Finite Group Databasebeta

← Group #65232

Character table — Group #65232

Order 320.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68
size11111111222222222222222222224444444444444444444444444444101010101010101020202020
order1222222222225510101010101010101010101010104444101010101010101020202020202020202020202020202020444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ41111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ511111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1
χ611111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ711111111-1-1-1-11111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-111
χ811111111-1-1-1-11111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1111111-1-1
χ9111-1-1-1-1111-1-111111111-1-1-1-1-1-1-1-1i−ii−i1111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-111-1-1i−ii−i
χ10111-1-1-1-1111-1-111111111-1-1-1-1-1-1-1-1i−ii−i1111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i-1-111-1-111−ii−ii
χ11111-1-1-1-1111-1-111111111-1-1-1-1-1-1-1-1−ii−ii1111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-1−ii−ii
χ12111-1-1-1-1111-1-111111111-1-1-1-1-1-1-1-1−ii−ii1111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii-1-111-1-111i−ii−i
χ13111-1-1-1-11-1-11111111111-1-1-1-1-1-1-1-1i−i−ii-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii11-1-1-1-111i−i−ii
χ14111-1-1-1-11-1-11111111111-1-1-1-1-1-1-1-1i−i−ii-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiii-1-11111-1-1−iii−i
χ15111-1-1-1-11-1-11111111111-1-1-1-1-1-1-1-1−iii−i-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-111−iii−i
χ16111-1-1-1-11-1-11111111111-1-1-1-1-1-1-1-1−iii−i-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i-1-11111-1-1i−i−ii
χ17222222222222−1+52−1−52−1+52−1+52−1+52−1−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−522222−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52000000000000
χ18222222222222−1+52−1−52−1+52−1+52−1+52−1−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52-2-2-2-2−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+521−521−521+521+521−521−521+521+52000000000000
χ19222222222222−1−52−1+52−1−52−1−52−1−52−1+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+522222−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52000000000000
χ20222222222222−1−52−1+52−1−52−1−52−1−52−1+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52-2-2-2-2−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−521+521+521−521−521+521+521−521−52000000000000
χ2122222222-2-2-2-2−1+52−1−52−1+52−1+52−1+52−1−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−5222-2-21−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+52000000000000
χ2222222222-2-2-2-2−1+52−1−52−1+52−1+52−1+52−1−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52-2-2221−521−521+521+521−521−521+521+521−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52000000000000
