Finite Group Databasebeta

← Group #13025148

Character table — Group #13025148

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86
size11112222222244444444444444444448888888888888888888888888888101010101010202020202040404040404040404040404080808080
order1222444488882588101010202020204040404040404040101016161616202040404040808080808080808080808080808080804444444888888888888161616168888
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
χ5111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111111-1-1-1-1-1-1-1-1
χ6111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ7111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i1111−i−iii
χ8111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii1111ii−i−i
χ91111-1-1111111-11-1-1111111111111111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1111-1-1ii−i−iii−i−i11-1-1i−ii−i
χ101111-1-1111111-11-1-1111111111111111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1111-1-1−i−iii−i−iii11-1-1−ii−ii
χ111111-1-1111111-11-1-1111111111111111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-11111-1-1-1-111-1-1111-1-11
χ121111-1-1111111-11-1-1111111111111111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-111-1-11111-1-1-1-111-111-1
χ131111-1-1111111-11-1-1111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1111-1-1ii−i−iii−i−i-1-111−ii−ii
χ141111-1-1111111-11-1-1111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1111-1-1−i−iii−i−iii-1-111i−ii−i
χ151111-1-1111111-11-1-1111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-11111-1-1-1-11111-1-1-111-1
χ161111-1-1111111-11-1-1111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-111-1-11111-1-111-1-11-1-11
χ1722222222-2-2-2-222-2-22222222-2-2-2-2-2-2-2-222000022-2-2-2-200000000000000002222222-2-2-2-20000000000000000
χ1822222222-2-2-2-222-2-22222222-2-2-2-2-2-2-2-222000022-2-2-2-20000000000000000-2-2-2-2-2-2-222220000000000000000
χ19222222-2-20000-2200222-2-2-2-200000000-2-2i2−i2i2−i2220000i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i22222-2-2-2000000000000i2−i2i2−i20000
χ20222222-2-20000-2200222-2-2-2-200000000-2-2i2−i2i2−i2220000i2i2i2i2−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2-2-2-2-2222000000000000−i2i2−i2i20000
χ21222222-2-20000-2200222-2-2-2-200000000-2-2−i2i2−i2i2220000−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i22222-2-2-2000000000000−i2i2−i2i20000
χ22222222-2-20000-2200222-2-2-2-200000000-2-2−i2i2−i2i2220000−i2−i2−i2−i2i2i2i2i2−i2−i2−i2−i2i2i2i2i2-2-2-2-2222000000000000i2−i2i2−i20000
χ232222-2-222-2-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-20000-2-22222000000000000000022-2-2-2-22-2-2220000000000000000
χ242222-2-222-2-2-2-2-22222222222-2-2-2-2-2-2-2-2-2-20000-2-222220000000000000000-2-22222-222-2-20000000000000000
χ252222-2-2-2-200002200222-2-2-2-20000000022i2−i2−i2i2-2-20000i2i2i2i2−i2−i2−i2−i2−i2−i2−i2−i2i2i2i2i222-2-222-2000000000000i2−i2−i2i20000
χ262222-2-2-2-200002200222-2-2-2-20000000022i2−i2−i2i2-2-20000i2i2i2i2−i2−i2−i2−i2−i2−i2−i2−i2i2i2i2i2-2-222-2-22000000000000−i2i2i2−i20000
χ272222-2-2-2-200002200222-2-2-2-20000000022−i2i2i2−i2-2-20000−i2−i2−i2−i2i2i2i2i2i2i2i2i2−i2−i2−i2−i222-2-222-2000000000000−i2i2i2−i20000
