Finite Group Databasebeta

← Group #12016073

Character table — Group #12016073

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98
size1111222222222244444444444444444488888888888888888888888888888888888888881616161616161616161616161616404040404040404080808080
order1222225510101010101022224410101010202020202020202044444444101010101010101020202020202020202020202020202020202020202020202088202020204040404040404040444444444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1
χ4111111111111111111111111111111111111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111
χ511111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ611111111111111111111111111111111-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ711111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111-1-111-1-1-1-111
χ811111111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-111-1-11111-1-1
χ91-11-11-11111-1-1-1-11-11-1-1111-1-1-1-1-1-11111i−ii−ii−ii−i1111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i1-1ii−i−i1111-1-1-1-11-1i−i1-1i−ii−i1-1
χ101-11-11-11111-1-1-1-11-11-1-1111-1-1-1-1-1-11111i−ii−ii−ii−i1111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−i1-1ii−i−i1111-1-1-1-1-11−ii-11−ii−ii-11
χ111-11-11-11111-1-1-1-11-11-1-1111-1-1-1-1-1-11111i−ii−i−ii−ii1111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii-11−i−iii-1-1-1-111111-1−ii1-1−iii−i-11
χ121-11-11-11111-1-1-1-11-11-1-1111-1-1-1-1-1-11111i−ii−i−ii−ii1111-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i−i−i−i−iiiii-11−i−iii-1-1-1-11111-11i−i-11i−i−ii1-1
χ131-11-11-11111-1-1-1-11-11-1-1111-1-1-1-1-1-11111−ii−iii−ii−i1111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i-11ii−i−i-1-1-1-111111-1i−i1-1i−i−ii-11
χ141-11-11-11111-1-1-1-11-11-1-1111-1-1-1-1-1-11111−ii−iii−ii−i1111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiiiiiii−i−i−i−i-11ii−i−i-1-1-1-11111-11−ii-11−iii−i1-1
χ151-11-11-11111-1-1-1-11-11-1-1111-1-1-1-1-1-11111−ii−ii−ii−ii1111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii1-1−i−iii1111-1-1-1-11-1−ii1-1−ii−ii1-1
χ161-11-11-11111-1-1-1-11-11-1-1111-1-1-1-1-1-11111−ii−ii−ii−ii1111-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iiiii1-1−i−iii1111-1-1-1-1-11i−i-11i−ii−i-11
χ17222222222222222-2-22-2-22222-2-2-2-2-2-2-2-20000000022-2-222-2-2000000000000000000000000000000000000002200-2-2000000
χ18222222222222222-2-22-2-22222-2-2-2-2-2-2-2-20000000022-2-222-2-200000000000000000000000000000000000000-2-20022000000
χ1922222222222222-222-2-2-22222-2-2-2-2-2-2-2-200000000-2-222-2-22200000000000000000000000000000000000000002200-2-20000
χ2022222222222222-222-2-2-22222-2-2-2-2-2-2-2-200000000-2-222-2-2220000000000000000000000000000000000000000-2-200220000
χ2122222222222222-2-2-2-222222222222222000022-2-2-2-2-2-2-2-2-2-20000000000000000-2-2-2-2-2-2-2-200222200000000000000000000
χ2222222222222222-2-2-2-2222222222222220000-2-222-2-2-2-2-2-2-2-200000000000000002222222200-2-2-2-200000000000000000000
χ23222222−1+52−1−52−1+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+52−1−52−1−5222222222−1+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+52−1−52−1−52−1+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+52−1−52−1−52000000000000
χ24222222−1+52−1−52−1+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+52−1−52−1−522222-2-2-2-2−1+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+52−1−52−1−52−1+52−1+52−1−52−1−521−521−521+521+521−521−521+521+52-2-21−521+521−521+521−521−521+521+521−521−521+521+52000000000000
