Finite Group Databasebeta

← Group #13021696

Character table — Group #13021696

Order 1280.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116
size11111111222222224444444444444444444444444455555555888888888888888888888888101010101010101020202020202020202020202020202020202020202020202020204040404040404040
order12224444222244442444444444510101010101010202020202020202022224444101010102020202020202020202020202020202020202020222244442444444444888888888888888844444444
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1iiiiiiii−i−i−i−i−i−i−i−iiiii−i−i−i−i
χ4111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−i−i−i−i−i−i−i−iiiiiiiii−i−i−i−iiiii
χ5111111111111111111-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1
χ6111111111111111111-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ7111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111iiiiiiii−i−i−i−i−i−i−i−i−i−i−i−iiiii
χ8111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111−i−i−i−i−i−i−i−iiiiiiiiiiiii−i−i−i−i
χ911111111-1-11111-1-1-1-11111-1-1-1-1111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-1
χ1011111111-1-11111-1-1-1-11111-1-1-1-1111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-111-1-111
χ1111111111-1-11111-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111iiii−i−i−i−i−i−i−i−iiiiiii−i−i−i−iii
χ1211111111-1-11111-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111−i−i−i−iiiiiiiii−i−i−i−i−i−iiiii−i−i
χ1311111111-1-11111-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-111-1-111
χ1411111111-1-11111-1-1-1-1-1-1-1-11111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-111-1-1
χ1511111111-1-11111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-111111111-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii−i−iiiii−i−i
χ1611111111-1-11111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-111-1-111111111-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−iii−i−i−i−iii
χ171111-1-1-1-111-1-111-1-1-11ii−i−iii−i−i111-1-1-1-111111-1-1-1-11111-1-1-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-1-1-11111-1-1-11ii−i−iii−i−iii−i−iii−i−iii−i−iii−i−i1-11-11-11-1
χ181111-1-1-1-111-1-111-1-1-11ii−i−iii−i−i111-1-1-1-111111-1-1-1-11111-1-1-1-111-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-1-1-11111-1-1-11ii−i−iii−i−i−i−iii−i−iii−i−iii−i−iii-11-11-11-11
χ191111-1-1-1-111-1-111-1-1-11ii−i−iii−i−i111-1-1-1-111111-1-1-1-1-1-1-1-1111111-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-111-1-1-1-1111-1−i−iii−i−iii11-1-111-1-1-1-111-1-111−ii−iii−ii−i
χ201111-1-1-1-111-1-111-1-1-11ii−i−iii−i−i111-1-1-1-111111-1-1-1-1-1-1-1-1111111-1-1iiii−i−i−i−iiiii−i−i−i−i11-1-111-1-1-1-1111-1−i−iii−i−iii-1-111-1-11111-1-111-1-1i−ii−i−ii−ii
χ211111-1-1-1-111-1-111-1-1-11−i−iii−i−iii111-1-1-1-111111-1-1-1-11111-1-1-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-1-1-11111-1-1-11−i−iii−i−iiiii−i−iii−i−iii−i−iii−i−i-11-11-11-11
χ221111-1-1-1-111-1-111-1-1-11−i−iii−i−iii111-1-1-1-111111-1-1-1-11111-1-1-1-111-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-1-1-11111-1-1-11−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii1-11-11-11-1
χ231111-1-1-1-111-1-111-1-1-11−i−iii−i−iii111-1-1-1-111111-1-1-1-1-1-1-1-1111111-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-1-1-1111-1ii−i−iii−i−i11-1-111-1-1-1-111-1-111i−ii−i−ii−ii
χ241111-1-1-1-111-1-111-1-1-11−i−iii−i−iii111-1-1-1-111111-1-1-1-1-1-1-1-1111111-1-1−i−i−i−iiiii−i−i−i−iiiii11-1-111-1-1-1-1111-1ii−i−iii−i−i-1-111-1-11111-1-111-1-1−ii−iii−ii−i
