Finite Group Databasebeta

← Group #13022213

Character table — Group #13022213

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size11112222224444444455558888888888101010101010161616161616161616161616202020202020202020202020202020202020202020202020202020204040404040404040
order12442224445888810202022448888101010202020222444404040404040404040404040444444448888888888888888888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1
χ31111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-11111
χ5111111111111111111-1-1-1-11111111111-1-1-1-1-1-1111111111111iiii−i−i−i−i-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-1-1-1ii−i−i
χ6111111111111111111-1-1-1-11111111111-1-1-1-1-1-1111111111111−i−i−i−iiiii-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-1-1-1−i−iii
χ7111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1iiii−i−i−i−i-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii1111−i−iii
χ8111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1−i−i−i−iiiii-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i1111ii−i−i
χ911111111111-1-1-1-1111111111-1-1111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1
χ1011111111111-1-1-1-1111111111-1-1111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-11111
χ1111111111111-1-1-1-11111111-1-111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ1211111111111-1-1-1-11111111-1-111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-111-1-1-1-1
χ1311111111111-1-1-1-1111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1iiii−i−i−i−i1111−i−i−i−iiiiiiiii−i−i−i−i-1-111−i−iii
χ1411111111111-1-1-1-1111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1−i−i−i−iiiii1111iiii−i−i−i−i−i−i−i−iiiii-1-111ii−i−i
χ1511111111111-1-1-1-1111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−i1111−i−i−i−iiiii−i−i−i−iiiii11-1-1ii−i−i
χ1611111111111-1-1-1-1111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiii1111iiii−i−i−i−iiiii−i−i−i−i11-1-1−i−iii
χ1711-1-11-1-11-111ii−i−i1-1-111-1-1i−i1-11-1-11-111-1-111-1ii−i−iii−i−i11-1-111-1-111-1-1ii−i−iii−i−iii−i−iii−i−iii−i−ii−i1-11-11-1
χ1811-1-11-1-11-111ii−i−i1-1-111-1-1i−i1-11-1-11-111-1-111-1ii−i−iii−i−i11-1-1-1-111-1-111ii−i−i−i−iii−i−iii−i−iii−i−iiii−i1-1-11-11
χ1911-1-11-1-11-111ii−i−i1-1-111-1-1−ii-111-1-11-111-1-111-1ii−i−i−i−iii-1-11111-1-111-1-1ii−i−iii−i−iii−i−i−i−iii−i−iii−ii-11-11-11
χ2011-1-11-1-11-111ii−i−i1-1-111-1-1−ii-111-1-11-111-1-111-1ii−i−i−i−iii-1-111-1-111-1-111ii−i−i−i−iii−i−iiiii−i−iii−i−i−ii-111-11-1
χ2111-1-11-1-11-111ii−i−i1-1-1-1-111i−i1-11-1-11-11-111-1-11ii−i−iii−i−i11-1-1ii−i−i−i−iii−i−iii-1-11111-1-1-1-11111-1-1−ii-11i−i−ii
χ2211-1-11-1-11-111ii−i−i1-1-1-1-111i−i1-11-1-11-11-111-1-11ii−i−iii−i−i11-1-1−i−iiiii−i−i−i−iii11-1-1-1-11111-1-1-1-111−ii-11−iii−i
χ2311-1-11-1-11-111ii−i−i1-1-1-1-111−ii-111-1-11-11-111-1-11ii−i−i−i−iii-1-111ii−i−i−i−iii−i−iii-1-11111-1-111-1-1-1-111i−i1-1−iii−i
χ2411-1-11-1-11-111ii−i−i1-1-1-1-111−ii-111-1-11-11-111-1-11ii−i−i−i−iii-1-111−i−iiiii−i−i−i−iii11-1-1-1-111-1-11111-1-1i−i1-1i−i−ii
χ2511-1-11-1-11-111−i−iii1-1-111-1-1i−i-111-1-11-111-1-111-1−i−iiiii−i−i-1-11111-1-111-1-1−i−iii−i−iii−i−iiiii−i−iii−i−ii−i-11-11-11
χ2611-1-11-1-11-111−i−iii1-1-111-1-1i−i-111-1-11-111-1-111-1−i−iiiii−i−i-1-111-1-111-1-111−i−iiiii−i−iii−i−i−i−iii−i−iiii−i-111-11-1
χ2711-1-11-1-11-111−i−iii1-1-111-1-1−ii1-11-1-11-111-1-111-1−i−iii−i−iii11-1-111-1-111-1-1−i−iii−i−iii−i−iii−i−iii−i−iii−ii1-11-11-1
χ2811-1-11-1-11-111−i−iii1-1-111-1-1−ii1-11-1-11-111-1-111-1−i−iii−i−iii11-1-1-1-111-1-111−i−iiiii−i−iii−i−iii−i−iii−i−i−ii1-1-11-11
