Finite Group Databasebeta

← Group #13016509

Character table — Group #13016509

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size11112222222222444444444444444444444444445555888888888888888888888888101010101010101010102020202020202020202040404040404040404040404040404040
order12222222444444244444444451010101010101020202020202020204444101010102020202020202020202020202020202020202020444444444444444444448888888888888888
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiii−i−i−i−iiiii−i−i−i−i
χ41111111111111111111111111111111111111111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−iiiii−i−i−i−iiiii
χ51111111111111111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ61111111111111111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ71111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111iiii−i−i−i−i−i−i−i−iiiii
χ81111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111−i−i−i−iiiiiiiii−i−i−i−i
χ9111111-1-111-1-1-1-1-11iiii−i−i−i−i111-1-1-1-111111-1-1-1-1111111-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-11111-1-1-1-1-1-11-1iiii−i−i−i−i11-1-111-1-1ii−i−iii−i−i
χ10111111-1-111-1-1-1-1-11iiii−i−i−i−i111-1-1-1-111111-1-1-1-1111111-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-11111-1-1-1-1-1-11-1iiii−i−i−i−i-1-111-1-111−i−iii−i−iii
χ11111111-1-111-1-1-1-1-11iiii−i−i−i−i111-1-1-1-111111-1-1-1-1-1-1-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-1-1-1-1-1111111-11−i−i−i−iiiiiii−i−i−i−iii-1-11111-1-1
χ12111111-1-111-1-1-1-1-11iiii−i−i−i−i111-1-1-1-111111-1-1-1-1-1-1-1-111-1-1iiiiiiii−i−i−i−i−i−i−i−i11-1-1-1-1-1-1111111-11−i−i−i−iiiii−i−iiiii−i−i11-1-1-1-111
χ13111111-1-111-1-1-1-1-11−i−i−i−iiiii111-1-1-1-111111-1-1-1-1111111-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-11111-1-1-1-1-1-11-1−i−i−i−iiiii11-1-111-1-1−i−iii−i−iii
χ14111111-1-111-1-1-1-1-11−i−i−i−iiiii111-1-1-1-111111-1-1-1-1111111-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-11111-1-1-1-1-1-11-1−i−i−i−iiiii-1-111-1-111ii−i−iii−i−i
χ15111111-1-111-1-1-1-1-11−i−i−i−iiiii111-1-1-1-111111-1-1-1-1-1-1-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-1-1-1-1-1111111-11iiii−i−i−i−iii−i−i−i−iii11-1-1-1-111
χ16111111-1-111-1-1-1-1-11−i−i−i−iiiii111-1-1-1-111111-1-1-1-1-1-1-1-111-1-1−i−i−i−i−i−i−i−iiiiiiiii11-1-1-1-1-1-1111111-11iiii−i−i−i−i−i−iiiii−i−i-1-11111-1-1
χ171111-1-111-1-111-1-1-1111-1-111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1111-111-1-111-1-11-11-11-11-11-11-11-11-1
χ181111-1-111-1-111-1-1-1111-1-111-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-1111-111-1-111-1-1-11-11-11-11-11-11-11-11
χ191111-1-111-1-111-1-1-1111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-111-1-1-11-1-111-1-111i−ii−i−ii−iii−ii−i−ii−ii
χ201111-1-111-1-111-1-1-1111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-111-1-1-11-1-111-1-111−ii−iii−ii−i−ii−iii−ii−i
