Finite Group Databasebeta

← Group #13043340

Character table — Group #13043340

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size112222222224444455888888888888810101010101010101010101010101010101616161616161616161616202020202020202020202020202020404040404040404040404040
order1222244448858881022222410101020202020404022244448816161616161616161010101010102020404040888161616161616161616161616222444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1
χ3111111111111111111-1-1-1-111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111-1-11111111111111-1-1-1-1-1-1-1-1-1iiii−i−i−i−i11111111111-1-1-1iiiiii−i−i−i−i−i−i-1-1-1-1i−iiii−i−i−i
χ61111111111111111-1-11111111111111-1-1-1-1-1-1-1-1-1−i−i−i−iiiii11111111111-1-1-1−i−i−i−i−i−iiiiiii-1-1-1-1−ii−i−i−iiii
χ71111111111111111-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1iiii−i−i−i−i-1-1-1-1-1-1-1-1111-1-1-1iiiiii−i−i−i−i−i−i1111−ii−i−i−iiii
χ81111111111111111-1-1-1-1-1-1111111111-1-1-1-1-1-1-1-1-1−i−i−i−iiiii-1-1-1-1-1-1-1-1111-1-1-1−i−i−i−i−i−iiiiiii1111i−iiii−i−i−i
χ9111-1-11-1-111111-1-111111-1-11-1-11-1-11111-1-111-1-111111111111111-1-1-1-11-1-11-1-111-1-1-1-111-1-1-1-111-1-1-1-111-111-1
χ10111-1-11-1-111111-1-111111-1-11-1-11-1-11111-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11-1-11-1-1-1-11111-1-1111111-1-111-1-11-1-11
χ11111-1-11-1-111111-1-1111-1-1111-1-11-1-11111-1-111-1-11111111111-1-1-1-111111-1-11-1-111-1-1-1-111-1-1-1-1-1-11111-1-11-1-11
χ12111-1-11-1-111111-1-1111-1-1111-1-11-1-11111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-111111-1-11-1-1-1-11111-1-11111-1-111-1-111-111-1
χ13111-1-11-1-111111-1-11-1-111-1-11-1-11-1-1111-111-1-111-1-1iiii−i−i−i−i1111-1-1-1-11-1-1-111ii−i−i−i−i−i−iiiii-1-111−iiii−i−i−ii
χ14111-1-11-1-111111-1-11-1-111-1-11-1-11-1-1111-111-1-111-1-1−i−i−i−iiiii1111-1-1-1-11-1-1-111−i−iiiiiii−i−i−i−i-1-111i−i−i−iiii−i
χ15111-1-11-1-111111-1-11-1-1-1-1111-1-11-1-1111-111-1-111-1-1iiii−i−i−i−i-1-1-1-111111-1-1-111ii−i−i−i−i−i−iiiii11-1-1i−i−i−iiii−i
χ16111-1-11-1-111111-1-11-1-1-1-1111-1-11-1-1111-111-1-111-1-1−i−i−i−iiiii-1-1-1-111111-1-1-111−i−iiiiiii−i−i−i−i11-1-1−iiii−i−i−ii
χ1711-11-1-11-11111-11-11111-11-1-11-1-11-1111-11-11-11-1111111111111-1-111-1-1-11-1-11-1-1-111-1-1-1-111-1-11-11-1-1-11-111-11
χ1811-11-1-11-11111-11-11111-11-1-11-1-11-1111-11-11-11-111-1-1-1-1-1-1-1-111-1-111-1-1-11-1-11-111-1-11111-1-1111-11-111-11-1-11-1
χ1911-11-1-11-11111-11-1111-11-11-11-1-11-1111-11-11-11-11111111111-1-111-1-111-11-1-11-1-1-111-1-1-1-111-1-1-11-1111-11-1-11-1