χ2911-1-11-1-11-111−i−iii1-1-1-1-111i−i-111-1-11-11-111-1-11−i−iiiii−i−i-1-111ii−i−i−i−iiiii−i−i11-1-1-1-111-1-11111-1-1−ii1-1−iii−i
χ3011-1-11-1-11-111−i−iii1-1-1-1-111i−i-111-1-11-11-111-1-11−i−iiiii−i−i-1-111−i−iiiii−i−iii−i−i-1-11111-1-111-1-1-1-111−ii1-1i−i−ii
χ3111-1-11-1-11-111−i−iii1-1-1-1-111−ii1-11-1-11-11-111-1-11−i−iii−i−iii11-1-1ii−i−i−i−iiiii−i−i11-1-1-1-11111-1-1-1-111i−i-11i−i−ii
χ3211-1-11-1-11-111−i−iii1-1-1-1-111−ii1-11-1-11-11-111-1-11−i−iii−i−iii11-1-1−i−iiiii−i−iii−i−i-1-11111-1-1-1-11111-1-1i−i-11−iii−i
χ3322222-2-2-22-220000222222200002-2-2-22-22-2-2-2-220000000000002-22-22-22-20000000000000000000000000000
χ3422222-2-2-22-220000222222200002-2-2-22-22-2-2-2-22000000000000-22-22-22-220000000000000000000000000000
χ3522222-2-2-22-220000222-2-2-2-200002-2-2-22-2-22222-20000000000002i−2i2i−2i−2i2i−2i2i0000000000000000000000000000
χ3622222-2-2-22-220000222-2-2-2-200002-2-2-22-2-22222-2000000000000−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000
χ372222-22-22-2-22000022222220000-22-22-2-2-22-2-22-20000000000000000000000002-22-22-22-20000000000000000
χ382222-22-22-2-22000022222220000-22-22-2-2-22-2-22-2000000000000000000000000-22-22-22-220000000000000000
χ392222-22-22-2-220000222-2-2-2-20000-22-22-2-22-222-220000000000000000000000002i−2i2i−2i−2i2i−2i2i0000000000000000
χ402222-22-22-2-220000222-2-2-2-20000-22-22-2-22-222-22000000000000000000000000−2i2i−2i2i2i−2i2i−2i0000000000000000
χ412222-2-22-2-2222-22-222222220000-2-22-2-22-2-222-2-22-22-200000000000000002-22-2000000000000000000000000
χ422222-2-22-2-2222-22-2222-2-2-2-20000-2-22-2-2222-2-2222-22-20000000000000000-22-22000000000000000000000000
χ432222-2-22-2-222-22-2222222220000-2-22-2-22-2-222-2-2-22-220000000000000000-22-22000000000000000000000000
χ442222-2-22-2-222-22-22222-2-2-2-20000-2-22-2-2222-2-222-22-2200000000000000002-22-2000000000000000000000000
χ4522-2-2222-2-2-2200002-2-222-2-20000222-2-2-2222-2-2-20000000000002-2-222-2-220000000000000000000000000000
χ4622-2-2222-2-2-2200002-2-222-2-20000222-2-2-2222-2-2-2000000000000-222-2-222-20000000000000000000000000000
χ4722-2-2222-2-2-2200002-2-2-2-2220000222-2-2-2-2-2-22220000000000002i−2i−2i2i−2i2i2i−2i0000000000000000000000000000
χ4822-2-2222-2-2-2200002-2-2-2-2220000222-2-2-2-2-2-2222000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000000000000000
χ4922-2-2-22-2-22222i−2i−2i2i2-2-222-2-20000-22-2-222-22-22-222i−2i−2i2i00000000000000002i−2i−2i2i000000000000000000000000
χ5022-2-2-22-2-22222i−2i−2i2i2-2-2-2-2220000-22-2-2222-22-22-22i−2i−2i2i0000000000000000−2i2i2i−2i000000000000000000000000
χ5122-2-2-22-2-2222−2i2i2i−2i2-2-222-2-20000-22-2-222-22-22-22−2i2i2i−2i0000000000000000−2i2i2i−2i000000000000000000000000
χ5222-2-2-22-2-2222−2i2i2i−2i2-2-2-2-2220000-22-2-2222-22-22-2−2i2i2i−2i00000000000000002i−2i−2i2i000000000000000000000000
χ5322-2-2-2-2222-2200002-2-222-2-20000-2-2222-2-2-22-2220000000000000000000000002i−2i−2i2i2i−2i−2i2i0000000000000000
χ5422-2-2-2-2222-2200002-2-222-2-20000-2-2222-2-2-22-222000000000000000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000
χ5522-2-2-2-2222-2200002-2-2-2-2220000-2-2222-222-22-2-20000000000000000000000002-2-22-222-20000000000000000
χ5622-2-2-2-2222-2200002-2-2-2-2220000-2-2222-222-22-2-2000000000000000000000000-222-22-2-220000000000000000
χ574444444444-14444-1-1-100004444-1-1-1-1-1-1000000-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000000000000000
χ584444444444-14444-1-1-10000-4-4-4-4-1-1-1-1-1-1000000-1-1-1-111111111000000000000000000000000000000000000