χ2322222222-2-2-2-2−1−52−1+52−1−52−1−52−1−52−1+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+5222-2-21+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−52000000000000
χ2422222222-2-2-2-2−1−52−1+52−1−52−1−52−1−52−1+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52-2-2221+521+521−521−521+521+521−521−521+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52000000000000
χ25222-2-2-2-2222-2-2−1+52−1−52−1+52−1+52−1+52−1−52−1−52−1−521−521−521+521+521−521−521+521+522i−2i2i−2i−1+52−1+52−1−52−1−521−521−521+521+52−ζ11−ζ19−ζ11−ζ19−ζ3−ζ7−ζ3−ζ7ζ11+ζ19ζ11+ζ19ζ3+ζ7ζ3+ζ7−ζ11−ζ19−ζ11−ζ19−ζ3−ζ7−ζ3−ζ7ζ11+ζ19ζ11+ζ19ζ3+ζ7ζ3+ζ7000000000000
χ26222-2-2-2-2222-2-2−1+52−1−52−1+52−1+52−1+52−1−52−1−52−1−521−521−521+521+521−521−521+521+52−2i2i−2i2i−1+52−1+52−1−52−1−521−521−521+521+52ζ11+ζ19ζ11+ζ19ζ3+ζ7ζ3+ζ7−ζ11−ζ19−ζ11−ζ19−ζ3−ζ7−ζ3−ζ7ζ11+ζ19ζ11+ζ19ζ3+ζ7ζ3+ζ7−ζ11−ζ19−ζ11−ζ19−ζ3−ζ7−ζ3−ζ7000000000000
χ27222-2-2-2-2222-2-2−1−52−1+52−1−52−1−52−1−52−1+52−1+52−1+521+521+521−521−521+521+521−521−522i−2i2i−2i−1−52−1−52−1+52−1+521+521+521−521−52−ζ3−ζ7−ζ3−ζ7−ζ11−ζ19−ζ11−ζ19ζ3+ζ7ζ3+ζ7ζ11+ζ19ζ11+ζ19−ζ3−ζ7−ζ3−ζ7−ζ11−ζ19−ζ11−ζ19ζ3+ζ7ζ3+ζ7ζ11+ζ19ζ11+ζ19000000000000
χ28222-2-2-2-2222-2-2−1−52−1+52−1−52−1−52−1−52−1+52−1+52−1+521+521+521−521−521+521+521−521−52−2i2i−2i2i−1−52−1−52−1+52−1+521+521+521−521−52ζ3+ζ7ζ3+ζ7ζ11+ζ19ζ11+ζ19−ζ3−ζ7−ζ3−ζ7−ζ11−ζ19−ζ11−ζ19ζ3+ζ7ζ3+ζ7ζ11+ζ19ζ11+ζ19−ζ3−ζ7−ζ3−ζ7−ζ11−ζ19−ζ11−ζ19000000000000
χ29222-2-2-2-22-2-222−1+52−1−52−1+52−1+52−1+52−1−52−1−52−1−521−521−521+521+521−521−521+521+522i−2i−2i2i1−521−521+521+52−1+52−1+52−1−52−1−52−ζ11−ζ19−ζ11−ζ19−ζ3−ζ7−ζ3−ζ7ζ11+ζ19ζ11+ζ19ζ3+ζ7ζ3+ζ7ζ11+ζ19ζ11+ζ19ζ3+ζ7ζ3+ζ7−ζ11−ζ19−ζ11−ζ19−ζ3−ζ7−ζ3−ζ7000000000000
χ30222-2-2-2-22-2-222−1+52−1−52−1+52−1+52−1+52−1−52−1−52−1−521−521−521+521+521−521−521+521+52−2i2i2i−2i1−521−521+521+52−1+52−1+52−1−52−1−52ζ11+ζ19ζ11+ζ19ζ3+ζ7ζ3+ζ7−ζ11−ζ19−ζ11−ζ19−ζ3−ζ7−ζ3−ζ7−ζ11−ζ19−ζ11−ζ19−ζ3−ζ7−ζ3−ζ7ζ11+ζ19ζ11+ζ19ζ3+ζ7ζ3+ζ7000000000000
χ31222-2-2-2-22-2-222−1−52−1+52−1−52−1−52−1−52−1+52−1+52−1+521+521+521−521−521+521+521−521−522i−2i−2i2i1+521+521−521−52−1−52−1−52−1+52−1+52−ζ3−ζ7−ζ3−ζ7−ζ11−ζ19−ζ11−ζ19ζ3+ζ7ζ3+ζ7ζ11+ζ19ζ11+ζ19ζ3+ζ7ζ3+ζ7ζ11+ζ19ζ11+ζ19−ζ3−ζ7−ζ3−ζ7−ζ11−ζ19−ζ11−ζ19000000000000
χ32222-2-2-2-22-2-222−1−52−1+52−1−52−1−52−1−52−1+52−1+52−1+521+521+521−521−521+521+521−521−52−2i2i2i−2i1+521+521−521−52−1−52−1−52−1+52−1+52ζ3+ζ7ζ3+ζ7ζ11+ζ19ζ11+ζ19−ζ3−ζ7−ζ3−ζ7−ζ11−ζ19−ζ11−ζ19−ζ3−ζ7−ζ3−ζ7−ζ11−ζ19−ζ11−ζ19ζ3+ζ7ζ3+ζ7ζ11+ζ19ζ11+ζ19000000000000
χ3322-22-22-2-20000222-2-22-2-22-22-22-22-2000000000000000000000000000000002i−2i2i−2i0000
χ3422-22-22-2-20000222-2-22-2-22-22-22-22-200000000000000000000000000000000−2i2i−2i2i0000
χ3522-2-22-22-20000222-2-22-2-2-22-22-22-22000000000000000000000000000000002i−2i−2i2i0000
