Finite Group Databasebeta

← Group #13013931

Character table — Group #13013931

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size11112222222244444444444444444448888888888888888888888888888101010101010202020202040404040404040404040404080808080
order1222444488884588101010202020204040404040404040161616162020202040404040808080808080808080808080808080802244444888888888888161616168888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ311111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i-1-1-1-1ii−i−i
χ411111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii-1-1-1-1−i−iii
χ51111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111-1-1-1-1-1-1-1-1
χ61111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ71111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i1111−i−iii
χ81111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii1111ii−i−i
χ91111-1-111-1-1-1-1-11111111111-1-1-1-1-1-1-1-1ii−i−i-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i111-11-1-111-1-1ii−i−iii−i−iii−i−i1-11-1
χ101111-1-111-1-1-1-1-11111111111-1-1-1-1-1-1-1-1ii−i−i-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i111-11-1-111-1-1−i−iii−i−iiiii−i−i-11-11
χ111111-1-111-1-1-1-1-11111111111-1-1-1-1-1-1-1-1ii−i−i-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i-1-1-11-111-1-11111-1-1-1-111−i−iii−iii−i
χ121111-1-111-1-1-1-1-11111111111-1-1-1-1-1-1-1-1ii−i−i-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i-1-1-11-111-1-111-1-11111-1-1−i−iiii−i−ii
χ131111-1-111-1-1-1-1-11111111111-1-1-1-1-1-1-1-1−i−iii-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii111-11-1-111-1-1ii−i−iii−i−i−i−iii-11-11
χ141111-1-111-1-1-1-1-11111111111-1-1-1-1-1-1-1-1−i−iii-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii111-11-1-111-1-1−i−iii−i−iii−i−iii1-11-1
χ151111-1-111-1-1-1-1-11111111111-1-1-1-1-1-1-1-1−i−iii-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii-1-1-11-111-1-11111-1-1-1-111ii−i−ii−i−ii
χ161111-1-111-1-1-1-1-11111111111-1-1-1-1-1-1-1-1−i−iii-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii-1-1-11-111-1-111-1-11111-1-1ii−i−i−iii−i
χ1722222222-2-2-2-222-2-22222222-2-2-2-2-2-2-2-200002222-2-2-2-200000000000000002222222-2-2-2-20000000000000000
