Finite Group Databasebeta

← Group #13016454

Character table — Group #13016454

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104
size11112222222222444444444444444444444444445555888888888888888888888888101010101010101010102020202020202020202040404040404040404040404040404040
order12222244444444445888888881010101010101020202020202020204444202020202020202040404040404040404040404040404040222244444444888888888888888888888888
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
χ511111111111111111-1-1-1-1-1-1-1-1111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ611111111111111111-1-1-1-1-1-1-1-1111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ711111111111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111iiii−i−i−i−i−i−i−i−iiiii
χ811111111111111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111−i−i−i−iiiiiiiii−i−i−i−i
χ9111111-1-1-1-1-1-1-1-1111iiii−i−i−i−i1111111-1-1-1-1-1-1-1-111111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-111-1-1-1-111iiii−i−i−i−i11-1-111-1-1ii−i−iii−i−i
χ10111111-1-1-1-1-1-1-1-1111iiii−i−i−i−i1111111-1-1-1-1-1-1-1-111111111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i-1-1-1-111-1-1-1-111iiii−i−i−i−i-1-111-1-111−i−iii−i−iii
χ11111111-1-1-1-1-1-1-1-1111iiii−i−i−i−i1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i1111-1-11111-1-1−i−i−i−iiiiiii−i−i−i−iii-1-11111-1-1
χ12111111-1-1-1-1-1-1-1-1111iiii−i−i−i−i1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−i1111-1-11111-1-1−i−i−i−iiiii−i−iiiii−i−i11-1-1-1-111
χ13111111-1-1-1-1-1-1-1-1111−i−i−i−iiiii1111111-1-1-1-1-1-1-1-111111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-111-1-1-1-111−i−i−i−iiiii11-1-111-1-1−i−iii−i−iii
χ14111111-1-1-1-1-1-1-1-1111−i−i−i−iiiii1111111-1-1-1-1-1-1-1-111111111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii-1-1-1-111-1-1-1-111−i−i−i−iiiii-1-111-1-111ii−i−iii−i−i
χ15111111-1-1-1-1-1-1-1-1111−i−i−i−iiiii1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii1111-1-11111-1-1iiii−i−i−i−iii−i−i−i−iii11-1-1-1-111
χ16111111-1-1-1-1-1-1-1-1111−i−i−i−iiiii1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii1111-1-11111-1-1iiii−i−i−i−i−i−iiiii−i−i-1-11111-1-1
χ171111-1-11111-1-1-1-11-11ii−i−iii−i−i-1-1-1-11111111-1-1-1-1111111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-1-1-111-1-11-1ii−i−iii−i−i1-11-11-11-1i−ii−ii−ii−i
χ181111-1-11111-1-1-1-11-11ii−i−iii−i−i-1-1-1-11111111-1-1-1-1111111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-1-1-111-1-11-1ii−i−iii−i−i-11-11-11-11−ii−ii−ii−ii
χ191111-1-11111-1-1-1-11-11ii−i−iii−i−i-1-1-1-11111111-1-1-1-1-1-1-1-111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i-1-11111-1-111-11−i−iii−i−iiii−ii−i−ii−ii-11-111-11-1
χ201111-1-11111-1-1-1-11-11ii−i−iii−i−i-1-1-1-11111111-1-1-1-1-1-1-1-111-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i-1-11111-1-111-11−i−iii−i−iii−ii−iii−ii−i1-11-1-11-11