χ251111-1-1-1-1-1-1-1-111111-1ii−i−i−i−iii111-1-1-1-111111-1-1-1-11111-1-1-1-1-1-111iiii−i−i−i−i−i−i−i−iiiii-1-111-1-1-1-111111-1ii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iii1-1-111-1-11
χ261111-1-1-1-1-1-1-1-111111-1ii−i−i−i−iii111-1-1-1-111111-1-1-1-11111-1-1-1-1-1-111iiii−i−i−i−i−i−i−i−iiiii-1-111-1-1-1-111111-1ii−i−i−i−iii−i−iiiii−i−i−i−iiiii−i−i-111-1-111-1
χ271111-1-1-1-1-1-1-1-111111-1ii−i−i−i−iii111-1-1-1-111111-1-1-1-1-1-1-1-11111-1-111iiii−i−i−i−i−i−i−i−iiiii-1-1111111-1-1-1-1-11−i−iiiii−i−i11-1-1-1-111-1-11111-1-1−iii−ii−i−ii
χ281111-1-1-1-1-1-1-1-111111-1ii−i−i−i−iii111-1-1-1-111111-1-1-1-1-1-1-1-11111-1-111iiii−i−i−i−i−i−i−i−iiiii-1-1111111-1-1-1-1-11−i−iiiii−i−i-1-11111-1-111-1-1-1-111i−i−ii−iii−i
χ291111-1-1-1-1-1-1-1-111111-1−i−iiiii−i−i111-1-1-1-111111-1-1-1-11111-1-1-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i-1-111-1-1-1-111111-1−i−iiiii−i−iii−i−i−i−iiiii−i−i−i−iii-111-1-111-1
χ301111-1-1-1-1-1-1-1-111111-1−i−iiiii−i−i111-1-1-1-111111-1-1-1-11111-1-1-1-1-1-111−i−i−i−iiiiiiiii−i−i−i−i-1-111-1-1-1-111111-1−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i1-1-111-1-11
χ311111-1-1-1-1-1-1-1-111111-1−i−iiiii−i−i111-1-1-1-111111-1-1-1-1-1-1-1-11111-1-111−i−i−i−iiiiiiiii−i−i−i−i-1-1111111-1-1-1-1-11ii−i−i−i−iii11-1-1-1-111-1-11111-1-1i−i−ii−iii−i
χ321111-1-1-1-1-1-1-1-111111-1−i−iiiii−i−i111-1-1-1-111111-1-1-1-1-1-1-1-11111-1-111−i−i−i−iiiiiiiii−i−i−i−i-1-1111111-1-1-1-1-11ii−i−i−i−iii-1-11111-1-111-1-1-1-111−iii−ii−i−ii
χ332222222222-2-2-2-222-2-200000000222-2-2-2-22-2-2-2-222222222222222-2-20000000000000000-2-222-2-222-2-222-2-200000000000000000000000000000000
χ342222222222-2-2-2-222-2-200000000222-2-2-2-22-2-2-2-22222-2-2-2-2-2-2-2-222-2-20000000000000000-2-22222-2-222-2-22200000000000000000000000000000000
χ3522222222-2-2-2-2-2-2-2-22200000000222-2-2-2-22-2-2-2-2222222222222-2-222000000000000000022-2-2-2-2-2-2-2-2-2-22200000000000000000000000000000000
χ3622222222-2-2-2-2-2-2-2-22200000000222-2-2-2-22-2-2-2-22222-2-2-2-2-2-2-2-2-2-222000000000000000022-2-222222222-2-200000000000000000000000000000000
χ372222-2-2-2-22222-2-2-2-22-20000000022222222-2-2-2-2-2-2-2-22222-2-2-2-222220000000000000000-2-2-2-22222-2-2-2-22-200000000000000000000000000000000
χ382222-2-2-2-22222-2-2-2-22-20000000022222222-2-2-2-2-2-2-2-2-2-2-2-2222222220000000000000000-2-2-2-2-2-2-2-22222-2200000000000000000000000000000000
χ392222-2-2-2-2-2-222-2-222-220000000022222222-2-2-2-2-2-2-2-22222-2-2-2-2-2-2-2-20000000000000000222222-2-2-2-222-2200000000000000000000000000000000
χ402222-2-2-2-2-2-222-2-222-220000000022222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-2-2-200000000000000002222-2-22222-2-22-200000000000000000000000000000000
χ4122-2-22i2i−2i−2i2-200002i−2i001+i−1−i1−i−1+i1+i−1−i1−i−1+i22-20000-200002i2i−2i−2i22-2-22i−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−2i002-2002i−2i001+i−1−i1−i−1+i1+i−1−i1−i−1+i000000000000000000000000
χ4222-2-22i2i−2i−2i2-200002i−2i001+i−1−i1−i−1+i1+i−1−i1−i−1+i22-20000-200002i2i−2i−2i-2-222−2i2i−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−2i00-2200−2i2i00−1−i1+i−1+i1−i−1−i1+i−1+i1−i000000000000000000000000
χ4322-2-22i2i−2i−2i2-200002i−2i00−1−i1+i−1+i1−i−1−i1+i−1+i1−i22-20000-200002i2i−2i−2i22-2-22i−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−2i002-2002i−2i00−1−i1+i−1+i1−i−1−i1+i−1+i1−i000000000000000000000000
χ4422-2-22i2i−2i−2i2-200002i−2i00−1−i1+i−1+i1−i−1−i1+i−1+i1−i22-20000-200002i2i−2i−2i-2-222−2i2i−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−2i00-2200−2i2i001+i−1−i1−i−1+i1+i−1−i1−i−1+i000000000000000000000000