χ282222-2-2-2-200002200222-2-2-2-20000000022−i2i2i2−i2-2-20000−i2−i2−i2−i2i2i2i2i2i2i2i2i2−i2−i2−i2−i2-2-222-2-22000000000000i2−i2−i2i20000
χ2922-2-2002-222-2-20200-2-22-2-2222222-2-2-2-20000000000000000000000000000002i−2i2i−2i0002i−2i00−2ζ26−2ζ42−2ζ58−2ζ742ζ26+2ζ42+2ζ58+2ζ74−2ζ14−2ζ46−2ζ62−2ζ782ζ14+2ζ46+2ζ62+2ζ780000000000
χ3022-2-2002-222-2-20200-2-22-2-2222222-2-2-2-20000000000000000000000000000002i−2i2i−2i0002i−2i002ζ26+2ζ42+2ζ58+2ζ74−2ζ26−2ζ42−2ζ58−2ζ742ζ14+2ζ46+2ζ62+2ζ78−2ζ14−2ζ46−2ζ62−2ζ780000000000
χ3122-2-2002-222-2-20200-2-22-2-2222222-2-2-2-2000000000000000000000000000000−2i2i−2i2i000−2i2i00−2ζ14−2ζ46−2ζ62−2ζ782ζ14+2ζ46+2ζ62+2ζ78−2ζ26−2ζ42−2ζ58−2ζ742ζ26+2ζ42+2ζ58+2ζ740000000000
χ3222-2-2002-222-2-20200-2-22-2-2222222-2-2-2-2000000000000000000000000000000−2i2i−2i2i000−2i2i002ζ14+2ζ46+2ζ62+2ζ78−2ζ14−2ζ46−2ζ62−2ζ782ζ26+2ζ42+2ζ58+2ζ74−2ζ26−2ζ42−2ζ58−2ζ740000000000
χ3322-2-2002-2-2-2220200-2-22-2-222-2-2-2-222220000000000000000000000000000002i−2i2i−2i000−2i2i−2ζ26−2ζ42−2ζ58−2ζ742ζ26+2ζ42+2ζ58+2ζ740000−2ζ14−2ζ46−2ζ62−2ζ782ζ14+2ζ46+2ζ62+2ζ7800000000
χ3422-2-2002-2-2-2220200-2-22-2-222-2-2-2-222220000000000000000000000000000002i−2i2i−2i000−2i2i2ζ26+2ζ42+2ζ58+2ζ74−2ζ26−2ζ42−2ζ58−2ζ7400002ζ14+2ζ46+2ζ62+2ζ78−2ζ14−2ζ46−2ζ62−2ζ7800000000
χ3522-2-2002-2-2-2220200-2-22-2-222-2-2-2-22222000000000000000000000000000000−2i2i−2i2i0002i−2i−2ζ14−2ζ46−2ζ62−2ζ782ζ14+2ζ46+2ζ62+2ζ780000−2ζ26−2ζ42−2ζ58−2ζ742ζ26+2ζ42+2ζ58+2ζ7400000000
χ3622-2-2002-2-2-2220200-2-22-2-222-2-2-2-22222000000000000000000000000000000−2i2i−2i2i0002i−2i2ζ14+2ζ46+2ζ62+2ζ78−2ζ14−2ζ46−2ζ62−2ζ7800002ζ26+2ζ42+2ζ58+2ζ74−2ζ26−2ζ42−2ζ58−2ζ7400000000
χ374444444444444-144-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-14444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000000
χ384444444444444-144-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-4-4-4-4-1-1-1-1-1-11111111111111111000000000000000000000000000
χ3944444444-4-4-4-44-1-4-4-1-1-1-1-1-1-111111111-1-10000-1-11111i5i5−i5−i5i5i5−i5−i5i5i5−i5−i5i5i5−i5−i5000000000000000000000000000
χ4044444444-4-4-4-44-1-4-4-1-1-1-1-1-1-111111111-1-10000-1-11111−i5−i5i5i5−i5−i5i5i5−i5−i5i5i5−i5−i5i5i5000000000000000000000000000
χ41444444-4-40000-4-100-1-1-11111i5i5−i5−i5i5i5−i5−i5112i2−2i22i2−2i2-1-1i5i5−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−i511−2i22i2−2i22i2-1-1i5i5−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−i5i5i5112i2−2i22i2−2i2-1-1−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−i5i5i511−2i22i2−2i22i2-1-1−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
χ454444-4-4444444-4-1-4-4-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11144-4-4111111-1-1-1-1-1-1-1-111111111000000000000000000000000000
χ464444-4-4444444-4-1-4-4-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-4-44411111111111111-1-1-1-1-1-1-1-1000000000000000000000000000
χ474444-4-444-4-4-4-4-4-144-1-1-1-1-1-1-11111111111000011-1-1-1-1i5i5−i5−i5i5i5−i5−i5−i5−i5i5i5−i5−i5i5i5000000000000000000000000000
χ484444-4-444-4-4-4-4-4-144-1-1-1-1-1-1-11111111111000011-1-1-1-1−i5−i5i5i5−i5−i5i5i5i5i5−i5−i5i5i5−i5−i5000000000000000000000000000
χ494444-4-4-4-400004-100-1-1-11111i5i5−i5−i5i5i5−i5−i5-1-12i2−2i2−2i22i211−i5−i5i5i5ζ14+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−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
