Finite Group Databasebeta

← Group #12015113

Character table — Group #12015113

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92
size11112222222222444444444444448888888888888888888888161616161616161616161616161616161616161616161616202020202020202040404040404040408080
order1222225510101010101022222222441010101044101010101010101010101010101010102020202044882020202020202020202020204040404040404040444444444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1
χ411111111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ51111111111111111-1-1-1-111111111-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-1
χ61111111111111111-1-1-1-111111111-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-111
χ71111111111111111-1-1-1-111111111-1-1111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-11111
χ81111111111111111-1-1-1-111111111-1-1111111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111111111-1-1-1-1
χ91-1-11-1111-1-1-1-1111111-1-1-1-11-1-1-1111-11111-1-11111-1-1-1-1-1-111-1-1i−ii−i11-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-111-1-1ii−i−i1-11-1i−i
χ101-1-11-1111-1-1-1-1111111-1-1-1-11-1-1-1111-11111-1-11111-1-1-1-1-1-111-1-1i−ii−i11-1-1iiii−i−i−i−iiiii−i−i−i−i-1-111-1-111−i−iii-11-11−ii
χ111-1-11-1111-1-1-1-1111111-1-1-1-11-1-1-1111-11111-1-11111-1-1-1-1-1-111-1-1−ii−ii11-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-1−i−iii1-11-1−ii
χ121-1-11-1111-1-1-1-1111111-1-1-1-11-1-1-1111-11111-1-11111-1-1-1-1-1-111-1-1−ii−ii11-1-1−i−i−i−iiiii−i−i−i−iiiii-1-111-1-111ii−i−i-11-11i−i
χ131-1-11-1111-1-1-1-11111-1-111-1-11-1-1-111-111111-1-1-1-1-1-11111-1-111-1-1i−i−ii-1-111iiii−i−i−i−i−i−i−i−iiiii11-1-1-1-111ii−i−i-111-1−ii
χ141-1-11-1111-1-1-1-11111-1-111-1-11-1-1-111-111111-1-1-1-1-1-11111-1-111-1-1i−i−ii-1-111iiii−i−i−i−i−i−i−i−iiiii-1-11111-1-1−i−iii1-1-11i−i
χ151-1-11-1111-1-1-1-11111-1-111-1-11-1-1-111-111111-1-1-1-1-1-11111-1-111-1-1−iii−i-1-111−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-111−i−iii-111-1i−i
χ161-1-11-1111-1-1-1-11111-1-111-1-11-1-1-111-111111-1-1-1-1-1-11111-1-111-1-1−iii−i-1-111−i−i−i−iiiiiiiii−i−i−i−i-1-11111-1-1ii−i−i1-1-11−ii
χ17222222222222222-200002-2-2-222220022-2-2-2-20000000022-2-2-2-200000000000000000000000022220000000000-2-200
χ18222222222222222-200002-2-2-222220022-2-2-2-20000000022-2-2-2-2000000000000000000000000-2-2-2-200000000002200
χ1922222222222222-222222-22-2-22222-2-2-2-2222222222222-2-2-2-2-2-20000-2-2-2-20000000000000000000000000000000000
χ2022222222222222-22-2-2-2-2-22-2-2222222-2-22222-2-2-2-2-2-2-2-2-2-2-2-2-2-2000022220000000000000000000000000000000000
χ2122222222222222-2-20000-2-222222200-2-2-2-2-2-200000000-2-22222000000000000000000000000000022220000-2-20000
χ2222222222222222-2-20000-2-222222200-2-2-2-2-2-200000000-2-222220000000000000000000000000000-2-2-2-20000220000
χ23222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−522222222222−1+52−1−52−1+52−1−5222−1+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+52−1−522222−1+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+52−1−52−1−52000000000000000000
χ24222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−522222222222−1+52−1−52−1+52−1−5222−1+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+52−1−52-2-2-2-2−1+52−1−52−1+52−1−521−521−521+521+521−521−521+521+521−521−521+521+521−521−521+521+52000000000000000000
χ25222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−5222-2-2-2-22222−1+52−1−52−1+52−1−52-2-2−1+52−1−52−1+52−1−52−1+52−1−521−521−521+521+521−521−521+521+52−1+52−1−52−1+52−1−52−1+52−1−5222-2-21−521+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
χ26222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−5222-2-2-2-22222−1+52−1−52−1+52−1−52-2-2−1+52−1−52−1+52−1−52−1+52−1−521−521−521+521+521−521−521+521+52−1+52−1−52−1+52−1−52−1+52−1−52-2-2221−521+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