χ2011-11-1-11-11111-11-1111-11-11-11-1-11-1111-11-11-11-111-1-1-1-1-1-1-1-1-1-111-1-111-11-1-11-111-1-11111-1-111-11-11-1-11-111-11
χ2111-11-1-11-11111-11-11-1-11-11-1-11-1-11-11111-11-11-11-1-1iiii−i−i−i−i11-1-111-1-1-11-11-11−i−iii−i−iii−i−iii-11-11−iii−ii−ii−i
χ2211-11-1-11-11111-11-11-1-11-11-1-11-1-11-11111-11-11-11-1-1−i−i−i−iiiii11-1-111-1-1-11-11-11ii−i−iii−i−iii−i−i-11-11i−i−ii−ii−ii
χ2311-11-1-11-11111-11-11-1-1-11-11-11-1-11-11111-11-11-11-1-1iiii−i−i−i−i-1-111-1-111-11-11-11−i−iii−i−iii−i−iii1-11-1i−i−ii−ii−ii
χ2411-11-1-11-11111-11-11-1-1-11-11-11-1-11-11111-11-11-11-1-1−i−i−i−iiiii-1-111-1-111-11-11-11ii−i−iii−i−iii−i−i1-11-1−iii−ii−ii−i
χ2511-1-11-1-111111-1-111111-1-11-1-11-1-11111-1-111-1-11111111111111-1-1-1-111-1-11-1-11-1-1-1-111-1-1-1-1111-1-11111-1-11-1-1
χ2611-1-11-1-111111-1-111111-1-11-1-11-1-11111-1-111-1-1111-1-1-1-1-1-1-1-111-1-1-1-111-1-11-1-111111-1-11111-1-11-1-11-1-1-111-111
χ2711-1-11-1-111111-1-11111-111-1-1-11-1-11111-1-111-1-111111111111-1-11111-1-1-1-11-1-11-1-1-1-111-1-1-1-111-111-1-1-1-111-111
χ2811-1-11-1-111111-1-11111-111-1-1-11-1-11111-1-111-1-1111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11-1-111111-1-11111-1-1-111-1111-1-11-1-1
χ2911-1-11-1-111111-1-111-1-11-1-11-1-11-1-1111111-1-111-1-1-1iiii−i−i−i−i11-1-1-1-111-1-1111-1−i−i−i−iiiiiii−i−i-111-1i−ii−i−i−iii
χ3011-1-11-1-111111-1-111-1-11-1-11-1-11-1-1111111-1-111-1-1-1−i−i−i−iiiii11-1-1-1-111-1-1111-1iiii−i−i−i−i−i−iii-111-1−ii−iiii−i−i
χ3111-1-11-1-111111-1-111-1-1-111-1-1-11-1-1111111-1-111-1-1-1iiii−i−i−i−i-1-11111-1-1-1-1111-1−i−i−i−iiiiiii−i−i1-1-11−ii−iiii−i−i
χ3211-1-11-1-111111-1-111-1-1-111-1-1-11-1-1111111-1-111-1-1-1−i−i−i−iiiii-1-11111-1-1-1-1111-1iiii−i−i−i−i−i−iii1-1-11i−ii−i−i−iii
χ33222222222-2-22-2-2-222200002222222-2-22222222-2-20000000000000000-2-2-2-2-2-2000000000000000000000000
χ34222222222-2-22-2-2-22-2-200002222222-2-2-2-2-2-2-2-2-2220000000000000000-2-2-2222000000000000000000000000
χ352222-2-2-22-2002000222000022-2-2-22-20022-2-2-2-220022−2−222−2−2000000000000002−22−22−22−22−22−2000000000000
χ362222-2-2-22-2002000222000022-2-2-22-20022-2-2-2-2200−2−222−2−22200000000000000−22−22−22−22−22−22000000000000
χ372222-2-2-22-20020002-2-2000022-2-2-22-200-2-22222-200i2i2−i2−i2−i2−i2i2i200000000000000i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2000000000000
χ382222-2-2-22-20020002-2-2000022-2-2-22-200-2-22222-200−i2−i2i2i2i2i2−i2−i200000000000000−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2000000000000
χ39222-22-22-2-200200022200002-22-22-2-2002-22-2-22-20022−2−222−2−2000000000000002−2−22−222−2−22−22000000000000