χ504444-4-4-4-400004-100-1-1-11111i5i5−i5−i5i5i5−i5−i5-1-1−2i22i22i2−2i211−i5−i5i5i5−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+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
χ514444-4-4-4-400004-100-1-1-11111−i5−i5i5i5−i5−i5i5i5-1-12i2−2i2−2i22i211i5i5−i5−i5ζ26+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−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
χ524444-4-4-4-400004-100-1-1-11111−i5−i5i5i5−i5−i5i5i5-1-1−2i22i22i2−2i211i5i5−i5−i5−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+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
χ5344-4-400-4400000400-4-4444-4-4000000000000000000000000000000000000004i−4i−4i4i000000000000000000000
χ5444-4-400-4400000400-4-4444-4-400000000000000000000000000000000000000−4i4i4i−4i000000000000000000000
χ554-44-400002i2−2i22i2−2i204004-4-400002i2−2i22i2−2i22i2−2i22i2−2i200000000000000000000000000004i−4i0000022−22000000000000000000
χ564-44-400002i2−2i22i2−2i204004-4-400002i2−2i22i2−2i22i2−2i22i2−2i20000000000000000000000000000−4i4i00000−2222000000000000000000
χ574-44-40000−2i22i2−2i22i204004-4-40000−2i22i2−2i22i2−2i22i2−2i22i200000000000000000000000000004i−4i00000−2222000000000000000000
χ584-44-40000−2i22i2−2i22i204004-4-40000−2i22i2−2i22i2−2i22i2−2i22i20000000000000000000000000000−4i4i0000022−22000000000000000000
χ594-4-444i−4i002i2−2i2−2i22i20422−22-44-400002i2−2i22i2−2i2−2i22i2−2i22i20000004i−4i22−2222−220000000000000000000000000000000000000000000
χ604-4-444i−4i002i2−2i2−2i22i20-122−221-11i5−i5i5−i5ζ14+ζ42+ζ46+ζ58−ζ14−ζ42−ζ46−ζ58ζ26+ζ62+ζ74+ζ78−ζ26−ζ62−ζ74−ζ78−ζ14−ζ42−ζ46−ζ58ζ14+ζ42+ζ46+ζ58−ζ26−ζ62−ζ74−ζ78ζ26+ζ62+ζ74+ζ785−50000−iiζ26−ζ62+ζ74−ζ78−ζ26+ζ62−ζ74+ζ78−ζ14+ζ42−ζ46+ζ58ζ14−ζ42+ζ46−ζ58ζ29−ζ47−ζ61+ζ63−ζ29+ζ47+ζ61−ζ63−ζ13−ζ31+ζ77+ζ79ζ13+ζ31−ζ77−ζ79ζ9+ζ27−ζ41−ζ43−ζ9−ζ27+ζ41+ζ43−ζ11−ζ57+ζ59+ζ73ζ11+ζ57−ζ59−ζ73ζ9−ζ27−ζ41+ζ43−ζ9+ζ27+ζ41−ζ43ζ11−ζ57−ζ59+ζ73−ζ11+ζ57+ζ59−ζ73−ζ29−ζ47+ζ61+ζ63ζ29+ζ47−ζ61−ζ63−ζ13+ζ31+ζ77−ζ79ζ13−ζ31−ζ77+ζ79000000000000000000000000000
χ614-4-444i−4i002i2−2i2−2i22i20-122−221-11i5−i5i5−i5ζ14+ζ42+ζ46+ζ58−ζ14−ζ42−ζ46−ζ58ζ26+ζ62+ζ74+ζ78−ζ26−ζ62−ζ74−ζ78−ζ14−ζ42−ζ46−ζ58ζ14+ζ42+ζ46+ζ58−ζ26−ζ62−ζ74−ζ78ζ26+ζ62+ζ74+ζ785−50000−iiζ26−ζ62+ζ74−ζ78−ζ26+ζ62−ζ74+ζ78−ζ14+ζ42−ζ46+ζ58ζ14−ζ42+ζ46−ζ58−ζ29+ζ47+ζ61−ζ63ζ29−ζ47−ζ61+ζ63ζ13+ζ31−ζ77−ζ79−ζ13−ζ31+ζ77+ζ79−ζ9−ζ27+ζ41+ζ43ζ9+ζ27−ζ41−ζ43ζ11+ζ57−ζ59−ζ73−ζ11−ζ57+ζ59+ζ73−ζ9+ζ27+ζ41−ζ43ζ9−ζ27−ζ41+ζ43−ζ11+ζ57+ζ59−ζ73ζ11−ζ57−ζ59+ζ73ζ29+ζ47−ζ61−ζ63−ζ29−ζ47+ζ61+ζ63ζ13−ζ31−ζ77+ζ79−ζ13+ζ31+ζ77−ζ79000000000000000000000000000
χ624-4-444i−4i002i2−2i2−2i22i20-122−221-11−i5i5−i5i5ζ26+ζ62+ζ74+ζ78−ζ26−ζ62−ζ74−ζ78ζ14+ζ42+ζ46+ζ58−ζ14−ζ42−ζ46−ζ58−ζ26−ζ62−ζ74−ζ78ζ26+ζ62+ζ74+ζ78−ζ14−ζ42−ζ46−ζ58ζ14+ζ42+ζ46+ζ58−550000−ii−ζ14+ζ42−ζ46+ζ58ζ14−ζ42+ζ46−ζ58ζ26−ζ62+ζ74−ζ78−ζ26+ζ62−ζ74+ζ78−ζ13−ζ31+ζ77+ζ79ζ13+ζ31−ζ77−ζ79−ζ29+ζ47+ζ61−ζ63ζ29−ζ47−ζ61+ζ63ζ11+ζ57−ζ59−ζ73−ζ11−ζ57+ζ59+ζ73ζ9+ζ27−ζ41−ζ43−ζ9−ζ27+ζ41+ζ43−ζ11+ζ57+ζ59−ζ73ζ11−ζ57−ζ59+ζ73ζ9−ζ27−ζ41+ζ43−ζ9+ζ27+ζ41−ζ43ζ13−ζ31−ζ77+ζ79−ζ13+ζ31+ζ77−ζ79−ζ29−ζ47+ζ61+ζ63ζ29+ζ47−ζ61−ζ63000000000000000000000000000
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Here ζ is a primitive root of unity of order 80 (ζ80 = 1); i = ζ20.