χ1822222222-2-2-2-222-2-22222222-2-2-2-2-2-2-2-200002222-2-2-2-20000000000000000-2-2-2-2-2-2-222220000000000000000
χ19222222-2-20000-2200222-2-2-2-200000000i2−i2i2−i222-2-20000i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i222-22-22-2000000000000i2−i2i2−i20000
χ20222222-2-20000-2200222-2-2-2-200000000i2−i2i2−i222-2-20000i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2-2-22-22-22000000000000−i2i2−i2i20000
χ21222222-2-20000-2200222-2-2-2-200000000−i2i2−i2i222-2-20000−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i222-22-22-2000000000000−i2i2−i2i20000
χ22222222-2-20000-2200222-2-2-2-200000000−i2i2−i2i222-2-20000−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2-2-22-22-22000000000000i2−i2i2−i20000
χ232222-2-2222222-22-2-22222222222222220000-2-2-2-2-2-2-2-20000000000000000222-22-2-2-2-2220000000000000000
χ242222-2-2222222-22-2-22222222222222220000-2-2-2-2-2-2-2-20000000000000000-2-2-22-22222-2-20000000000000000
χ252222-2-2-2-200002200222-2-2-2-2000000002−2−22-2-22200002222−2−2−2−2−2−2−2−2222222-2-2-2-220000000000002−2−220000
χ262222-2-2-2-200002200222-2-2-2-2000000002−2−22-2-22200002222−2−2−2−2−2−2−2−22222-2-22222-2000000000000−222−20000
χ272222-2-2-2-200002200222-2-2-2-200000000−222−2-2-2220000−2−2−2−222222222−2−2−2−222-2-2-2-22000000000000−222−20000
χ282222-2-2-2-200002200222-2-2-2-200000000−222−2-2-2220000−2−2−2−222222222−2−2−2−2-2-22222-20000000000002−2−220000
χ2922-2-2002-222-2-202002-2-222-2-22222-2-2-2-200000000000000000000000000002-220-200002-22−22−22−22−200000000
χ3022-2-2002-222-2-202002-2-222-2-22222-2-2-2-200000000000000000000000000002-220-200002-2−22−22−22−2200000000
χ3122-2-2002-222-2-202002-2-222-2-22222-2-2-2-20000000000000000000000000000-22-2020000-22i2−i2i2−i2−i2i2−i2i200000000
χ3222-2-2002-222-2-202002-2-222-2-22222-2-2-2-20000000000000000000000000000-22-2020000-22−i2i2−i2i2i2−i2i2−i200000000
χ3322-2-2002-2-2-22202002-2-222-2-2-2-2-2-2222200000000000000000000000000002-220-20000-22i2−i2−i2i2i2−i2−i2i200000000
χ3422-2-2002-2-2-22202002-2-222-2-2-2-2-2-2222200000000000000000000000000002-220-20000-22−i2i2i2−i2−i2i2i2−i200000000
χ3522-2-2002-2-2-22202002-2-222-2-2-2-2-2-222220000000000000000000000000000-22-20200002-22−2−22−222−200000000
