Finite Group Databasebeta

← Group #12014485

Character table — Group #12014485

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size11112222222222444444444488888888888888888888888888888888101010101616161616161616161616161616161616161616202020202020404040404040404040404040
order1222225510101010101044444410101010444488888888202020202020202020202020202020202020202044442020202040404040404040404040404040404040444444444488888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ5111111111111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-1-1
χ6111111111111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ7111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-11111
χ8111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1
χ91111111111111111-1-1-1-1111111-1-1ii−i−iii−i−i1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111iiii−i−i−i−iiiii−i−i−i−i11-1-1-1-111-1-1ii−i−iii−i−i
χ101111111111111111-1-1-1-1111111-1-1ii−i−iii−i−i1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111iiii−i−i−i−iiiii−i−i−i−i-1-11111-1-111−i−iii−i−iii
χ111111111111111111-1-1-1-1111111-1-1−i−iii−i−iii1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111−i−i−i−iiiii−i−i−i−iiiii11-1-1-1-111-1-1−i−iii−i−iii
χ121111111111111111-1-1-1-1111111-1-1−i−iii−i−iii1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−i−i−iiiii−i−i−i−iiiii-1-11111-1-111ii−i−iii−i−i
χ131111111111111111-1-1-1-11111-1-111ii−i−i−i−iii1111-1-1-1-111111111-1-1-1-11111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii11-1-1-1-1-1-111ii−i−i−i−iii
χ141111111111111111-1-1-1-11111-1-111ii−i−i−i−iii1111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii-1-1111111-1-1−i−iiiii−i−i
χ151111111111111111-1-1-1-11111-1-111−i−iiiii−i−i1111-1-1-1-111111111-1-1-1-11111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-1-1-111−i−iiiii−i−i
χ161111111111111111-1-1-1-11111-1-111−i−iiiii−i−i1111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i-1-1111111-1-1ii−i−i−i−iii
χ171-11-1-1111-1-1-1-1111-11-11-111-1-1i−ii−i1-11-1i−ii−i11-1-111-1-1iiii−i−i−i−i11-1-1ii−i−iii−i−i11-1-111-1-1ii−i−iii−i−ii−iii−i−i1-11-1i−ii−i1-11-1
χ181-11-1-1111-1-1-1-1111-11-11-111-1-1i−ii−i1-11-1i−ii−i11-1-111-1-1iiii−i−i−i−i11-1-1−i−iiiii−i−i11-1-111-1-1ii−i−iii−i−i−ii−i−iii-11-11−ii−ii-11-11
χ191-11-1-1111-1-1-1-1111-11-11-111-1-1i−ii−i-11-11−ii−ii11-1-111-1-1iiii−i−i−i−i11-1-1ii−i−iii−i−i-1-111-1-111−i−iii−i−iiii−iii−i−i1-11-1−ii−ii-11-11
χ201-11-1-1111-1-1-1-1111-11-11-111-1-1i−ii−i-11-11−ii−ii11-1-111-1-1iiii−i−i−i−i11-1-1−i−iiiii−i−i-1-111-1-111−i−iii−i−iii−ii−i−iii-11-11i−ii−i1-11-1
χ211-11-1-1111-1-1-1-1111-11-11-111-1-1−ii−ii1-11-1−ii−ii11-1-111-1-1−i−i−i−iiiii11-1-1ii−i−i−i−iii11-1-111-1-1−i−iii−i−iiii−iii−i−i-11-11i−ii−i-11-11
χ221-11-1-1111-1-1-1-1111-11-11-111-1-1−ii−ii1-11-1−ii−ii11-1-111-1-1−i−i−i−iiiii11-1-1−i−iii−i−iii11-1-111-1-1−i−iii−i−iii−ii−i−iii1-11-1−ii−ii1-11-1
χ231-11-1-1111-1-1-1-1111-11-11-111-1-1−ii−ii-11-11i−ii−i11-1-111-1-1−i−i−i−iiiii11-1-1ii−i−i−i−iii-1-111-1-111ii−i−iii−i−ii−iii−i−i-11-11−ii−ii1-11-1
χ241-11-1-1111-1-1-1-1111-11-11-111-1-1−ii−ii-11-11i−ii−i11-1-111-1-1−i−i−i−iiiii11-1-1−i−iii−i−iii-1-111-1-111ii−i−iii−i−i−ii−i−iii1-11-1i−ii−i-11-11
χ251-11-1-1111-1-1-1-1111-1-11-1111-1-1i−i−iii−i−ii-111-111-1-1-1-111−i−i−i−iiiii-1-111ii−i−iii−i−iii−i−i−i−iii-1-11111-1-1i−i−i−iii1-1-11-111-1i−i−ii
χ261-11-1-1111-1-1-1-1111-1-11-1111-1-1i−i−iii−i−ii-111-111-1-1-1-111−i−i−i−iiiii-1-111−i−iiiii−i−iii−i−i−i−iii-1-11111-1-1−iiii−i−i-111-11-1-11−iii−i
χ271-11-1-1111-1-1-1-1111-1-11-1111-1-1i−i−ii−iii−i1-1-1111-1-1-1-111−i−i−i−iiiii-1-111ii−i−iii−i−i−i−iiiii−i−i11-1-1-1-111i−i−i−iii1-1-111-1-11−iii−i
χ281-11-1-1111-1-1-1-1111-1-11-1111-1-1i−i−ii−iii−i1-1-1111-1-1-1-111−i−i−i−iiiii-1-111−i−iiiii−i−i−i−iiiii−i−i11-1-1-1-111−iiii−i−i-111-1-111-1i−i−ii