χ211111-1-111-1-111-1-1-11-1-111-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1111-1-1-111-1-1111-11-11-11-1-11-11-11-11
χ221111-1-111-1-111-1-1-11-1-111-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111-1-1111-1-1-111-1-111-11-11-11-111-11-11-11-1
χ231111-1-111-1-111-1-1-11-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-111-1-1-1111-1-111-1-1i−ii−i−ii−ii−ii−iii−ii−i
χ241111-1-111-1-111-1-1-11-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-111-1-1-1111-1-111-1-1−ii−iii−ii−ii−ii−i−ii−ii
χ251111-1-1-1-1-1-1-1-11111ii−i−i−i−iii111-1-1-1-11-1-1-1-111111111-1-111iiii−i−i−i−i−i−i−i−iiiii11-1-1-1-1-1-1-1-111-1-111ii−i−i−i−iii1-1-111-1-11i−i−iii−i−ii
χ261111-1-1-1-1-1-1-1-11111ii−i−i−i−iii111-1-1-1-11-1-1-1-111111111-1-111iiii−i−i−i−i−i−i−i−iiiii11-1-1-1-1-1-1-1-111-1-111ii−i−i−i−iii-111-1-111-1−iii−i−iii−i
χ271111-1-1-1-1-1-1-1-11111ii−i−i−i−iii111-1-1-1-11-1-1-1-11111-1-1-1-1-1-111iiii−i−i−i−i−i−i−i−iiiii11-1-1111111-1-111-1-1−i−iiiii−i−ii−i−ii−iii−i-111-11-1-11
χ281111-1-1-1-1-1-1-1-11111ii−i−i−i−iii111-1-1-1-11-1-1-1-11111-1-1-1-1-1-111iiii−i−i−i−i−i−i−i−iiiii11-1-1111111-1-111-1-1−i−iiiii−i−i−iii−ii−i−ii1-1-11-111-1
χ291111-1-1-1-1-1-1-1-11111−i−iiiii−i−i111-1-1-1-11-1-1-1-111111111-1-111−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-1-1-1-1-111-1-111−i−iiiii−i−i1-1-111-1-11−iii−i−iii−i
χ301111-1-1-1-1-1-1-1-11111−i−iiiii−i−i111-1-1-1-11-1-1-1-111111111-1-111−i−i−i−iiiiiiiii−i−i−i−i11-1-1-1-1-1-1-1-111-1-111−i−iiiii−i−i-111-1-111-1i−i−iii−i−ii
χ311111-1-1-1-1-1-1-1-11111−i−iiiii−i−i111-1-1-1-11-1-1-1-11111-1-1-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i11-1-1111111-1-111-1-1ii−i−i−i−iiii−i−ii−iii−i1-1-11-111-1
χ321111-1-1-1-1-1-1-1-11111−i−iiiii−i−i111-1-1-1-11-1-1-1-11111-1-1-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i11-1-1111111-1-111-1-1ii−i−i−i−iii−iii−ii−i−ii-111-11-1-11
χ3322222222-2-2-2-2-2-22-20000000022222222-2-2-2-2-2-2-2-2222222220000000000000000-2-2-2-222-2-222-2-2-2-2-22000000000000000000000000
χ3422222222-2-2-2-2-2-22-20000000022222222-2-2-2-2-2-2-2-2-2-2-2-222220000000000000000-2-2-2-2-2-222-2-222222-2000000000000000000000000
χ35222222-2-2-2-22222-2-200000000222-2-2-2-22-2-2-2-22222222222-2-20000000000000000-2-22222-2-2-2-22222-2-2000000000000000000000000
χ36222222-2-2-2-22222-2-200000000222-2-2-2-22-2-2-2-22222-2-2-2-222-2-20000000000000000-2-222-2-22222-2-2-2-222000000000000000000000000
χ372222-2-22222-2-222-2-20000000022222222222222222222-2-2-2-20000000000000000-2-2-2-2-2-2222222-2-2-2-2000000000000000000000000
χ382222-2-22222-2-222-2-2000000002222222222222222-2-2-2-2-2-2-2-20000000000000000-2-2-2-222-2-2-2-2-2-22222000000000000000000000000