χ25222222−1+52−1−52−1+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+52−1−52−1−52-2-2-2-22222−1+52−1−52−1+52−1−52−1+52−1−52−1+52−1−521−521−521+521+521−521−521+521+521−521−521+521+521−521−521+521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52-2-2−1+52−1−52−1+52−1−521−521−521+521+521−521−521+521+52000000000000
χ26222222−1+52−1−52−1+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+52−1−52−1−52-2-2-2-2-2-2-2-2−1+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+521−521−521+521+521−521−521+521+52221−521+521−521+52−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52000000000000
χ27222222−1+52−1−52−1+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+52−1−52−1−52000022-2-21−521+521−521+521−521+521−521+52ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ181−521−521+521+521−521−521+521+5200−1+52−1−52−1+52−1−52ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18000000000000
χ28222222−1+52−1−52−1+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+52−1−52−1−52000022-2-21−521+521−521+521−521+521−521+52−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ181−521−521+521+521−521−521+521+5200−1+52−1−52−1+52−1−52−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18000000000000
χ29222222−1+52−1−52−1+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+52−1−52−1−520000-2-2221−521+521−521+521−521+521−521+52ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52001−521+521−521+52−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18000000000000
χ30222222−1+52−1−52−1+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+52−1−52−1−520000-2-2221−521+521−521+521−521+521−521+52−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18−ζ6+ζ14ζ6−ζ14ζ2−ζ18−ζ2+ζ18−1+52−1+52−1−52−1−52−1+52−1+52−1−52−1−52001−521+521−521+52ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18ζ6−ζ14−ζ6+ζ14−ζ2+ζ18ζ2−ζ18000000000000
χ31222222−1−52−1+52−1−52−1+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+5222222222−1−52−1+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+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+52000000000000
χ32222222−1−52−1+52−1−52−1+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+522222-2-2-2-2−1−52−1+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+52−1−52−1−52−1+52−1+521+521+521−521−521+521+521−521−52-2-21+521−521+521−521+521+521−521−521+521+521−521−52000000000000
χ33222222−1−52−1+52−1−52−1+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+52-2-2-2-22222−1−52−1+52−1−52−1+52−1−52−1+52−1−52−1+521+521+521−521−521+521+521−521−521+521+521−521−521+521+521−521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52-2-2−1−52−1+52−1−52−1+521+521+521−521−521+521+521−521−52000000000000
χ34222222−1−52−1+52−1−52−1+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+52-2-2-2-2-2-2-2-2−1−52−1+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+521−521−521+521+521−521−521+521+521−521−52221+521−521+521−52−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52000000000000
χ35222222−1−52−1+52−1−52−1+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+52000022-2-21+521−521+521−521+521−521+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−ζ141+521+521−521−521+521+521−521−5200−1−52−1+52−1−52−1+52−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14000000000000
χ36222222−1−52−1+52−1−52−1+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+52000022-2-21+521−521+521−521+521−521+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+ζ141+521+521−521−521+521+521−521−5200−1−52−1+52−1−52−1+52ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14000000000000