χ291-11-1-1111-1-1-1-1111-1-11-1111-1-1−iii−ii−i−ii1-1-1111-1-1-1-111iiii−i−i−i−i-1-111ii−i−i−i−iiiii−i−i−i−iii11-1-1-1-111i−i−i−iii-111-1-111-1−iii−i
χ301-11-1-1111-1-1-1-1111-1-11-1111-1-1−iii−ii−i−ii1-1-1111-1-1-1-111iiii−i−i−i−i-1-111−i−iii−i−iiiii−i−i−i−iii11-1-1-1-111−iiii−i−i1-1-111-1-11i−i−ii
χ311-11-1-1111-1-1-1-1111-1-11-1111-1-1−iii−i−iii−i-111-111-1-1-1-111iiii−i−i−i−i-1-111ii−i−i−i−iii−i−iiiii−i−i-1-11111-1-1i−i−i−iii-111-11-1-11i−i−ii
χ321-11-1-1111-1-1-1-1111-1-11-1111-1-1−iii−i−iii−i-111-111-1-1-1-111iiii−i−i−i−i-1-111−i−iii−i−iii−i−iiiii−i−i-1-11111-1-1−iiii−i−i1-1-11-111-1−iii−i
χ3322222222222222-2-22-2-222222000000000000-2-2-2-2-2-2220000000022-2-2222200000000000000000000-2-22-22-2000000000000
χ3422222222222222-2-22-2-222222000000000000-2-2-2-2-2-2220000000022-2-2-2-2-2-20000000000000000000022-22-22000000000000
χ3522222222222222-2-2-222-22222000000000000-2-2-2-222-2-200000000-2-222222200000000000000000000-2-2-22-22000000000000
χ3622222222222222-2-2-222-22222000000000000-2-2-2-222-2-200000000-2-222-2-2-2-200000000000000000000222-22-2000000000000
χ37222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52222222−1+52−1−52−1+52−1−52222222222222−1+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+52−1−520000−1+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+52−1−52000000000000000000
χ38222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52222222−1+52−1−52−1+52−1−522222-2-2-2-2-2-2-2-2−1+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+52−1−52−1−52−1+52−1−52−1+52−1−520000−1+52−1−52−1+52−1−521−521+521−521+521−521+521−521+521−521+521−521+521−521+521−521+52000000000000000000
χ39222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52222222−1+52−1−52−1+52−1−52-2-2-2-22222-2-2-2-2−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−521−521−521+521+521−521−521+521+52−1+52−1−52−1+52−1−5200001−521+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+52000000000000000000
χ40222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52222222−1+52−1−52−1+52−1−52-2-2-2-2-2-2-2-22222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−521−521−521+521+521−521−521+521+52−1+52−1−52−1+52−1−5200001−521+521−521+521−521+521−521+521−521+521−521+52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52000000000000000000
χ41222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−5222-2-2-2-2−1+52−1−52−1+52−1−5222-2-22i2i−2i−2i2i2i−2i−2i−1+52−1−52−1+52−1−521−521+521−521+521−521−521+521+521−521−521+521+521−521+521−521+520000−1+52−1−52−1+52−1−52−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7000000000000000000
χ42222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−5222-2-2-2-2−1+52−1−52−1+52−1−5222-2-2−2i−2i2i2i−2i−2i2i2i−1+52−1−52−1+52−1−521−521+521−521+521−521−521+521+521−521−521+521+521−521+521−521+520000−1+52−1−52−1+52−1−52ζ11+ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7000000000000000000
χ43222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−5222-2-2-2-2−1+52−1−52−1+52−1−52-2-2222i2i−2i−2i−2i−2i2i2i−1+52−1−52−1+52−1−521−521+521−521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−521−521+521−521+5200001−521+521−521+52−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7000000000000000000
χ44222222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−5222-2-2-2-2−1+52−1−52−1+52−1−52-2-222−2i−2i2i2i2i2i−2i−2i−1+52−1−52−1+52−1−521−521+521−521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−521−521+521−521+5200001−521+521−521+52ζ11+ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7000000000000000000
χ45222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52222222−1−52−1+52−1−52−1+52222222222222−1−52−1+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+520000−1−52−1+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+52000000000000000000