χ392222-2-2-2-22222-2-22-200000000222-2-2-2-222222-2-2-2-22222-2-2220000000000000000-2-222-2-222-2-2-2-222-22000000000000000000000000
χ402222-2-2-2-22222-2-22-200000000222-2-2-2-222222-2-2-2-2-2-2-2-2-2-2220000000000000000-2-22222-2-22222-2-22-2000000000000000000000000
χ412-22-22-200002i−2i2i−2i001+i−1−i1+i−1−i1−i−1+i1−i−1+i22-20000-200002i2i−2i−2i2i−2i2i−2i2-2001+i1+i−1−i−1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i1−i1−i−1+i−1+i002i−2i2i−2i00002-22-2001−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000000000
χ422-22-22-200002i−2i2i−2i001+i−1−i1+i−1−i1−i−1+i1−i−1+i22-20000-200002i2i−2i−2i−2i2i−2i2i2-2001+i1+i−1−i−1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i1−i1−i−1+i−1+i002i−2i−2i2i0000-22-2200−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000000000
χ432-22-22-200002i−2i2i−2i00−1−i1+i−1−i1+i−1+i1−i−1+i1−i22-20000-200002i2i−2i−2i2i−2i2i−2i2-200−1−i−1−i1+i1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1+i−1+i1−i1−i002i−2i2i−2i00002-22-200−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000000000
χ442-22-22-200002i−2i2i−2i00−1−i1+i−1−i1+i−1+i1−i−1+i1−i22-20000-200002i2i−2i−2i−2i2i−2i2i2-200−1−i−1−i1+i1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1+i−1+i1−i1−i002i−2i−2i2i0000-22-22001−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000000000
χ452-22-22-20000−2i2i−2i2i001−i−1+i1−i−1+i1+i−1−i1+i−1−i22-20000-20000−2i−2i2i2i2i−2i2i−2i2-2001−i1−i−1+i−1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i1+i1+i−1−i−1−i00−2i2i2i−2i0000-22-2200−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000000000
χ462-22-22-20000−2i2i−2i2i001−i−1+i1−i−1+i1+i−1−i1+i−1−i22-20000-20000−2i−2i2i2i−2i2i−2i2i2-2001−i1−i−1+i−1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i1+i1+i−1−i−1−i00−2i2i−2i2i00002-22-2001+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000000000
χ472-22-22-20000−2i2i−2i2i00−1+i1−i−1+i1−i−1−i1+i−1−i1+i22-20000-20000−2i−2i2i2i2i−2i2i−2i2-200−1+i−1+i1−i1−i−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1−i−1−i1+i1+i00−2i2i2i−2i0000-22-22001+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000000000
χ482-22-22-20000−2i2i−2i2i00−1+i1−i−1+i1−i−1−i1+i−1−i1+i22-20000-20000−2i−2i2i2i−2i2i−2i2i2-200−1+i−1+i1−i1−i−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1−i−1−i1+i1+i00−2i2i−2i2i00002-22-200−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000000000
χ492-22-2-2200002i−2i−2i2i001+i−1−i−1−i1+i1−i−1+i−1+i1−i22-20000-20000−2i−2i2i2i2i−2i2i−2i-22001+i1+i−1−i−1−i−1−i−1−i1+i1+i1−i1−i−1+i−1+i−1+i−1+i1−i1−i002i−2i−2i2i0000-222-2001−i−1+i−1+i1−i1+i−1−i−1−i1+i0000000000000000
χ502-22-2-2200002i−2i−2i2i001+i−1−i−1−i1+i1−i−1+i−1+i1−i22-20000-20000−2i−2i2i2i−2i2i−2i2i-22001+i1+i−1−i−1−i−1−i−1−i1+i1+i1−i1−i−1+i−1+i−1+i−1+i1−i1−i002i−2i2i−2i00002-2-2200−1+i1−i1−i−1+i−1−i1+i1+i−1−i0000000000000000