χ4522-2-22i2i−2i−2i-220000−2i2i001+i−1−i1−i−1+i−1−i1+i−1+i1−i22-20000-200002i2i−2i−2i22-2-22i−2i2i−2i-22001+i1+i−1−i−1−i1−i1−i−1+i−1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i00−2i2i00-2200−2i2i001+i−1−i1−i−1+i−1−i1+i−1+i1−i000000000000000000000000
χ4622-2-22i2i−2i−2i-220000−2i2i001+i−1−i1−i−1+i−1−i1+i−1+i1−i22-20000-200002i2i−2i−2i-2-222−2i2i−2i2i-22001+i1+i−1−i−1−i1−i1−i−1+i−1+i−1−i−1−i1+i1+i−1+i−1+i1−i1−i00−2i2i002-2002i−2i00−1−i1+i−1+i1−i1+i−1−i1−i−1+i000000000000000000000000
χ4722-2-22i2i−2i−2i-220000−2i2i00−1−i1+i−1+i1−i1+i−1−i1−i−1+i22-20000-200002i2i−2i−2i22-2-22i−2i2i−2i-2200−1−i−1−i1+i1+i−1+i−1+i1−i1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i00−2i2i00-2200−2i2i00−1−i1+i−1+i1−i1+i−1−i1−i−1+i000000000000000000000000
χ4822-2-22i2i−2i−2i-220000−2i2i00−1−i1+i−1+i1−i1+i−1−i1−i−1+i22-20000-200002i2i−2i−2i-2-222−2i2i−2i2i-2200−1−i−1−i1+i1+i−1+i−1+i1−i1−i1+i1+i−1−i−1−i1−i1−i−1+i−1+i00−2i2i002-2002i−2i001+i−1−i1−i−1+i−1−i1+i−1+i1−i000000000000000000000000
χ4922-2-2−2i−2i2i2i2-20000−2i2i001−i−1+i1+i−1−i1−i−1+i1+i−1−i22-20000-20000−2i−2i2i2i22-2-2−2i2i−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−i00−2i2i002-200−2i2i001−i−1+i1+i−1−i1−i−1+i1+i−1−i000000000000000000000000
χ5022-2-2−2i−2i2i2i2-20000−2i2i001−i−1+i1+i−1−i1−i−1+i1+i−1−i22-20000-20000−2i−2i2i2i-2-2222i−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−i00−2i2i00-22002i−2i00−1+i1−i−1−i1+i−1+i1−i−1−i1+i000000000000000000000000
χ5122-2-2−2i−2i2i2i2-20000−2i2i00−1+i1−i−1−i1+i−1+i1−i−1−i1+i22-20000-20000−2i−2i2i2i22-2-2−2i2i−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+i00−2i2i002-200−2i2i00−1+i1−i−1−i1+i−1+i1−i−1−i1+i000000000000000000000000
χ5222-2-2−2i−2i2i2i2-20000−2i2i00−1+i1−i−1−i1+i−1+i1−i−1−i1+i22-20000-20000−2i−2i2i2i-2-2222i−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+i00−2i2i00-22002i−2i001−i−1+i1+i−1−i1−i−1+i1+i−1−i000000000000000000000000
χ5322-2-2−2i−2i2i2i-2200002i−2i001−i−1+i1+i−1−i−1+i1−i−1−i1+i22-20000-20000−2i−2i2i2i22-2-2−2i2i−2i2i-22001−i1−i−1+i−1+i1+i1+i−1−i−1−i−1+i−1+i1−i1−i−1−i−1−i1+i1+i002i−2i00-22002i−2i001−i−1+i1+i−1−i−1+i1−i−1−i1+i000000000000000000000000
χ5422-2-2−2i−2i2i2i-2200002i−2i001−i−1+i1+i−1−i−1+i1−i−1−i1+i22-20000-20000−2i−2i2i2i-2-2222i−2i2i−2i-22001−i1−i−1+i−1+i1+i1+i−1−i−1−i−1+i−1+i1−i1−i−1−i−1−i1+i1+i002i−2i002-200−2i2i00−1+i1−i−1−i1+i1−i−1+i1+i−1−i000000000000000000000000
χ5522-2-2−2i−2i2i2i-2200002i−2i00−1+i1−i−1−i1+i1−i−1+i1+i−1−i22-20000-20000−2i−2i2i2i22-2-2−2i2i−2i2i-2200−1+i−1+i1−i1−i−1−i−1−i1+i1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i002i−2i00-22002i−2i00−1+i1−i−1−i1+i1−i−1+i1+i−1−i000000000000000000000000
χ5622-2-2−2i−2i2i2i-2200002i−2i00−1+i1−i−1−i1+i1−i−1+i1+i−1−i22-20000-20000−2i−2i2i2i-2-2222i−2i2i−2i-2200−1+i−1+i1−i1−i−1−i−1−i1+i1+i1−i1−i−1+i−1+i1+i1+i−1−i−1−i002i−2i002-200−2i2i001−i−1+i1+i−1−i−1+i1−i−1−i1+i000000000000000000000000
χ572-2-222-22-2002-22-20000000000002-2-222-2-2222-2-22-22-22-22-222-2-20000000000000000000000002-2002-200000000000000002i−2i2i−2i00002i−2i2i−2i00000000
χ582-2-222-22-2002-22-20000000000002-2-222-2-2222-2-22-22-22-22-222-2-20000000000000000000000002-2002-20000000000000000−2i2i−2i2i0000−2i2i−2i2i00000000
χ592-2-222-22-2002-22-20000000000002-2-222-2-2222-2-22-22-2-22-22-2-222000000000000000000000000-2200-2200000000000000002-22-20000-22-2200000000
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Here ζ is a primitive root of unity of order 20 (ζ20 = 1); i = ζ5.