χ46222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52222222−1−52−1+52−1−52−1+522222-2-2-2-2-2-2-2-2−1−52−1+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+52−1−52−1+52−1−52−1+520000−1−52−1+52−1−52−1+521+521−521+521−521+521−521+521−521+521−521+521−521+521−521+521−52000000000000000000
χ47222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52222222−1−52−1+52−1−52−1+52-2-2-2-22222-2-2-2-2−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+521+521+521−521−521+521+521−521−52−1−52−1+52−1−52−1+5200001+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+521−52000000000000000000
χ48222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52222222−1−52−1+52−1−52−1+52-2-2-2-2-2-2-2-22222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+521+521+521−521−521+521+521−521−52−1−52−1+52−1−52−1+5200001+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+52000000000000000000
χ49222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+5222-2-2-2-2−1−52−1+52−1−52−1+5222-2-22i2i−2i−2i2i2i−2i−2i−1−52−1+52−1−52−1+521+521−521+521−521+521+521−521−521+521+521−521−521+521−521+521−520000−1−52−1+52−1−52−1+52−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19000000000000000000
χ50222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+5222-2-2-2-2−1−52−1+52−1−52−1+5222-2-2−2i−2i2i2i−2i−2i2i2i−1−52−1+52−1−52−1+521+521−521+521−521+521+521−521−521+521+521−521−521+521−521+521−520000−1−52−1+52−1−52−1+52ζ3+ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19000000000000000000
χ51222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+5222-2-2-2-2−1−52−1+52−1−52−1+52-2-2222i2i−2i−2i−2i−2i2i2i−1−52−1+52−1−52−1+521+521−521+521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521−521+521−5200001+521−521+521−52−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19000000000000000000
χ52222222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+5222-2-2-2-2−1−52−1+52−1−52−1+52-2-222−2i−2i2i2i2i2i−2i−2i−1−52−1+52−1−52−1+521+521−521+521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521−521+521−5200001+521−521+521−52ζ3+ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19−ζ3−ζ7−ζ11−ζ19ζ3+ζ7ζ11+ζ19ζ3+ζ7ζ11+ζ19000000000000000000
χ532-22-2-2222-2-2-2-222-2222-2-222-2-2000000000000-2-222-2-2-2-20000000022222i2i−2i−2i00000000000000000000−2i2i2i−2i−2i2i000000000000
χ542-22-2-2222-2-2-2-222-2222-2-222-2-2000000000000-2-222-2-2-2-2000000002222−2i−2i2i2i000000000000000000002i−2i−2i2i2i−2i000000000000
χ552-22-2-2222-2-2-2-222-22-2-22222-2-2000000000000-2-222222200000000-2-2-2-22i2i−2i−2i00000000000000000000−2i2i−2i2i2i−2i000000000000
χ562-22-2-2222-2-2-2-222-22-2-22222-2-2000000000000-2-222222200000000-2-2-2-2−2i−2i2i2i000000000000000000002i−2i2i−2i−2i2i000000000000
χ572-22-2-22−1+52−1−521−521+521−521+52−1+52−1−522-22-22-2−1+52−1−521−521+522i−2i2i−2i2-22-22i−2i2i−2i−1+52−1−521−521+52−1+52−1−521−521+52−ζ11−ζ19−ζ11−ζ19−ζ3−ζ7−ζ3−ζ7ζ11+ζ19ζ11+ζ19ζ3+ζ7ζ3+ζ7−1+52−1−521−521+520000−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ7−1+52−1−521−521+52−1+52−1−521−521+52−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ7−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ7000000000000000000
χ582-22-2-22−1+52−1−521−521+521−521+52−1+52−1−522-22-22-2−1+52−1−521−521+522i−2i2i−2i-22-22−2i2i−2i2i−1+52−1−521−521+52−1+52−1−521−521+52−ζ11−ζ19−ζ11−ζ19−ζ3−ζ7−ζ3−ζ7ζ11+ζ19ζ11+ζ19ζ3+ζ7ζ3+ζ7−1+52−1−521−521+520000−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ71−521+52−1+52−1−521−521+52−1+52−1−52ζ11+ζ19ζ3+ζ7−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ7−ζ11−ζ19−ζ3−ζ7000000000000000000
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Here ζ is a primitive root of unity of order 20 (ζ20 = 1); i = ζ5.