χ512-22-2-2200002i−2i−2i2i00−1−i1+i1+i−1−i−1+i1−i1−i−1+i22-20000-20000−2i−2i2i2i2i−2i2i−2i-2200−1−i−1−i1+i1+i1+i1+i−1−i−1−i−1+i−1+i1−i1−i1−i1−i−1+i−1+i002i−2i−2i2i0000-222-200−1+i1−i1−i−1+i−1−i1+i1+i−1−i0000000000000000
χ522-22-2-2200002i−2i−2i2i00−1−i1+i1+i−1−i−1+i1−i1−i−1+i22-20000-20000−2i−2i2i2i−2i2i−2i2i-2200−1−i−1−i1+i1+i1+i1+i−1−i−1−i−1+i−1+i1−i1−i1−i1−i−1+i−1+i002i−2i2i−2i00002-2-22001−i−1+i−1+i1−i1+i−1−i−1−i1+i0000000000000000
χ532-22-2-220000−2i2i2i−2i001−i−1+i−1+i1−i1+i−1−i−1−i1+i22-20000-200002i2i−2i−2i2i−2i2i−2i-22001−i1−i−1+i−1+i−1+i−1+i1−i1−i1+i1+i−1−i−1−i−1−i−1−i1+i1+i00−2i2i−2i2i00002-2-2200−1−i1+i1+i−1−i−1+i1−i1−i−1+i0000000000000000
χ542-22-2-220000−2i2i2i−2i001−i−1+i−1+i1−i1+i−1−i−1−i1+i22-20000-200002i2i−2i−2i−2i2i−2i2i-22001−i1−i−1+i−1+i−1+i−1+i1−i1−i1+i1+i−1−i−1−i−1−i−1−i1+i1+i00−2i2i2i−2i0000-222-2001+i−1−i−1−i1+i1−i−1+i−1+i1−i0000000000000000
χ552-22-2-220000−2i2i2i−2i00−1+i1−i1−i−1+i−1−i1+i1+i−1−i22-20000-200002i2i−2i−2i2i−2i2i−2i-2200−1+i−1+i1−i1−i1−i1−i−1+i−1+i−1−i−1−i1+i1+i1+i1+i−1−i−1−i00−2i2i−2i2i00002-2-22001+i−1−i−1−i1+i1−i−1+i−1+i1−i0000000000000000
χ562-22-2-220000−2i2i2i−2i00−1+i1−i1−i−1+i−1−i1+i1+i−1−i22-20000-200002i2i−2i−2i−2i2i−2i2i-2200−1+i−1+i1−i1−i1−i1−i−1+i−1+i−1−i−1−i1+i1+i1+i1+i−1−i−1−i00−2i2i2i−2i0000-222-200−1−i1+i1+i−1−i−1+i1−i1−i−1+i0000000000000000
χ57444444444444444444444444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000000000000000
χ584444444444444444-4-4-4-4-4-4-4-4-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000-1-1-1-11111111111111111-1-1-1-1000000000000000000000000000000000000
χ5944444444-4-4-4-4-4-44-400000000-1-1-1-1-1-1-1-1111111110000-1-1-1-15−55−55−55−55−55−55−55−51111000000000000000000000000000000000000
χ6044444444-4-4-4-4-4-44-400000000-1-1-1-1-1-1-1-1111111110000-1-1-1-1−55−55−55−55−55−55−55−551111000000000000000000000000000000000000
χ61444444-4-444-4-4-4-4-444i4i4i4i−4i−4i−4i−4i-1-1-11111-1-1-1-1-111110000-1-111−i−i−i−i−i−i−i−iiiiiiiii-1-111000000000000000000000000000000000000
χ62444444-4-444-4-4-4-4-44−4i−4i−4i−4i4i4i4i4i-1-1-11111-1-1-1-1-111110000-1-111iiiiiiii−i−i−i−i−i−i−i−i-1-111000000000000000000000000000000000000
χ63444444-4-4-4-44444-4-400000000-1-1-11111-11111-1-1-1-10000-1-111i5−i5i5−i5i5−i5i5−i5−i5i5−i5i5−i5i5−i5i511-1-1000000000000000000000000000000000000
χ64444444-4-4-4-44444-4-400000000-1-1-11111-11111-1-1-1-10000-1-111−i5i5−i5i5−i5i5−i5i5i5−i5i5−i5i5−i5i5−i511-1-1000000000000000000000000000000000000
χ654444-4-44444-4-444-4-400000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000011115−55−5−55−555−55−5−55−551111000000000000000000000000000000000000
χ664444-4-44444-4-444-4-400000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100001111−55−555−55−5−55−555−55−51111000000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 20 (ζ20 = 1); i = ζ5.