χ27222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52-222222-22-2-2−1+52−1−52−1+52−1−52-2-21−521+52−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−521−521+521−521+521−521+5200001−521+521−521+52−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7000000000000000000
χ28222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52-222222-22-2-2−1+52−1−52−1+52−1−52-2-21−521+52−1+52−1−52−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−521−521+521−521+521−521+5200001−521+521−521+52ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7000000000000000000
χ29222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52-22-2-2-2-2-22-2-2−1+52−1−52−1+52−1−52221−521+52−1+52−1−52−1+52−1−521−521−521+521+521−521−521+521+521−521+521−521+521−521+520000−1+52−1−52−1+52−1−52−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7000000000000000000
χ30222222−1+52−1−52−1+52−1+52−1−52−1−52−1+52−1−52-22-2-2-2-2-22-2-2−1+52−1−52−1+52−1−52221−521+52−1+52−1−52−1+52−1−521−521−521+521+521−521−521+521+521−521+521−521+521−521+520000−1+52−1−52−1+52−1−52ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7000000000000000000
χ31222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+522222222222−1−52−1+52−1−52−1+5222−1−52−1+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+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+52000000000000000000
χ32222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+522222222222−1−52−1+52−1−52−1+5222−1−52−1+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+52-2-2-2-2−1−52−1+52−1−52−1+521+521+521−521−521+521+521−521−521+521+521−521−521+521+521−521−52000000000000000000
χ33222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+5222-2-2-2-22222−1−52−1+52−1−52−1+52-2-2−1−52−1+52−1−52−1+52−1−52−1+521+521+521−521−521+521+521−521−52−1−52−1+52−1−52−1+52−1−52−1+5222-2-21+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
χ34222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+5222-2-2-2-22222−1−52−1+52−1−52−1+52-2-2−1−52−1+52−1−52−1+52−1−52−1+521+521+521−521−521+521+521−521−52−1−52−1+52−1−52−1+52−1−52−1+52-2-2221+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
χ35222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52-222222-22-2-2−1−52−1+52−1−52−1+52-2-21+521−52−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521−521+521−521+521−5200001+521−521+521−52ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19000000000000000000
χ36222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52-222222-22-2-2−1−52−1+52−1−52−1+52-2-21+521−52−1−52−1+52−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521−521+521−521+521−5200001+521−521+521−52−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19000000000000000000
χ37222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52-22-2-2-2-2-22-2-2−1−52−1+52−1−52−1+52221+521−52−1−52−1+52−1−52−1+521+521+521−521−521+521+521−521−521+521−521+521−521+521−520000−1−52−1+52−1−52−1+52ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19000000000000000000
χ38222222−1−52−1+52−1−52−1−52−1+52−1+52−1−52−1+52-22-2-2-2-2-22-2-2−1−52−1+52−1−52−1+52221+521−52−1−52−1+52−1−52−1+521+521+521−521−521+521+521−521−521+521−521+521−521+521−520000−1−52−1+52−1−52−1+52−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19−ζ3+ζ7ζ3−ζ7−ζ11+ζ19ζ11−ζ19ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19ζ3−ζ7−ζ3+ζ7ζ11−ζ19−ζ11+ζ19000000000000000000
χ392-2-22-2222-2-2-2-2222-20000-22-22-2-2220022-2-22200000000-2-2-2-22200000000000000000000000022-2-20000000000-2200
χ402-2-22-2222-2-2-2-2222-20000-22-22-2-2220022-2-22200000000-2-2-2-222000000000000000000000000-2-22200000000002-200
χ412-2-22-2222-2-2-2-222-2222-2-22-2-22-2-222-22-2-222-2-22222-2-2-2-222-2-2220000-2-2220000000000000000000000000000000000