χ40222-22-22-2-200200022200002-22-22-2-2002-22-2-22-200−2−222−2−22200000000000000−222−22−2−222−22−2000000000000
χ41222-22-22-2-20020002-2-200002-22-22-2-200-22-222-2200i2i2−i2−i2−i2−i2i2i200000000000000i2−i2−i2i2−i2i2−i2i2i2−i2i2−i2000000000000
χ42222-22-22-2-20020002-2-200002-22-22-2-200-22-222-2200−i2−i2i2i2i2i2−i2−i200000000000000−i2i2i2−i2i2−i2i2−i2−i2i2−i2i2000000000000
χ43222-2-22-2-22-2-22-22222200002-2-22-2-22-2-22-2-222-2-2-2-20000000000000000-222-222000000000000000000000000
χ44222-2-22-2-22-2-22-2222-2-200002-2-22-2-22-2-2-222-2-222220000000000000000-2222-2-2000000000000000000000000
χ4522-2222-2-2-20020002220000-2222-2-2-200-222-22-2-20022−2−222−2−200000000000000−222−2−22−222−2−22000000000000
χ4622-2222-2-2-20020002220000-2222-2-2-200-222-22-2-200−2−222−2−222000000000000002−2−222−22−2−222−2000000000000
χ4722-2222-2-2-20020002-2-20000-2222-2-2-2002-2-22-22200i2i2−i2−i2−i2−i2i2i200000000000000−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2000000000000
χ4822-2222-2-2-20020002-2-20000-2222-2-2-2002-2-22-22200−i2−i2i2i2i2i2−i2−i200000000000000i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2000000000000
χ4922-22-2-22-22-2-222-222220000-22-2-22-22-2-2-22-22-22-2-2-200000000000000002-222-22000000000000000000000000
χ5022-22-2-22-22-2-222-222-2-20000-22-2-22-22-2-22-22-22-222200000000000000002-22-22-2000000000000000000000000
χ5122-2-22-2-222-2-2222-22220000-2-22-2-222-2-2-2-222-2-22-2-2000000000000000022-222-2000000000000000000000000
χ5222-2-22-2-222-2-2222-22-2-20000-2-22-2-222-2-222-2-222-222000000000000000022-2-2-22000000000000000000000000
χ5322-2-2-2222-20020002220000-2-2-2222-200-2-2-2-22220022−2−222−2−200000000000000−22−222−2−22−222−2000000000000
χ5422-2-2-2222-20020002220000-2-2-2222-200-2-2-2-222200−2−222−2−222000000000000002−22−2−222−22−2−22000000000000
χ5522-2-2-2222-20020002-2-20000-2-2-2222-2002222-2-2-200i2i2−i2−i2−i2−i2i2i200000000000000−i2i2−i2i2i2−i2i2−i2i2−i2−i2i2000000000000
χ5622-2-2-2222-20020002-2-20000-2-2-2222-2002222-2-2-200−i2−i2i2i2i2i2−i2−i200000000000000i2−i2i2−i2−i2i2−i2i2−i2i2i2−i2000000000000
χ5744444444444-1444-1004444-1-1-1-1-1-1-1-1-100000000000000000-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000000
χ5844444444444-1444-100-4-4-4-4-1-1-1-1-1-1-1-1-10000000000000000011111111-1-1-1000000000000000000000000000
χ59444444444-4-4-1-4-4-4-1000000-1-1-1-1-1-1-111000000000000000005−55−55−55−5111000000000000000000000000000
χ60444444444-4-4-1-4-4-4-1000000-1-1-1-1-1-1-11100000000000000000−55−55−55−55111000000000000000000000000000
