252522i−2i2i5−2i5000000000000−2ζ7−2ζ232ζ7+2ζ23−2ζ31−2ζ392ζ31+2ζ39−2ζ13−2ζ372ζ13+2ζ37−2ζ21−2ζ292ζ21+2ζ2900000000000000000000000000000000000000

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