χ422-2-22-2222-2-2-2-222-22-2-2222-2-22-2-2222-2-2-222-2-2-2-2-2-2222222-2-222000022-2-20000000000000000000000000000000000
χ432-2-22-2222-2-2-2-222-2-20000222-2-2-22200-2-2-2-222000000002222-2-2000000000000000000000000000022-2-20000-220000
χ442-2-22-2222-2-2-2-222-2-20000222-2-2-22200-2-2-2-222000000002222-2-20000000000000000000000000000-2-22200002-20000
χ452-2-22-22−1+52−1−521−521−521+521+52−1+52−1−522222-2-2-2-22-21−521+52−1+52−1−522-2−1+52−1−52−1+52−1−521−521+52−1+52−1+52−1−52−1−521−521−521+521+521−521+52−1+52−1−521−521+522i−2i2i−2i−1+52−1−521−521+52−ζ11−ζ19−ζ11−ζ19−ζ3−ζ7−ζ3−ζ7ζ11+ζ19ζ11+ζ19ζ3+ζ7ζ3+ζ7−ζ11−ζ19−ζ11−ζ19−ζ3−ζ7−ζ3−ζ7ζ11+ζ19ζ11+ζ19ζ3+ζ7ζ3+ζ7000000000000000000
χ462-2-22-22−1+52−1−521−521−521+521+52−1+52−1−522222-2-2-2-22-21−521+52−1+52−1−522-2−1+52−1−52−1+52−1−521−521+52−1+52−1+52−1−52−1−521−521−521+521+521−521+52−1+52−1−521−521+52−2i2i−2i2i−1+52−1−521−521+52ζ11+ζ19ζ11+ζ19ζ3+ζ7ζ3+ζ7−ζ11−ζ19−ζ11−ζ19−ζ3−ζ7−ζ3−ζ7ζ11+ζ19ζ11+ζ19ζ3+ζ7ζ3+ζ7−ζ11−ζ19−ζ11−ζ19−ζ3−ζ7−ζ3−ζ7000000000000000000
χ472-2-22-22−1+52−1−521−521−521+521+52−1+52−1−5222-2-222-2-22-21−521+52−1+52−1−52-22−1+52−1−52−1+52−1−521−521+521−521−521+521+52−1+52−1+52−1−52−1−521−521+52−1+52−1−521−521+522i−2i−2i2i1−521+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−ζ7000000000000000000
χ482-2-22-22−1+52−1−521−521−521+521+52−1+52−1−5222-2-222-2-22-21−521+52−1+52−1−52-22−1+52−1−52−1+52−1−521−521+521−521−521+521+52−1+52−1+52−1−52−1−521−521+52−1+52−1−521−521+52−2i2i2i−2i1−521+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+ζ7000000000000000000
χ492-2-22-22−1+52−1−521−521−521+521+52−1+52−1−52-2222-2-22-2-221−521+52−1+52−1−52-221−521+52−1+52−1−521−521+52−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1−521−521+52−1+52−1−5200001−521+52−1+52−1−52ζ6−ζ14−ζ6+ζ14ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ14−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ14−ζ2+ζ18ζ2−ζ18000000000000000000
χ502-2-22-22−1+52−1−521−521−521+521+52−1+52−1−52-2222-2-22-2-221−521+52−1+52−1−52-221−521+52−1+52−1−521−521+52−1+52−1+52−1−52−1−521−521−521+521+52−1+52−1−521−521+52−1+52−1−5200001−521+52−1+52−1−52−ζ6+ζ14ζ6−ζ14−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ14−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14ζ2−ζ18−ζ2+ζ18000000000000000000
χ512-2-22-22−1+52−1−521−521−521+521+52−1+52−1−52-22-2-2222-2-221−521+52−1+52−1−522-21−521+52−1+52−1−521−521+521−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1−521−521+52−1+52−1−520000−1+52−1−521−521+52ζ6−ζ14−ζ6+ζ14ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14ζ2−ζ18−ζ2+ζ18000000000000000000
χ522-2-22-22−1+52−1−521−521−521+521+52−1+52−1−52-22-2-2222-2-221−521+52−1+52−1−522-21−521+52−1+52−1−521−521+521−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1−521−521+52−1+52−1−520000−1+52−1−521−521+52−ζ6+ζ14ζ6−ζ14−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ14−ζ2+ζ18ζ2−ζ18000000000000000000
χ532-2-22-22−1−52−1+521+521+521−521−52−1−52−1+522222-2-2-2-22-21+521−52−1−52−1+522-2−1−52−1+52−1−52−1+521+521−52−1−52−1−52−1+52−1+521+521+521−521−521+521−52−1−52−1+521+521−522i−2i2i−2i−1−52−1+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+ζ19000000000000000000
χ542-2-22-22−1−52−1+521+521+521−521−52−1−52−1+522222-2-2-2-22-21+521−52−1−52−1+522-2−1−52−1+52−1−52−1+521+521−52−1−52−1−52−1+52−1+521+521+521−521−521+521−52−1−52−1+521+521−52−2i2i−2i2i−1−52−1+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−ζ19000000000000000000
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χ918-8-888-8−2+25−2−252−252−252+252+25−2+25−2−250000000000−2+25−2−252−252+250000000000000000000000000000000000000000000000000000000000000000
χ928-8-888-8−2−25−2+252+252+252−252−25−2−25−2+250000000000−2−25−2+252+252−250000000000000000000000000000000000000000000000000000000000000000

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