χ3622-2-22-22-20000222-2-22-2-2-22-22-22-2200000000000000000000000000000000−2i2i2i−2i0000
χ372-222-2-22-2000022-22-2-22-2-22-222-22-200000000000000000000000000002i−2i2i−2i00000000
χ382-222-2-22-2000022-22-2-22-2-22-222-22-20000000000000000000000000000−2i2i−2i2i00000000
χ392-22-222-2-2000022-22-2-22-22-22-2-22-2200000000000000000000000000002i−2i−2i2i00000000
χ402-22-222-2-2000022-22-2-22-22-22-2-22-220000000000000000000000000000−2i2i2i−2i00000000
χ412-2-222-2-222-22-222-2-22-2-22-2-2-2-2222200002-22-22-22-20000000000000000000000000000
χ422-2-222-2-222-22-2−1+52−1−521−521−52−1+521+521+52−1−521−521−521+521+52−1+52−1+52−1−52−1−520000−1+521−52−1−521+52−1+521−52−1−521+52ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18000000000000
χ432-2-222-2-222-22-2−1+52−1−521−521−52−1+521+521+52−1−521−521−521+521+52−1+52−1+52−1−52−1−520000−1+521−52−1−521+52−1+521−52−1−521+52−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18000000000000
χ442-2-222-2-222-22-2−1−52−1+521+521+52−1−521−521−52−1+521+521+521−521−52−1−52−1−52−1+52−1+520000−1−521+52−1+521−52−1−521+52−1+521−52−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14000000000000
χ452-2-222-2-222-22-2−1−52−1+521+521+52−1−521−521−52−1+521+521+521−521−52−1−52−1−52−1+52−1+520000−1−521+52−1+521−52−1−521+52−1+521−52ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14000000000000
χ462-2-222-2-22-22-2222-2-22-2-22-2-2-2-222220000-22-22-22-220000000000000000000000000000
χ472-2-222-2-22-22-22−1+52−1−521−521−52−1+521+521+52−1−521−521−521+521+52−1+52−1+52−1−52−1−5200001−52−1+521+52−1−521−52−1+521+52−1−52ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18000000000000
χ482-2-222-2-22-22-22−1+52−1−521−521−52−1+521+521+52−1−521−521−521+521+52−1+52−1+52−1−52−1−5200001−52−1+521+52−1−521−52−1+521+52−1−52−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18000000000000
χ492-2-222-2-22-22-22−1−52−1+521+521+52−1−521−521−52−1+521+521+521−521−52−1−52−1−52−1+52−1+5200001+52−1−521−52−1+521+52−1−521−52−1+52−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14000000000000
χ502-2-222-2-22-22-22−1−52−1+521+521+52−1−521−521−52−1+521+521+521−521−52−1−52−1−52−1+52−1+5200001+52−1−521−52−1+521+52−1−521−52−1+52ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14000000000000
χ512-2-2-2-22222-2-2222-2-22-2-222222-2-2-2-200002-22-2-22-220000000000000000000000000000
χ522-2-2-2-22222-2-22−1+52−1−521−521−52−1+521+521+52−1−52−1+52−1+52−1−52−1−521−521−521+521+520000−1+521−52−1−521+521−52−1+521+52−1−52−ζ11+ζ19ζ11−ζ19−ζ3+ζ7ζ3−ζ7ζ11−ζ19−ζ11+ζ19ζ3−ζ7−ζ3+ζ7−ζ11+ζ19ζ11−ζ19−ζ3+ζ7ζ3−ζ7ζ11−ζ19−ζ11+ζ19ζ3−ζ7−ζ3+ζ7000000000000
χ532-2-2-2-22222-2-22−1+52−1−521−521−52−1+521+521+52−1−52−1+52−1+52−1−52−1−521−521−521+521+520000−1+521−52−1−521+521−52−1+521+52−1−52ζ11−ζ19−ζ11+ζ19ζ3−ζ7−ζ3+ζ7−ζ11+ζ19ζ11−ζ19−ζ3+ζ7ζ3−ζ7ζ11−ζ19−ζ11+ζ19ζ3−ζ7−ζ3+ζ7−ζ11+ζ19ζ11−ζ19−ζ3+ζ7ζ3−ζ7000000000000