χ61444-4-44-4-4444-14-4-4-10044-4-4-111-111-1-1-100000000000000000-1-1-1-11111-111000000000000000000000000000
χ62444-4-44-4-4444-14-4-4-100-4-444-111-111-1-1-1000000000000000001111-1-1-1-1-111000000000000000000000000000
χ63444-4-44-4-44-4-4-1-444-1000000-111-111-111000000000000000005−55−5−55−551-1-1000000000000000000000000000
χ64444-4-44-4-44-4-4-1-444-1000000-111-111-11100000000000000000−55−555−55−51-1-1000000000000000000000000000
χ6544-44-4-44-4444-1-44-4-1004-44-41-111-11-1-1-100000000000000000-1-111-1-1111-11000000000000000000000000000
χ6644-44-4-44-4444-1-44-4-100-44-441-111-11-1-1-10000000000000000011-1-111-1-11-11000000000000000000000000000
χ6744-44-4-44-44-4-4-14-44-10000001-111-11-111000000000000000005−5−555−5−55-11-1000000000000000000000000000
χ6844-44-4-44-44-4-4-14-44-10000001-111-11-11100000000000000000−555−5−555−5-11-1000000000000000000000000000
χ6944-4-44-4-44444-1-4-44-1004-4-4411-111-1-1-1-100000000000000000-1-11111-1-111-1000000000000000000000000000
χ7044-4-44-4-44444-1-4-44-100-444-411-111-1-1-1-10000000000000000011-1-1-1-11111-1000000000000000000000000000
χ7144-4-44-4-444-4-4-144-4-100000011-111-1-111000000000000000005−5−55−555−5-1-11000000000000000000000000000
χ7244-4-44-4-444-4-4-144-4-100000011-111-1-11100000000000000000−555−55−5−55-1-11000000000000000000000000000
χ734-4000000022−224000-44-40000000000022−22000000022−22−2ζ9−2ζ31−2ζ41−2ζ47−2ζ57−2ζ63−2ζ73−2ζ792ζ9+2ζ31+2ζ41+2ζ47+2ζ57+2ζ63+2ζ73+2ζ79−2ζ11−2ζ13−2ζ27−2ζ29−2ζ43−2ζ59−2ζ61−2ζ772ζ11+2ζ13+2ζ27+2ζ29+2ζ43+2ζ59+2ζ61+2ζ77−2ζ9−2ζ31−2ζ41−2ζ47−2ζ57−2ζ63−2ζ73−2ζ792ζ9+2ζ31+2ζ41+2ζ47+2ζ57+2ζ63+2ζ73+2ζ79−2ζ11−2ζ13−2ζ27−2ζ29−2ζ43−2ζ59−2ζ61−2ζ772ζ11+2ζ13+2ζ27+2ζ29+2ζ43+2ζ59+2ζ61+2ζ7700000000000000000000000000000000000000
χ744-4000000022−224000-44-40000000000022−22000000022−222ζ9+2ζ31+2ζ41+2ζ47+2ζ57+2ζ63+2ζ73+2ζ79−2ζ9−2ζ31−2ζ41−2ζ47−2ζ57−2ζ63−2ζ73−2ζ792ζ11+2ζ13+2ζ27+2ζ29+2ζ43+2ζ59+2ζ61+2ζ77−2ζ11−2ζ13−2ζ27−2ζ29−2ζ43−2ζ59−2ζ61−2ζ772ζ9+2ζ31+2ζ41+2ζ47+2ζ57+2ζ63+2ζ73+2ζ79−2ζ9−2ζ31−2ζ41−2ζ47−2ζ57−2ζ63−2ζ73−2ζ792ζ11+2ζ13+2ζ27+2ζ29+2ζ43+2ζ59+2ζ61+2ζ77−2ζ11−2ζ13−2ζ27−2ζ29−2ζ43−2ζ59−2ζ61−2ζ7700000000000000000000000000000000000000
χ754-4000000022−224000-4-440000000000022−220000000−2222−2ζ11+2ζ13−2ζ27+2ζ29−2ζ43−2ζ59+2ζ61+2ζ772ζ11−2ζ13+2ζ27−2ζ29+2ζ43+2ζ59−2ζ61−2ζ77−2ζ9+2ζ31−2ζ41+2ζ47−2ζ57+2ζ63−2ζ73+2ζ792ζ9−2ζ31+2ζ41−2ζ47+2ζ57−2ζ63+2ζ73−2ζ792ζ11−2ζ13+2ζ27−2ζ29+2ζ43+2ζ59−2ζ61−2ζ77−2ζ11+2ζ13−2ζ27+2ζ29−2ζ43−2ζ59+2ζ61+2ζ772ζ9−2ζ31+2ζ41−2ζ47+2ζ57−2ζ63+2ζ73−2ζ79−2ζ9+2ζ31−2ζ41+2ζ47−2ζ57+2ζ63−2ζ73+2ζ7900000000000000000000000000000000000000