χ211111-1-11111-1-1-1-11-11−i−iii−i−iii-1-1-1-11111111-1-1-1-1111111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-1-1-111-1-11-1−i−iii−i−iii1-11-11-11-1−ii−ii−ii−ii
χ221111-1-11111-1-1-1-11-11−i−iii−i−iii-1-1-1-11111111-1-1-1-1111111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-1-1-111-1-11-1−i−iii−i−iii-11-11-11-11i−ii−ii−ii−i
χ231111-1-11111-1-1-1-11-11−i−iii−i−iii-1-1-1-11111111-1-1-1-1-1-1-1-111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii-1-11111-1-111-11ii−i−iii−i−ii−ii−i−ii−ii1-11-1-11-11
χ241111-1-11111-1-1-1-11-11−i−iii−i−iii-1-1-1-11111111-1-1-1-1-1-1-1-111-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii-1-11111-1-111-11ii−i−iii−i−i−ii−iii−ii−i-11-111-11-1
χ251111-1-1-1-1-1-111111-1111-1-1-1-111-1-1-1-1111-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1111-111-1-1-1-1111-1-111-1-111-1-111-1-11
χ261111-1-1-1-1-1-111111-1111-1-1-1-111-1-1-1-1111-1-1-1-11111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-111-1-1-1-1111-111-1-1-1-111-111-1-111-1-111-1-111-1
χ271111-1-1-1-1-1-111111-1111-1-1-1-111-1-1-1-1111-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-11111-1-1-11-1-11111-1-1i−i−ii−iii−ii−i−ii−iii−i
χ281111-1-1-1-1-1-111111-1111-1-1-1-111-1-1-1-1111-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-11111-1-1-11-1-11111-1-1−iii−ii−i−ii−iii−ii−i−ii
χ291111-1-1-1-1-1-111111-11-1-11111-1-1-1-1-1-1111-1-1-1-11111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1111-1-1-11111-1-11-1-111-1-11-111-1-111-1
χ301111-1-1-1-1-1-111111-11-1-11111-1-1-1-1-1-1111-1-1-1-11111111111-1-1-1-111-1-1-1-111111111-1-1-1-1-1-111-1-1-1-1111-1-1-11111-1-1-111-1-111-11-1-111-1-11
χ311111-1-1-1-1-1-111111-11-1-11111-1-1-1-1-1-1111-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-111111111-1-1-1-111-1-11111-1-1-1111-1-1-1-111i−i−ii−iii−i−iii−ii−i−ii
χ321111-1-1-1-1-1-111111-11-1-11111-1-1-1-1-1-1111-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-111111111-1-1-1-111-1-11111-1-1-1111-1-1-1-111−iii−ii−i−iii−i−ii−iii−i
χ3322222222-2-222-2-2-2-22000000002222222-2-2-2-2-2-2-2-22222-2-2-2-222220000000000000000-2-2-2-2222222-2-2000000000000000000000000
χ3422222222-2-222-2-2-2-22000000002222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2222200000000000000002222-2-2-2-2-2-222000000000000000000000000
χ35222222-2-222-2-222-2-22000000002222222222222222222-2-2-2-2-2-2-2-20000000000000000222222-2-2-2-2-2-2000000000000000000000000
χ36222222-2-222-2-222-2-2200000000222222222222222-2-2-2-2-2-2-2-2-2-2-2-20000000000000000-2-2-2-2-2-2222222000000000000000000000000
χ372222-2-222-2-2-2-222-22200000000-2-2-2-2222-2-2-2-222222222-2-22222-2-20000000000000000-2-222-2-222-2-2-22000000000000000000000000
χ382222-2-222-2-2-2-222-22200000000-2-2-2-2222-2-2-2-22222-2-2-2-2-2-22222-2-2000000000000000022-2-222-2-2222-2000000000000000000000000