χ3622-2-2002-2-2-22202002-2-222-2-2-2-2-2-222220000000000000000000000000000-22-20200002-2−222−22−2−2200000000
χ374444444444444-144-1-1-1-1-1-1-1-1-1-1-1-1-1-1-14444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000000
χ384444444444444-144-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-4-4-4-4-1-1-1-1-1-1-1-11111111111111111000000000000000000000000000
χ3944444444-4-4-4-44-1-4-4-1-1-1-1-1-1-1111111110000-1-1-1-11111i5i5−i5−i5i5i5−i5−i5i5i5−i5−i5i5i5−i5−i5000000000000000000000000000
χ4044444444-4-4-4-44-1-4-4-1-1-1-1-1-1-1111111110000-1-1-1-11111−i5−i5i5i5−i5−i5i5i5−i5−i5i5i5−i5−i5i5i5000000000000000000000000000
χ41444444-4-40000-4-100-1-1-11111i5i5−i5−i5i5i5−i5−i52i2−2i22i2−2i2-1-111i5i5−i5−i5ζ14+ζ42+ζ46+ζ58ζ14+ζ42+ζ46+ζ58ζ26+ζ62+ζ74+ζ78ζ26+ζ62+ζ74+ζ78−ζ14−ζ42−ζ46−ζ58−ζ14−ζ42−ζ46−ζ58−ζ26−ζ62−ζ74−ζ78−ζ26−ζ62−ζ74−ζ78ζ14+ζ42+ζ46+ζ58ζ14+ζ42+ζ46+ζ58ζ26+ζ62+ζ74+ζ78ζ26+ζ62+ζ74+ζ78−ζ14−ζ42−ζ46−ζ58−ζ14−ζ42−ζ46−ζ58−ζ26−ζ62−ζ74−ζ78−ζ26−ζ62−ζ74−ζ78000000000000000000000000000
χ42444444-4-40000-4-100-1-1-11111i5i5−i5−i5i5i5−i5−i5−2i22i2−2i22i2-1-111i5i5−i5−i5−ζ14−ζ42−ζ46−ζ58−ζ14−ζ42−ζ46−ζ58−ζ26−ζ62−ζ74−ζ78−ζ26−ζ62−ζ74−ζ78ζ14+ζ42+ζ46+ζ58ζ14+ζ42+ζ46+ζ58ζ26+ζ62+ζ74+ζ78ζ26+ζ62+ζ74+ζ78−ζ14−ζ42−ζ46−ζ58−ζ14−ζ42−ζ46−ζ58−ζ26−ζ62−ζ74−ζ78−ζ26−ζ62−ζ74−ζ78ζ14+ζ42+ζ46+ζ58ζ14+ζ42+ζ46+ζ58ζ26+ζ62+ζ74+ζ78ζ26+ζ62+ζ74+ζ78000000000000000000000000000
χ43444444-4-40000-4-100-1-1-11111−i5−i5i5i5−i5−i5i5i52i2−2i22i2−2i2-1-111−i5−i5i5i5ζ26+ζ62+ζ74+ζ78ζ26+ζ62+ζ74+ζ78ζ14+ζ42+ζ46+ζ58ζ14+ζ42+ζ46+ζ58−ζ26−ζ62−ζ74−ζ78−ζ26−ζ62−ζ74−ζ78−ζ14−ζ42−ζ46−ζ58−ζ14−ζ42−ζ46−ζ58ζ26+ζ62+ζ74+ζ78ζ26+ζ62+ζ74+ζ78ζ14+ζ42+ζ46+ζ58ζ14+ζ42+ζ46+ζ58−ζ26−ζ62−ζ74−ζ78−ζ26−ζ62−ζ74−ζ78−ζ14−ζ42−ζ46−ζ58−ζ14−ζ42−ζ46−ζ58000000000000000000000000000
χ44444444-4-40000-4-100-1-1-11111−i5−i5i5i5−i5−i5i5i5−2i22i2−2i22i2-1-111−i5−i5i5i5−ζ26−ζ62−ζ74−ζ78−ζ26−ζ62−ζ74−ζ78−ζ14−ζ42−ζ46−ζ58−ζ14−ζ42−ζ46−ζ58ζ26+ζ62+ζ74+ζ78ζ26+ζ62+ζ74+ζ78ζ14+ζ42+ζ46+ζ58ζ14+ζ42+ζ46+ζ58−ζ26−ζ62−ζ74−ζ78−ζ26−ζ62−ζ74−ζ78−ζ14−ζ42−ζ46−ζ58−ζ14−ζ42−ζ46−ζ58ζ26+ζ62+ζ74+ζ78ζ26+ζ62+ζ74+ζ78ζ14+ζ42+ζ46+ζ58ζ14+ζ42+ζ46+ζ58000000000000000000000000000
χ454444-4-4444444-4-1-4-4-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100001111111155−5−555−5−5−5−555−5−555000000000000000000000000000
