Finite Group Databasebeta

← Group #12016409

Character table — Group #12016409

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110
size111122222222222222222244444444444444444444444444888888888888888888888816161616161616161616161616161616161616162020202020202020404040404040404040404040
order1222224444558888101010101010444488101010102020202020202020404040404040404088202020202020202040404040404040404040404044882020202020202020404040404040404016161616161616162222444416161616
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111
χ41111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ51111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1
χ61111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ71111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1
χ81111111111111111111111-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111
χ911-1-11-111-1-11111-1-1-1-1-1-111ii−i−i-1111-1-11111-1-1-1-11111-1-1-1-1i−iiiii−i−i−i−i11-1-1iiii−i−i−i−i1-1i−i1111-1-1-1-1iiii−i−i−i−i1111-1-1-1-111-1-1ii−i−iii−i−i
χ1011-1-11-111-1-11111-1-1-1-1-1-111ii−i−i-1111-1-11111-1-1-1-11111-1-1-1-1i−iiiii−i−i−i−i11-1-1iiii−i−i−i−i1-1i−i1111-1-1-1-1iiii−i−i−i−i-1-1-1-11111-1-111−i−iii−i−iii
χ1111-1-11-111-1-11111-1-1-1-1-1-111ii−i−i-1111-1-11111-1-1-1-11111-1-1-1-1i−iiiii−i−i−i−i11-1-1iiii−i−i−i−i-11−ii-1-1-1-11111−i−i−i−iiiii1111-1-1-1-1-1-111−i−iiiii−i−i
χ1211-1-11-111-1-11111-1-1-1-1-1-111ii−i−i-1111-1-11111-1-1-1-11111-1-1-1-1i−iiiii−i−i−i−i11-1-1iiii−i−i−i−i-11−ii-1-1-1-11111−i−i−i−iiiii-1-1-1-1111111-1-1ii−i−i−i−iii
χ1311-1-11-111-1-11111-1-1-1-1-1-111−i−iii-1111-1-11111-1-1-1-11111-1-1-1-1−ii−i−i−i−iiiii11-1-1−i−i−i−iiiii1-1−ii1111-1-1-1-1−i−i−i−iiiii1111-1-1-1-111-1-1−i−iii−i−iii
χ1411-1-11-111-1-11111-1-1-1-1-1-111−i−iii-1111-1-11111-1-1-1-11111-1-1-1-1−ii−i−i−i−iiiii11-1-1−i−i−i−iiiii1-1−ii1111-1-1-1-1−i−i−i−iiiii-1-1-1-11111-1-111ii−i−iii−i−i
χ1511-1-11-111-1-11111-1-1-1-1-1-111−i−iii-1111-1-11111-1-1-1-11111-1-1-1-1−ii−i−i−i−iiiii11-1-1−i−i−i−iiiii-11i−i-1-1-1-11111iiii−i−i−i−i1111-1-1-1-1-1-111ii−i−i−i−iii
χ1611-1-11-111-1-11111-1-1-1-1-1-111−i−iii-1111-1-11111-1-1-1-11111-1-1-1-1−ii−i−i−i−iiiii11-1-1−i−i−i−iiiii-11i−i-1-1-1-11111iiii−i−i−i−i-1-1-1-1111111-1-1−i−iiiii−i−i
χ17222222222222-2-2-2-22222222222-2-2222222222222-2-2-2-2-2-2-2-2-2-222222222-2-2-2-2-2-2-2-2-2-2-2-20000000000000000000000000000000000000000
χ18222222222222-2-2-2-2222222-2-2-2-2-2-2222222222222-2-2-2-2-2-2-2-222-2-2-2-2-2-2-2-2-2-2-2-2222222220000000000000000000000000000000000000000
χ192222222222−1+52−1−522222−1+52−1+52−1−52−1−52−1+52−1−52222222−1+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+52−1−52−1−5222−1+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+52−1−52−1−5200000000000000000000
χ202222222222−1+52−1−522222−1+52−1+52−1−52−1−52−1+52−1−52222222−1+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+52−1−52−1−5222−1+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+52−1−52−1−52-2-2-2-21−521−521+521+521−521−521+521+521−521−521+521+521−521−521+521+5200000000000000000000
χ212222222222−1+52−1−522222−1+52−1+52−1−52−1−52−1+52−1−52-2-2-2-222−1+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+52−1−52−1−52-2-21−521−521+521+521−521−521+521+52−1+52−1−52−1+52−1−521−521−521+521+521−521−521+521+5222-2-2−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+5200000000000000000000