χ594444444444-1-4-4-4-4-1-1-1000044-4-4-1-1-1-1-1-10000001111-1-1-1-11111000000000000000000000000000000000000
χ604444444444-1-4-4-4-4-1-1-10000-4-444-1-1-1-1-1-100000011111111-1-1-1-1000000000000000000000000000000000000
χ614444-4-44-4-44-14-44-4-1-1-10000000011-111-1000000-11-115−55−55−55−5000000000000000000000000000000000000
χ624444-4-44-4-44-14-44-4-1-1-10000000011-111-1000000-11-11−55−55−55−55000000000000000000000000000000000000
χ634444-4-44-4-44-1-44-44-1-1-10000000011-111-10000001-11-15−55−5−55−55000000000000000000000000000000000000
χ644444-4-44-4-44-1-44-44-1-1-10000000011-111-10000001-11-1−55−555−55−5000000000000000000000000000000000000
χ6544-4-44-4-44-44-14i4i−4i−4i-11100004i−4i4-4-111-11-1000000−i−iii−i−iii-1-111000000000000000000000000000000000000
χ6644-4-44-4-44-44-14i4i−4i−4i-1110000−4i4i-44-111-11-1000000−i−iiiii−i−i11-1-1000000000000000000000000000000000000
χ6744-4-44-4-44-44-1−4i−4i4i4i-11100004i−4i-44-111-11-1000000ii−i−i−i−iii11-1-1000000000000000000000000000000000000
χ6844-4-44-4-44-44-1−4i−4i4i4i-1110000−4i4i4-4-111-11-1000000ii−i−iii−i−i-1-111000000000000000000000000000000000000
χ6944-4-4-44-4-444-14i−4i−4i4i-111000000001-111-1-1000000−iii−ii5−i5−i5i55−5−55000000000000000000000000000000000000
χ7044-4-4-44-4-444-14i−4i−4i4i-111000000001-111-1-1000000−iii−i−i5i5i5−i5−555−5000000000000000000000000000000000000
χ7144-4-4-44-4-444-1−4i4i4i−4i-111000000001-111-1-1000000i−i−iii5−i5−i5i5−555−5000000000000000000000000000000000000
χ7244-4-4-44-4-444-1−4i4i4i−4i-111000000001-111-1-1000000i−i−ii−i5i5i5−i55−5−55000000000000000000000000000000000000
χ734-44i−4i00000040000-44i−4i4-44i−4i000000000000000000000000000000000000000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900000000
χ744-44i−4i00000040000-44i−4i4-44i−4i0000000000000000000000000000000000000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ3900000000
χ754-44i−4i00000040000-44i−4i-44−4i4i000000000000000000000000000000000000000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700000000
χ764-44i−4i00000040000-44i−4i-44−4i4i0000000000000000000000000000000000000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ3700000000
χ774-4−4i4i00000040000-4−4i4i4-4−4i4i000000000000000000000000000000000000000000000000−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ3700000000
χ784-4−4i4i00000040000-4−4i4i4-4−4i4i0000000000000000000000000000000000000000000000002ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ3700000000
χ794-4−4i4i00000040000-4−4i4i-444i−4i000000000000000000000000000000000000000000000000−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ392ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ3900000000
χ804-4−4i4i00000040000-4−4i4i-444i−4i0000000000000000000000000000000000000000000000002ζ13+2ζ21+2ζ29+2ζ37−2ζ13−2ζ21−2ζ29−2ζ37−2ζ7−2ζ23−2ζ31−2ζ392ζ7+2ζ23+2ζ31+2ζ39−2ζ13−2ζ21−2ζ29−2ζ372ζ13+2ζ21+2ζ29+2ζ372ζ7+2ζ23+2ζ31+2ζ39−2ζ7−2ζ23−2ζ31−2ζ3900000000
χ8188888-8-8-88-8-20000-2-2-200000000-2222-22000000000000000000000000000000000000000000000000000000
χ828888-88-88-8-8-20000-2-2-2000000002-22-222000000000000000000000000000000000000000000000000000000
χ8388-8-8888-8-8-8-20000-22200000000-2-2-2222000000000000000000000000000000000000000000000000000000
χ8488-8-8-8-8888-8-20000-2220000000022-2-2-22000000000000000000000000000000000000000000000000000000
χ8516-1616i−16i000000-400004−4i4i00000000000000000000000000000000000000000000000000000000000000000000
χ8616-16−16i16i000000-4000044i−4i00000000000000000000000000000000000000000000000000000000000000000000

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