χ464444-4-4444444-4-1-4-4-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000011111111−5−555−5−55555−5−555−5−5000000000000000000000000000
χ474444-4-444-4-4-4-4-4-144-1-1-1-1-1-1-1111111114i4i−4i−4i1111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii000000000000000000000000000
χ484444-4-444-4-4-4-4-4-144-1-1-1-1-1-1-111111111−4i−4i4i4i1111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i000000000000000000000000000
χ494444-4-4-4-400004-100-1-1-11111i5i5−i5−i5i5i5−i5−i522−22−222211-1-1−i5−i5i5i5−ζ14+ζ42−ζ46+ζ58−ζ14+ζ42−ζ46+ζ58ζ26−ζ62+ζ74−ζ78ζ26−ζ62+ζ74−ζ78ζ14−ζ42+ζ46−ζ58ζ14−ζ42+ζ46−ζ58−ζ26+ζ62−ζ74+ζ78−ζ26+ζ62−ζ74+ζ78ζ14−ζ42+ζ46−ζ58ζ14−ζ42+ζ46−ζ58−ζ26+ζ62−ζ74+ζ78−ζ26+ζ62−ζ74+ζ78−ζ14+ζ42−ζ46+ζ58−ζ14+ζ42−ζ46+ζ58ζ26−ζ62+ζ74−ζ78ζ26−ζ62+ζ74−ζ78000000000000000000000000000
χ504444-4-4-4-400004-100-1-1-11111i5i5−i5−i5i5i5−i5−i5−222222−2211-1-1−i5−i5i5i5ζ14−ζ42+ζ46−ζ58ζ14−ζ42+ζ46−ζ58−ζ26+ζ62−ζ74+ζ78−ζ26+ζ62−ζ74+ζ78−ζ14+ζ42−ζ46+ζ58−ζ14+ζ42−ζ46+ζ58ζ26−ζ62+ζ74−ζ78ζ26−ζ62+ζ74−ζ78−ζ14+ζ42−ζ46+ζ58−ζ14+ζ42−ζ46+ζ58ζ26−ζ62+ζ74−ζ78ζ26−ζ62+ζ74−ζ78ζ14−ζ42+ζ46−ζ58ζ14−ζ42+ζ46−ζ58−ζ26+ζ62−ζ74+ζ78−ζ26+ζ62−ζ74+ζ78000000000000000000000000000
χ514444-4-4-4-400004-100-1-1-11111−i5−i5i5i5−i5−i5i5i522−22−222211-1-1i5i5−i5−i5ζ26−ζ62+ζ74−ζ78ζ26−ζ62+ζ74−ζ78−ζ14+ζ42−ζ46+ζ58−ζ14+ζ42−ζ46+ζ58−ζ26+ζ62−ζ74+ζ78−ζ26+ζ62−ζ74+ζ78ζ14−ζ42+ζ46−ζ58ζ14−ζ42+ζ46−ζ58−ζ26+ζ62−ζ74+ζ78−ζ26+ζ62−ζ74+ζ78ζ14−ζ42+ζ46−ζ58ζ14−ζ42+ζ46−ζ58ζ26−ζ62+ζ74−ζ78ζ26−ζ62+ζ74−ζ78−ζ14+ζ42−ζ46+ζ58−ζ14+ζ42−ζ46+ζ58000000000000000000000000000
χ524444-4-4-4-400004-100-1-1-11111−i5−i5i5i5−i5−i5i5i5−222222−2211-1-1i5i5−i5−i5−ζ26+ζ62−ζ74+ζ78−ζ26+ζ62−ζ74+ζ78ζ14−ζ42+ζ46−ζ58ζ14−ζ42+ζ46−ζ58ζ26−ζ62+ζ74−ζ78ζ26−ζ62+ζ74−ζ78−ζ14+ζ42−ζ46+ζ58−ζ14+ζ42−ζ46+ζ58ζ26−ζ62+ζ74−ζ78ζ26−ζ62+ζ74−ζ78−ζ14+ζ42−ζ46+ζ58−ζ14+ζ42−ζ46+ζ58−ζ26+ζ62−ζ74+ζ78−ζ26+ζ62−ζ74+ζ78ζ14−ζ42+ζ46−ζ58ζ14−ζ42+ζ46−ζ58000000000000000000000000000
χ5344-4-400-44000004004-4-4-4-4440000000000000000000000000000000000004-4-4040000000000000000000000
χ5444-4-400-44000004004-4-4-4-444000000000000000000000000000000000000-4440-40000000000000000000000
χ554-44-4000022−2222−220400-44-4000022−2222−2222−2222−22000000000000000000000000000000040-4022−22000000000000000000