χ392222-2-2-2-22222-2-2-22200000000-2-2-2-22222222-2-2-2-22222-2-222-2-222000000000000000022-2-2-2-2-2-222-22000000000000000000000000
χ402222-2-2-2-22222-2-2-22200000000-2-2-2-22222222-2-2-2-2-2-2-2-2-2-222-2-2220000000000000000-2-2222222-2-22-2000000000000000000000000
χ4122-2-22-22i−2i002i−2i000021+i−1−i1+i−1−i1−i−1+i1−i−1+i22-2-22-2-20000000022-2-200002i−2i2i−2i1+i1+i−1−i−1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i1−i1−i−1+i−1+i00002-22i−2i2i−2i001+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000000000
χ4222-2-22-22i−2i002i−2i000021+i−1−i1+i−1−i1−i−1+i1−i−1+i22-2-22-2-200000000-2-22200002i−2i2i−2i1+i1+i−1−i−1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i1−i1−i−1+i−1+i0000-22−2i2i−2i2i00−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000000000
χ4322-2-22-22i−2i002i−2i00002−1−i1+i−1−i1+i−1+i1−i−1+i1−i22-2-22-2-20000000022-2-200002i−2i2i−2i−1−i−1−i1+i1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1+i−1+i1−i1−i00002-22i−2i2i−2i00−1−i1+i−1−i1+i−1+i1−i−1+i1−i0000000000000000
χ4422-2-22-22i−2i002i−2i00002−1−i1+i−1−i1+i−1+i1−i−1+i1−i22-2-22-2-200000000-2-22200002i−2i2i−2i−1−i−1−i1+i1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i−1+i−1+i1−i1−i0000-22−2i2i−2i2i001+i−1−i1+i−1−i1−i−1+i1−i−1+i0000000000000000
χ4522-2-22-2−2i2i00−2i2i000021−i−1+i1−i−1+i1+i−1−i1+i−1−i22-2-22-2-20000000022-2-20000−2i2i−2i2i1−i1−i−1+i−1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i1+i1+i−1−i−1−i00002-2−2i2i−2i2i001−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000000000
χ4622-2-22-2−2i2i00−2i2i000021−i−1+i1−i−1+i1+i−1−i1+i−1−i22-2-22-2-200000000-2-2220000−2i2i−2i2i1−i1−i−1+i−1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i1+i1+i−1−i−1−i0000-222i−2i2i−2i00−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000000000
χ4722-2-22-2−2i2i00−2i2i00002−1+i1−i−1+i1−i−1−i1+i−1−i1+i22-2-22-2-20000000022-2-20000−2i2i−2i2i−1+i−1+i1−i1−i−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1−i−1−i1+i1+i00002-2−2i2i−2i2i00−1+i1−i−1+i1−i−1−i1+i−1−i1+i0000000000000000
χ4822-2-22-2−2i2i00−2i2i00002−1+i1−i−1+i1−i−1−i1+i−1−i1+i22-2-22-2-200000000-2-2220000−2i2i−2i2i−1+i−1+i1−i1−i−1+i−1+i1−i1−i−1−i−1−i1+i1+i−1−i−1−i1+i1+i0000-222i−2i2i−2i001−i−1+i1−i−1+i1+i−1−i1+i−1−i0000000000000000
χ4922-2-2-222i−2i00−2i2i000021−i−1+i−1+i1−i−1−i1+i1+i−1−i-2-2222-2-20000000022-2-200002i−2i−2i2i1−i1−i−1+i−1+i−1+i−1+i1−i1−i−1−i−1−i1+i1+i1+i1+i−1−i−1−i0000-222i−2i−2i2i001−i−1+i−1+i1−i−1−i1+i1+i−1−i0000000000000000
χ5022-2-2-222i−2i00−2i2i000021−i−1+i−1+i1−i−1−i1+i1+i−1−i-2-2222-2-200000000-2-22200002i−2i−2i2i1−i1−i−1+i−1+i−1+i−1+i1−i1−i−1−i−1−i1+i1+i1+i1+i−1−i−1−i00002-2−2i2i2i−2i00−1+i1−i1−i−1+i1+i−1−i−1−i1+i0000000000000000
χ5122-2-2-222i−2i00−2i2i00002−1+i1−i1−i−1+i1+i−1−i−1−i1+i-2-2222-2-20000000022-2-200002i−2i−2i2i−1+i−1+i1−i1−i1−i1−i−1+i−1+i1+i1+i−1−i−1−i−1−i−1−i1+i1+i0000-222i−2i−2i2i00−1+i1−i1−i−1+i1+i−1−i−1−i1+i0000000000000000