χ542-2-2-2-22222-2-22−1−52−1+521+521+52−1−521−521−52−1+52−1−52−1−52−1+52−1+521+521+521−521−520000−1−521+52−1+521−521+52−1−521−52−1+52ζ3−ζ7−ζ3+ζ7−ζ11+ζ19ζ11−ζ19−ζ3+ζ7ζ3−ζ7ζ11−ζ19−ζ11+ζ19ζ3−ζ7−ζ3+ζ7−ζ11+ζ19ζ11−ζ19−ζ3+ζ7ζ3−ζ7ζ11−ζ19−ζ11+ζ19000000000000
χ552-2-2-2-22222-2-22−1−52−1+521+521+52−1−521−521−52−1+52−1−52−1−52−1+52−1+521+521+521−521−520000−1−521+52−1+521−521+52−1−521−52−1+52−ζ3+ζ7ζ3−ζ7ζ11−ζ19−ζ11+ζ19ζ3−ζ7−ζ3+ζ7−ζ11+ζ19ζ11−ζ19−ζ3+ζ7ζ3−ζ7ζ11−ζ19−ζ11+ζ19ζ3−ζ7−ζ3+ζ7−ζ11+ζ19ζ11−ζ19000000000000
χ562-2-2-2-2222-222-222-2-22-2-222222-2-2-2-20000-22-222-22-20000000000000000000000000000
χ572-2-2-2-2222-222-2−1+52−1−521−521−52−1+521+521+52−1−52−1+52−1+52−1−52−1−521−521−521+521+5200001−52−1+521+52−1−52−1+521−52−1−521+52−ζ11+ζ19ζ11−ζ19−ζ3+ζ7ζ3−ζ7ζ11−ζ19−ζ11+ζ19ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19ζ3−ζ7−ζ3+ζ7−ζ11+ζ19ζ11−ζ19−ζ3+ζ7ζ3−ζ7000000000000
χ582-2-2-2-2222-222-2−1+52−1−521−521−52−1+521+521+52−1−52−1+52−1+52−1−52−1−521−521−521+521+5200001−52−1+521+52−1−52−1+521−52−1−521+52ζ11−ζ19−ζ11+ζ19ζ3−ζ7−ζ3+ζ7−ζ11+ζ19ζ11−ζ19−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19−ζ3+ζ7ζ3−ζ7ζ11−ζ19−ζ11+ζ19ζ3−ζ7−ζ3+ζ7000000000000
χ592-2-2-2-2222-222-2−1−52−1+521+521+52−1−521−521−52−1+52−1−52−1−52−1+52−1+521+521+521−521−5200001+52−1−521−52−1+52−1−521+52−1+521−52ζ3−ζ7−ζ3+ζ7−ζ11+ζ19ζ11−ζ19−ζ3+ζ7ζ3−ζ7ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7ζ11−ζ19−ζ11+ζ19ζ3−ζ7−ζ3+ζ7−ζ11+ζ19ζ11−ζ19000000000000
χ602-2-2-2-2222-222-2−1−52−1+521+521+52−1−521−521−52−1+52−1−52−1−52−1+52−1+521+521+521−521−5200001+52−1−521−52−1+52−1−521+52−1+521−52−ζ3+ζ7ζ3−ζ7ζ11−ζ19−ζ11+ζ19ζ3−ζ7−ζ3+ζ7−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7−ζ11+ζ19ζ11−ζ19−ζ3+ζ7ζ3−ζ7ζ11−ζ19−ζ11+ζ19000000000000
χ6144-44-44-4-40000−1+5−1−5−1+51−51−5−1−51+51+5−1+51−5−1−51+5−1+51−5−1−51+50000000000000000000000000000000000000000
χ6244-44-44-4-40000−1−5−1+5−1−51+51+5−1+51−51−5−1−51+5−1+51−5−1−51+5−1+51−50000000000000000000000000000000000000000
χ6344-4-44-44-40000−1+5−1−5−1+51−51−5−1−51+51+51−5−1+51+5−1−51−5−1+51+5−1−50000000000000000000000000000000000000000
χ6444-4-44-44-40000−1−5−1+5−1−51+51+5−1+51−51−51+5−1−51−5−1+51+5−1−51−5−1+50000000000000000000000000000000000000000
χ654-444-4-44-40000−1+5−1−51−5−1+51−51+5−1−51+51−5−1+51+5−1−5−1+51−5−1−51+50000000000000000000000000000000000000000
χ664-444-4-44-40000−1−5−1+51+5−1−51+51−5−1+51−51+5−1−51−5−1+5−1−51+5−1+51−50000000000000000000000000000000000000000
χ674-44-444-4-40000−1+5−1−51−5−1+51−51+5−1−51+5−1+51−5−1−51+51−5−1+51+5−1−50000000000000000000000000000000000000000
χ684-44-444-4-40000−1−5−1+51+5−1−51+51−5−1+51−5−1−51+5−1+51−51+5−1−51−5−1+50000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 20 (ζ20 = 1); i = ζ5.