χ564-44-4000022−2222−220400-44-4000022−2222−2222−2222−220000000000000000000000000000000-4040−2222000000000000000000
χ574-44-40000−2222−22220400-44-40000−2222−2222−2222−2222000000000000000000000000000000040-40−2222000000000000000000
χ584-44-40000−2222−22220400-44-40000−2222−2222−2222−22220000000000000000000000000000000-404022−22000000000000000000
χ594-4-444i−4i0022−22−2222042i2−2i2-4-44000022−2222−22−2222−222200004i−4i002i2−2i22i2−2i20000000000000000000000000000000000000000000
χ604-4-444i−4i0022−22−22220-12i2−2i211-1i5−i5i5−i5−ζ14+ζ42−ζ46+ζ58ζ14−ζ42+ζ46−ζ58ζ26−ζ62+ζ74−ζ78−ζ26+ζ62−ζ74+ζ78ζ14−ζ42+ζ46−ζ58−ζ14+ζ42−ζ46+ζ58−ζ26+ζ62−ζ74+ζ78ζ26−ζ62+ζ74−ζ780000−ii5−5ζ26+ζ62+ζ74+ζ78−ζ26−ζ62−ζ74−ζ78ζ14+ζ42+ζ46+ζ58−ζ14−ζ42−ζ46−ζ58ζ9−ζ41−ζ47+ζ63−ζ9+ζ41+ζ47−ζ63ζ31−ζ57+ζ73−ζ79−ζ31+ζ57−ζ73+ζ79ζ27−ζ29−ζ43+ζ61−ζ27+ζ29+ζ43−ζ61−ζ11−ζ13+ζ59+ζ77ζ11+ζ13−ζ59−ζ77ζ27+ζ29−ζ43−ζ61−ζ27−ζ29+ζ43+ζ61ζ11−ζ13−ζ59+ζ77−ζ11+ζ13+ζ59−ζ77ζ9−ζ41+ζ47−ζ63−ζ9+ζ41−ζ47+ζ63−ζ31−ζ57+ζ73+ζ79ζ31+ζ57−ζ73−ζ79000000000000000000000000000
χ614-4-444i−4i0022−22−22220-12i2−2i211-1i5−i5i5−i5−ζ14+ζ42−ζ46+ζ58ζ14−ζ42+ζ46−ζ58ζ26−ζ62+ζ74−ζ78−ζ26+ζ62−ζ74+ζ78ζ14−ζ42+ζ46−ζ58−ζ14+ζ42−ζ46+ζ58−ζ26+ζ62−ζ74+ζ78ζ26−ζ62+ζ74−ζ780000−ii5−5ζ26+ζ62+ζ74+ζ78−ζ26−ζ62−ζ74−ζ78ζ14+ζ42+ζ46+ζ58−ζ14−ζ42−ζ46−ζ58−ζ9+ζ41+ζ47−ζ63ζ9−ζ41−ζ47+ζ63−ζ31+ζ57−ζ73+ζ79ζ31−ζ57+ζ73−ζ79−ζ27+ζ29+ζ43−ζ61ζ27−ζ29−ζ43+ζ61ζ11+ζ13−ζ59−ζ77−ζ11−ζ13+ζ59+ζ77−ζ27−ζ29+ζ43+ζ61ζ27+ζ29−ζ43−ζ61−ζ11+ζ13+ζ59−ζ77ζ11−ζ13−ζ59+ζ77−ζ9+ζ41−ζ47+ζ63ζ9−ζ41+ζ47−ζ63ζ31+ζ57−ζ73−ζ79−ζ31−ζ57+ζ73+ζ79000000000000000000000000000
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χ634-4-444i−4i0022−22−22220-12i2−2i211-1−i5i5−i5i5ζ26−ζ62+ζ74−ζ78−ζ26+ζ62−ζ74+ζ78−ζ14+ζ42−ζ46+ζ58ζ14−ζ42+ζ46−ζ58−ζ26+ζ62−ζ74+ζ78ζ26−ζ62+ζ74−ζ78ζ14−ζ42+ζ46−ζ58−ζ14+ζ42−ζ46+ζ580000−ii−55ζ14+ζ42+ζ46+ζ58−ζ14−ζ42−ζ46−ζ58ζ26+ζ62+ζ74+ζ78−ζ26−ζ62−ζ74−ζ78−ζ31+ζ57−ζ73+ζ79ζ31−ζ57+ζ73−ζ79ζ9−ζ41−ζ47+ζ63−ζ9+ζ41+ζ47−ζ63ζ11+ζ13−ζ59−ζ77−ζ11−ζ13+ζ59+ζ77ζ27−ζ29−ζ43+ζ61−ζ27+ζ29+ζ43−ζ61ζ11−ζ13−ζ59+ζ77−ζ11+ζ13+ζ59−ζ77−ζ27−ζ29+ζ43+ζ61ζ27+ζ29−ζ43−ζ61ζ31+ζ57−ζ73−ζ79−ζ31−ζ57+ζ73+ζ79ζ9−ζ41+ζ47−ζ63−ζ9+ζ41−ζ47+ζ63000000000000000000000000000
χ644-4-444i−4i00−222222−2204−2i22i2-4-440000−2222−222222−2222−2200004i−4i00−2i22i2−2i22i20000000000000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 80 (ζ80 = 1); i = ζ20.