χ222222222222−1+52−1−522222−1+52−1+52−1−52−1−52−1+52−1−52-2-2-2-222−1+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+52−1−52−1−52-2-21−521−521+521+521−521−521+521+52−1+52−1−52−1+52−1−521−521−521+521+521−521−521+521+52-2-2221−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−5200000000000000000000
χ232222222222−1+52−1−52-2-2-2-2−1+52−1+52−1−52−1−52−1+52−1−522222-2-2−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−521−521−521+521+521−521−521+521+52-2-2−1+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+520000ζ24−ζ56−ζ24+ζ56−ζ8+ζ72ζ8−ζ72ζ24−ζ56−ζ24+ζ56−ζ8+ζ72ζ8−ζ72ζ24−ζ56−ζ24+ζ56−ζ8+ζ72ζ8−ζ72ζ24−ζ56−ζ24+ζ56−ζ8+ζ72ζ8−ζ7200000000000000000000
χ242222222222−1+52−1−52-2-2-2-2−1+52−1+52−1−52−1−52−1+52−1−522222-2-2−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−521−521−521+521+521−521−521+521+52-2-2−1+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+520000−ζ24+ζ56ζ24−ζ56ζ8−ζ72−ζ8+ζ72−ζ24+ζ56ζ24−ζ56ζ8−ζ72−ζ8+ζ72−ζ24+ζ56ζ24−ζ56ζ8−ζ72−ζ8+ζ72−ζ24+ζ56ζ24−ζ56ζ8−ζ72−ζ8+ζ7200000000000000000000
χ252222222222−1+52−1−52-2-2-2-2−1+52−1+52−1−52−1−52−1+52−1−52-2-2-2-2-2-2−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−521−521−521+521+521−521−521+521+52221−521−521+521+521−521−521+521+521−521+521−521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−520000ζ24−ζ56−ζ24+ζ56−ζ8+ζ72ζ8−ζ72ζ24−ζ56−ζ24+ζ56−ζ8+ζ72ζ8−ζ72−ζ24+ζ56ζ24−ζ56ζ8−ζ72−ζ8+ζ72−ζ24+ζ56ζ24−ζ56ζ8−ζ72−ζ8+ζ7200000000000000000000
χ262222222222−1+52−1−52-2-2-2-2−1+52−1+52−1−52−1−52−1+52−1−52-2-2-2-2-2-2−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−521−521−521+521+521−521−521+521+52221−521−521+521+521−521−521+521+521−521+521−521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−520000−ζ24+ζ56ζ24−ζ56ζ8−ζ72−ζ8+ζ72−ζ24+ζ56ζ24−ζ56ζ8−ζ72−ζ8+ζ72ζ24−ζ56−ζ24+ζ56−ζ8+ζ72ζ8−ζ72ζ24−ζ56−ζ24+ζ56−ζ8+ζ72ζ8−ζ7200000000000000000000
χ272222222222−1−52−1+522222−1−52−1−52−1+52−1+52−1−52−1+52222222−1−52−1+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+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+5200000000000000000000
χ282222222222−1−52−1+522222−1−52−1−52−1+52−1+52−1−52−1+52222222−1−52−1+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+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+52-2-2-2-21+521+521−521−521+521+521−521−521+521+521−521−521+521+521−521−5200000000000000000000
χ292222222222−1−52−1+522222−1−52−1−52−1+52−1+52−1−52−1+52-2-2-2-222−1−52−1+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+52-2-21+521+521−521−521+521+521−521−52−1−52−1+52−1−52−1+521+521+521−521−521+521+521−521−5222-2-2−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−5200000000000000000000
χ302222222222−1−52−1+522222−1−52−1−52−1+52−1+52−1−52−1+52-2-2-2-222−1−52−1+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+52-2-21+521+521−521−521+521+521−521−52−1−52−1+52−1−52−1+521+521+521−521−521+521+521−521−52-2-2221+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+5200000000000000000000
χ312222222222−1−52−1+52-2-2-2-2−1−52−1−52−1+52−1+52−1−52−1+522222-2-2−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+521+521+521−521−521+521+521−521−52-2-2−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521−521+521−521+521+521−521−521+521+521−521−520000−ζ8+ζ72ζ8−ζ72−ζ24+ζ56ζ24−ζ56−ζ8+ζ72ζ8−ζ72−ζ24+ζ56ζ24−ζ56−ζ8+ζ72ζ8−ζ72−ζ24+ζ56ζ24−ζ56−ζ8+ζ72ζ8−ζ72−ζ24+ζ56ζ24−ζ5600000000000000000000