χ5222-2-2-222i−2i00−2i2i00002−1+i1−i1−i−1+i1+i−1−i−1−i1+i-2-2222-2-200000000-2-22200002i−2i−2i2i−1+i−1+i1−i1−i1−i1−i−1+i−1+i1+i1+i−1−i−1−i−1−i−1−i1+i1+i00002-2−2i2i2i−2i001−i−1+i−1+i1−i−1−i1+i1+i−1−i0000000000000000
χ5322-2-2-22−2i2i002i−2i000021+i−1−i−1−i1+i−1+i1−i1−i−1+i-2-2222-2-20000000022-2-20000−2i2i2i−2i1+i1+i−1−i−1−i−1−i−1−i1+i1+i−1+i−1+i1−i1−i1−i1−i−1+i−1+i0000-22−2i2i2i−2i001+i−1−i−1−i1+i−1+i1−i1−i−1+i0000000000000000
χ5422-2-2-22−2i2i002i−2i000021+i−1−i−1−i1+i−1+i1−i1−i−1+i-2-2222-2-200000000-2-2220000−2i2i2i−2i1+i1+i−1−i−1−i−1−i−1−i1+i1+i−1+i−1+i1−i1−i1−i1−i−1+i−1+i00002-22i−2i−2i2i00−1−i1+i1+i−1−i1−i−1+i−1+i1−i0000000000000000
χ5522-2-2-22−2i2i002i−2i00002−1−i1+i1+i−1−i1−i−1+i−1+i1−i-2-2222-2-20000000022-2-20000−2i2i2i−2i−1−i−1−i1+i1+i1+i1+i−1−i−1−i1−i1−i−1+i−1+i−1+i−1+i1−i1−i0000-22−2i2i2i−2i00−1−i1+i1+i−1−i1−i−1+i−1+i1−i0000000000000000
χ5622-2-2-22−2i2i002i−2i00002−1−i1+i1+i−1−i1−i−1+i−1+i1−i-2-2222-2-200000000-2-2220000−2i2i2i−2i−1−i−1−i1+i1+i1+i1+i−1−i−1−i1−i1−i−1+i−1+i−1+i−1+i1−i1−i00002-22i−2i−2i2i001+i−1−i−1−i1+i−1+i1−i1−i−1+i0000000000000000
χ574444444444444444-144444444-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000000000000000
χ584444444444444444-1-4-4-4-4-4-4-4-4-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000-1-1-1-1-1-1-1-11111111111111111000000000000000000000000000000000000
χ5944444444-4-444-4-4-4-4-100000000-1-1-1-1-1-1-11111111100001111-1-1-1-1i5−i5i5−i5i5−i5i5−i5i5−i5i5−i5i5−i5i5−i5000000000000000000000000000000000000
χ6044444444-4-444-4-4-4-4-100000000-1-1-1-1-1-1-11111111100001111-1-1-1-1−i5i5−i5i5−i5i5−i5i5−i5i5−i5i5−i5i5−i5i5000000000000000000000000000000000000
χ61444444-4-444-4-444-4-4-100000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-10000111111115−55−55−55−5−55−55−55−55000000000000000000000000000000000000
χ62444444-4-444-4-444-4-4-100000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000011111111−55−55−55−555−55−55−55−5000000000000000000000000000000000000
χ63444444-4-4-4-4-4-4-4-444-14i4i4i4i−4i−4i−4i−4i-1-1-1-1-1-1-1111111110000-1-1-1-11111−i−i−i−i−i−i−i−iiiiiiiii000000000000000000000000000000000000
χ64444444-4-4-4-4-4-4-4-444-1−4i−4i−4i−4i4i4i4i4i-1-1-1-1-1-1-1111111110000-1-1-1-11111iiiiiiii−i−i−i−i−i−i−i−i000000000000000000000000000000000000
χ654444-4-44444-4-4-4-44-4-14i4i−4i−4i4i4i−4i−4i1111-1-1-1-1-1-1-111110000-1-111-1-111−i−i−i−iiiii−i−i−i−iiiii000000000000000000000000000000000000
χ664444-4-44444-4-4-4-44-4-1−4i−4i4i4i−4i−4i4i4i1111-1-1-1-1-1-1-111110000-1-111-1-111iiii−i−i−i−iiiii−i−i−i−i000000000000000000000000000000000000
χ674444-4-444-4-4-4-444-44-1000000001111-1-1-11111-1-1-1-1000011-1-1-1-1115−55−5−55−555−55−5−55−55000000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 20 (ζ20 = 1); i = ζ5.