χ764-4000000022−224000-4-440000000000022−220000000−22222ζ11−2ζ13+2ζ27−2ζ29+2ζ43+2ζ59−2ζ61−2ζ77−2ζ11+2ζ13−2ζ27+2ζ29−2ζ43−2ζ59+2ζ61+2ζ772ζ9−2ζ31+2ζ41−2ζ47+2ζ57−2ζ63+2ζ73−2ζ79−2ζ9+2ζ31−2ζ41+2ζ47−2ζ57+2ζ63−2ζ73+2ζ79−2ζ11+2ζ13−2ζ27+2ζ29−2ζ43−2ζ59+2ζ61+2ζ772ζ11−2ζ13+2ζ27−2ζ29+2ζ43+2ζ59−2ζ61−2ζ77−2ζ9+2ζ31−2ζ41+2ζ47−2ζ57+2ζ63−2ζ73+2ζ792ζ9−2ζ31+2ζ41−2ζ47+2ζ57−2ζ63+2ζ73−2ζ7900000000000000000000000000000000000000
χ774-40000000−22224000-44-400000000000−22220000000−2222−2ζ11−2ζ13−2ζ27−2ζ29−2ζ43−2ζ59−2ζ61−2ζ772ζ11+2ζ13+2ζ27+2ζ29+2ζ43+2ζ59+2ζ61+2ζ772ζ9+2ζ31+2ζ41+2ζ47+2ζ57+2ζ63+2ζ73+2ζ79−2ζ9−2ζ31−2ζ41−2ζ47−2ζ57−2ζ63−2ζ73−2ζ79−2ζ11−2ζ13−2ζ27−2ζ29−2ζ43−2ζ59−2ζ61−2ζ772ζ11+2ζ13+2ζ27+2ζ29+2ζ43+2ζ59+2ζ61+2ζ772ζ9+2ζ31+2ζ41+2ζ47+2ζ57+2ζ63+2ζ73+2ζ79−2ζ9−2ζ31−2ζ41−2ζ47−2ζ57−2ζ63−2ζ73−2ζ7900000000000000000000000000000000000000
χ784-40000000−22224000-44-400000000000−22220000000−22222ζ11+2ζ13+2ζ27+2ζ29+2ζ43+2ζ59+2ζ61+2ζ77−2ζ11−2ζ13−2ζ27−2ζ29−2ζ43−2ζ59−2ζ61−2ζ77−2ζ9−2ζ31−2ζ41−2ζ47−2ζ57−2ζ63−2ζ73−2ζ792ζ9+2ζ31+2ζ41+2ζ47+2ζ57+2ζ63+2ζ73+2ζ792ζ11+2ζ13+2ζ27+2ζ29+2ζ43+2ζ59+2ζ61+2ζ77−2ζ11−2ζ13−2ζ27−2ζ29−2ζ43−2ζ59−2ζ61−2ζ77−2ζ9−2ζ31−2ζ41−2ζ47−2ζ57−2ζ63−2ζ73−2ζ792ζ9+2ζ31+2ζ41+2ζ47+2ζ57+2ζ63+2ζ73+2ζ7900000000000000000000000000000000000000
χ794-40000000−22224000-4-4400000000000−2222000000022−222ζ9−2ζ31+2ζ41−2ζ47+2ζ57−2ζ63+2ζ73−2ζ79−2ζ9+2ζ31−2ζ41+2ζ47−2ζ57+2ζ63−2ζ73+2ζ79−2ζ11+2ζ13−2ζ27+2ζ29−2ζ43−2ζ59+2ζ61+2ζ772ζ11−2ζ13+2ζ27−2ζ29+2ζ43+2ζ59−2ζ61−2ζ77−2ζ9+2ζ31−2ζ41+2ζ47−2ζ57+2ζ63−2ζ73+2ζ792ζ9−2ζ31+2ζ41−2ζ47+2ζ57−2ζ63+2ζ73−2ζ792ζ11−2ζ13+2ζ27−2ζ29+2ζ43+2ζ59−2ζ61−2ζ77−2ζ11+2ζ13−2ζ27+2ζ29−2ζ43−2ζ59+2ζ61+2ζ7700000000000000000000000000000000000000
χ804-40000000−22224000-4-4400000000000−2222000000022−22−2ζ9+2ζ31−2ζ41+2ζ47−2ζ57+2ζ63−2ζ73+2ζ792ζ9−2ζ31+2ζ41−2ζ47+2ζ57−2ζ63+2ζ73−2ζ792ζ11−2ζ13+2ζ27−2ζ29+2ζ43+2ζ59−2ζ61−2ζ77−2ζ11+2ζ13−2ζ27+2ζ29−2ζ43−2ζ59+2ζ61+2ζ772ζ9−2ζ31+2ζ41−2ζ47+2ζ57−2ζ63+2ζ73−2ζ79−2ζ9+2ζ31−2ζ41+2ζ47−2ζ57+2ζ63−2ζ73+2ζ79−2ζ11+2ζ13−2ζ27+2ζ29−2ζ43−2ζ59+2ζ61+2ζ772ζ11−2ζ13+2ζ27−2ζ29+2ζ43+2ζ59−2ζ61−2ζ7700000000000000000000000000000000000000
χ818888-8-8-88-800-2000-2000000-2-2222-22000000000000000000000000000000000000000000000000000000000
χ82888-88-88-8-800-2000-2000000-22-22-222000000000000000000000000000000000000000000000000000000000
χ8388-8888-8-8-800-2000-20000002-2-2-2222000000000000000000000000000000000000000000000000000000000
χ8488-8-8-8888-800-2000-2000000222-2-2-22000000000000000000000000000000000000000000000000000000000
χ8516-16000000082−82-400040000000000000−22220000000000000000000000000000000000000000000000000000000
χ8616-160000000−8282-40004000000000000022−220000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 80 (ζ80 = 1); i = ζ20.