χ322222222222−1−52−1+52-2-2-2-2−1−52−1−52−1+52−1+52−1−52−1+522222-2-2−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+521+521+521−521−521+521+521−521−52-2-2−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+521+521−521+521−521+521+521−521−521+521+521−521−520000ζ8−ζ72−ζ8+ζ72ζ24−ζ56−ζ24+ζ56ζ8−ζ72−ζ8+ζ72ζ24−ζ56−ζ24+ζ56ζ8−ζ72−ζ8+ζ72ζ24−ζ56−ζ24+ζ56ζ8−ζ72−ζ8+ζ72ζ24−ζ56−ζ24+ζ5600000000000000000000
χ332222222222−1−52−1+52-2-2-2-2−1−52−1−52−1+52−1+52−1−52−1+52-2-2-2-2-2-2−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+521+521+521−521−521+521+521−521−52221+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+520000−ζ8+ζ72ζ8−ζ72−ζ24+ζ56ζ24−ζ56−ζ8+ζ72ζ8−ζ72−ζ24+ζ56ζ24−ζ56ζ8−ζ72−ζ8+ζ72ζ24−ζ56−ζ24+ζ56ζ8−ζ72−ζ8+ζ72ζ24−ζ56−ζ24+ζ5600000000000000000000
χ342222222222−1−52−1+52-2-2-2-2−1−52−1−52−1+52−1+52−1−52−1+52-2-2-2-2-2-2−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+521+521+521−521−521+521+521−521−52221+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+520000ζ8−ζ72−ζ8+ζ72ζ24−ζ56−ζ24+ζ56ζ8−ζ72−ζ8+ζ72ζ24−ζ56−ζ24+ζ56−ζ8+ζ72ζ8−ζ72−ζ24+ζ56ζ24−ζ56−ζ8+ζ72ζ8−ζ72−ζ24+ζ56ζ24−ζ5600000000000000000000
χ352222-2-22-2-222200002222222-22-200-2-2-2-222-2-2-2-22200000000002-22-22-22-20000000000000000000000000000000022−2−222−2−2000000002−22−2
χ362222-2-22-2-222200002222222-22-200-2-2-2-222-2-2-2-22200000000002-22-22-22-200000000000000000000000000000000−2−222−2−22200000000−22−22
χ372222-2-22-2-22220000222222-22-2200-2-2-2-222-2-2-2-2220000000000-22-22-22-220000000000000000000000000000000022−2−222−2−200000000−22−22
χ382222-2-22-2-22220000222222-22-2200-2-2-2-222-2-2-2-2220000000000-22-22-22-2200000000000000000000000000000000−2−222−2−222000000002−22−2
χ392222-2-2-222-22222222222220000-2-2-2-2-2-2-2-22222-2-2222222220000000000-2-2-2-200000000000000000000000000000000000000002-22-20000
χ402222-2-2-222-22222222222220000-2-2-2-2-2-2-2-22222-2-2222222220000000000-2-2-2-20000000000000000000000000000000000000000-22-220000
χ412222-2-2-222-222-2-2-2-2222222000022-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-2000000000022220000000000000000000000000000000000002-22-200000000
χ422222-2-2-222-222-2-2-2-2222222000022-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-200000000002222000000000000000000000000000000000000-22-2200000000
χ4322-2-22-222-2-222-2-222-2-2-2-2222i2i−2i−2i2-222-2-22222-2-2-2-2-2-2-2-22222−2i2i2i2i2i2i−2i−2i−2i−2i-2-222−2i−2i−2i−2i2i2i2i2i0000000000000000000000000000000000000000
χ4422-2-22-222-2-222-2-222-2-2-2-222−2i−2i2i2i2-222-2-22222-2-2-2-2-2-2-2-222222i−2i−2i−2i−2i−2i2i2i2i2i-2-2222i2i2i2i−2i−2i−2i−2i0000000000000000000000000000000000000000
χ4522-2-22-222-2-2−1+52−1−5222-2-21−521−521+521+52−1+52−1−522i2i−2i−2i-22−1+52−1−521−521+52−1+52−1−52−1+52−1−521−521+521−521+52−1+52−1+52−1−52−1−521−521−521+521+522i−2i−ζ44−ζ76−ζ44−ζ76−ζ12−ζ28−ζ12−ζ28ζ44+ζ76ζ44+ζ76ζ12+ζ28ζ12+ζ28−1+52−1−521−521+52−ζ44−ζ76−ζ44−ζ76−ζ12−ζ28−ζ12−ζ28ζ44+ζ76ζ44+ζ76ζ12+ζ28ζ12+ζ282-22i−2i−1+52−1+52−1−52−1−521−521−521+521+52−ζ44−ζ76−ζ44−ζ76−ζ12−ζ28−ζ12−ζ28ζ44+ζ76ζ44+ζ76ζ12+ζ28ζ12+ζ2800000000000000000000
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Here ζ is a primitive root of unity of order 80 (ζ80 = 1); i = ζ20.