χ37222222−1−52−1+52−1−52−1+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+520000-2-2221+521−521+521−521+521−521+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−ζ14−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52001+521−521+521−52ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14ζ2−ζ18−ζ2+ζ18ζ6−ζ14−ζ6+ζ14000000000000
χ38222222−1−52−1+52−1−52−1+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+520000-2-2221+521−521+521−521+521−521+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+ζ14−1−52−1−52−1+52−1+52−1−52−1−52−1+52−1+52001+521−521+521−52−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14−ζ2+ζ18ζ2−ζ18−ζ6+ζ14ζ6−ζ14000000000000
χ392-22-22-22222-2-2-2-222-2-22-222-2-22222-2-2-2-20000000022-2-2-2-222000000000000000000000000000000000000002-200-22000000
χ402-22-22-22222-2-2-2-222-2-22-222-2-22222-2-2-2-20000000022-2-2-2-22200000000000000000000000000000000000000-22002-2000000
χ412-22-22-22222-2-2-2-2-22-22-2222-2-2-2-2-2-2222200002i−2i−2i2i-2-2-2-222220000000000000000−2i−2i−2i−2i2i2i2i2i002i2i−2i−2i00000000000000000000
χ422-22-22-22222-2-2-2-2-22-22-2222-2-2-2-2-2-222220000−2i2i2i−2i-2-2-2-2222200000000000000002i2i2i2i−2i−2i−2i−2i00−2i−2i2i2i00000000000000000000
χ432-22-22-22222-2-2-2-2-2-2222-222-2-22222-2-2-2-200000000-2-22222-2-200000000000000000000000000000000000000002i−2i00−2i2i0000
χ442-22-22-22222-2-2-2-2-2-2222-222-2-22222-2-2-2-200000000-2-22222-2-20000000000000000000000000000000000000000−2i2i002i−2i0000
χ452-22-22-2−1+52−1−52−1+52−1−521−521+521−521+522-22-2-22−1+52−1−521−521+521−521−521+521+52−1+52−1+52−1−52−1−522i−2i2i−2i2i−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+ζ7−ζ11−ζ19−ζ11−ζ19−ζ3−ζ7−ζ3−ζ7ζ11+ζ19ζ11+ζ19ζ3+ζ7ζ3+ζ72-2−ζ11−ζ19−ζ3−ζ7ζ11+ζ19ζ3+ζ7−1+52−1+52−1−52−1−521−521−521+521+52000000000000
χ462-22-22-2−1+52−1−52−1+52−1−521−521+521−521+522-22-2-22−1+52−1−521−521+521−521−521+521+52−1+52−1+52−1−52−1−522i−2i2i−2i−2i2i−2i2i−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+ζ7ζ11+ζ19ζ11+ζ19ζ3+ζ7ζ3+ζ7−ζ11−ζ19−ζ11−ζ19−ζ3−ζ7−ζ3−ζ7-22ζ11+ζ19ζ3+ζ7−ζ11−ζ19−ζ3−ζ71−521−521+521+52−1+52−1+52−1−52−1−52000000000000
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χ9188-8-800−2+25−2−252−252+25−2+25−2−252−252+25000000000000000000000000000000000000000000000000002ζ11−2ζ19−2ζ11+2ζ19−2ζ3+2ζ72ζ3−2ζ72ζ11−2ζ19−2ζ11+2ζ19−2ζ3+2ζ72ζ3−2ζ700000000000000000000000000
χ9288-8-800−2−25−2+252+252−25−2−25−2+252+252−25000000000000000000000000000000000000000000000000002ζ3−2ζ7−2ζ3+2ζ72ζ11−2ζ19−2ζ11+2ζ192ζ3−2ζ7−2ζ3+2ζ72ζ11−2ζ19−2ζ11+2ζ1900000000000000000000000000
χ9388-8-800−2−25−2+252+252−25−2−25−2+252+252−2500000000000000000000000000000000000000000000000000−2ζ3+2ζ72ζ3−2ζ7−2ζ11+2ζ192ζ11−2ζ19−2ζ3+2ζ72ζ3−2ζ7−2ζ11+2ζ192ζ11−2ζ1900000000000000000000000000
χ948-8-880088-8-8-8-888000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ958-8-8800−2+25−2−252−252+252−252+25−2+25−2−25000000000000000000000000000000000000000000000000002ζ6−2ζ14−2ζ6+2ζ142ζ2−2ζ18−2ζ2+2ζ18−2ζ6+2ζ142ζ6−2ζ14−2ζ2+2ζ182ζ2−2ζ1800000000000000000000000000
χ968-8-8800−2+25−2−252−252+252−252+25−2+25−2−2500000000000000000000000000000000000000000000000000−2ζ6+2ζ142ζ6−2ζ14−2ζ2+2ζ182ζ2−2ζ182ζ6−2ζ14−2ζ6+2ζ142ζ2−2ζ18−2ζ2+2ζ1800000000000000000000000000
χ978-8-8800−2−25−2+252+252−252+252−25−2−25−2+2500000000000000000000000000000000000000000000000000−2ζ2+2ζ182ζ2−2ζ182ζ6−2ζ14−2ζ6+2ζ142ζ2−2ζ18−2ζ2+2ζ18−2ζ6+2ζ142ζ6−2ζ1400000000000000000000000000
χ988-8-8800−2−25−2+252+252−252+252−25−2−25−2+25000000000000000000000000000000000000000000000000002ζ2−2ζ18−2ζ2+2ζ18−2ζ6+2ζ142ζ6−2ζ14−2ζ2+2ζ182ζ2−2ζ182ζ6−2ζ14−2ζ6+2ζ1400000000000000000000000000

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