Finite Group Databasebeta

← Group #72277078

Character table — Group #72277078

Order 5376.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119
size111122444444666677777777881212141414141616161616242424242424242424242828282828282828282828284848484848484848484856565656565656565656565656565656565656565656565656565656112112112112112112112112112112112112112112112112112112112112112112
order122222222244714141433666666221414666644488141414141414141428286666666612121212282828282828565656562222444466666666666612121212121212124444121212121212121212121212121224242424
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-11111
χ3111111111111111111111111111111111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-111-1-111-1-111111111-1-1-1-11111-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-11111-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1
χ5111111111111111111111111-1-1111111-111-1-1111-1-1-1-1111111111111111-1-11111-1-1-1-1111111-1-1-1-1-1-1111111111111-1-1-1-1-11-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-1111111-111-1-1111-1-1-1-1111111111111111-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-11111-1-1-1-111111111-1-1-1-1
χ7111111111111111111111111-1-1111111-1-1-111111-1-1-1-1111111111111111-1-1-1-1-1-1111111-1-11111-1-1-1-11111-1-1-1-1111111111-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111
χ8111111111111111111111111-1-1111111-1-1-111111-1-1-1-1111111111111111-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1111-1-1-1-111-1-1-1-111111111
χ91111111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321111−1−i32−1+i32−1−i32−1+i32111111111111111−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1+i32111111111111111111−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i321111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32
χ101111111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321111−1−i32−1+i32−1−i32−1+i32111111111111111−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1+i321111111111-1-1-1-1-1-1-1-1−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i321+i321+i321−i321−i321+i321+i321−i321−i321+i321+i321−i321−i32-1-1-1-11+i321−i32−1−i32−1+i321+i321−i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32
χ111111111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321111−1−i32−1+i32−1−i32−1+i321-1-1-1-11111111111−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1+i3211-1-1-1-1-1-1-1-111-1-111-1-1−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32-1-1111+i321−i32−1−i32−1+i321+i321−i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32
χ121111111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321111−1−i32−1+i32−1−i32−1+i321-1-1-1-11111111111−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1+i3211-1-1-1-1-1-1-1-1-1-111-1-111−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i3211-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i321+i321+i321−i321−i321+i321+i321−i321−i32
χ131111111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-111−1−i32−1+i32−1−i32−1+i32-111-1-1111-1-1-1-1111−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-11111-1-1-1-1111111-1-11+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32-11-1-11+i321−i321+i321−i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i321+i321+i321−i321−i32
χ141111111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-111−1−i32−1+i32−1−i32−1+i32-111-1-1111-1-1-1-1111−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-11111-1-1-1-1-1-1-1-1-1-1111+i321+i321−i321−i321+i321+i321−i321−i321+i321+i321−i321−i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i321-111−1−i32−1+i321+i321−i321+i321−i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32
χ151111111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-111−1−i32−1+i32−1−i32−1+i32-1-1-111111-1-1-1-1111−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-1-1-1-1-1111111-1-111111+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i321-1-1-1−1−i32−1+i321+i321−i321+i321−i321+i321+i321−i321−i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32
χ161111111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-111−1−i32−1+i32−1−i32−1+i32-1-1-111111-1-1-1-1111−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-1-1-1-1-11111-1-111-1-1-1-11+i321+i321−i321−i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i321+i321+i321−i321−i32-11111+i321−i321+i321−i32−1−i32−1+i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32
χ171111111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321111−1+i32−1−i32−1+i32−1−i32111111111111111−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1−i32111111111111111111−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i321111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32
χ181111111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321111−1+i32−1−i32−1+i32−1−i32111111111111111−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1−i321111111111-1-1-1-1-1-1-1-1−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i321−i321−i321+i321+i321−i321−i321+i321+i321−i321−i321+i321+i32-1-1-1-11−i321+i32−1+i32−1−i321−i321+i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32
χ191111111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321111−1+i32−1−i32−1+i32−1−i321-1-1-1-11111111111−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1−i3211-1-1-1-1-1-1-1-111-1-111-1-1−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32-1-1111−i321+i32−1+i32−1−i321−i321+i321−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32
χ201111111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321111−1+i32−1−i32−1+i32−1−i321-1-1-1-11111111111−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1−i3211-1-1-1-1-1-1-1-1-1-111-1-111−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i3211-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i321−i321−i321+i321+i321−i321−i321+i321+i32
χ211111111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-111−1+i32−1−i32−1+i32−1−i32-111-1-1111-1-1-1-1111−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-11111-1-1-1-1111111-1-11−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32-11-1-11−i321+i321−i321+i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i321−i321−i321+i321+i32
χ221111111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-111−1+i32−1−i32−1+i32−1−i32-111-1-1111-1-1-1-1111−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-11111-1-1-1-1-1-1-1-1-1-1111−i321−i321+i321+i321−i321−i321+i321+i321−i321−i321+i321+i321−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i321-111−1+i32−1−i321−i321+i321−i321+i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32
χ231111111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-111−1+i32−1−i32−1+i32−1−i32-1-1-111111-1-1-1-1111−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-1-1-1-1-1111111-1-111111−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i321-1-1-1−1+i32−1−i321−i321+i321−i321+i321−i321−i321+i321+i321−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32
χ241111111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-111−1+i32−1−i32−1+i32−1−i32-1-1-111111-1-1-1-1111−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-1-1-1-1-11111-1-111-1-1-1-11−i321−i321+i321+i321−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i321−i321−i321+i321+i32-11111−i321+i321−i321+i32−1+i32−1−i321−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32
χ252222222-22-2-2-222222222222200222222000002-2-200002-2-22-22-22-22-2-2-2-2-2000000000000220000000000002222000000000-2000000-2-2000000000000
χ262222222-22-2-2-222222222222200222222000002-2-200002-2-22-22-22-22-2-2-2-2-2000000000000-2-2000000000000-2-2-2-2000000000200000022000000000000
χ272222222-22-2-2-22222−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i30022−1−i3−1+i3−1−i3−1+i3000002-2-200002-2-2−1−i31+i3−1+i31−i3−1−i31+i3−1+i31−i31+i31−i31+i31−i300000000000022000000000000−1−i3−1−i3−1+i3−1+i3000000000-20000001+i31−i3000000000000
χ282222222-22-2-2-22222−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i30022−1−i3−1+i3−1−i3−1+i3000002-2-200002-2-2−1−i31+i3−1+i31−i3−1−i31+i3−1+i31−i31+i31−i31+i31−i3000000000000-2-20000000000001+i31+i31−i31−i30000000002000000−1−i3−1+i3000000000000
χ292222222-22-2-2-22222−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i30022−1+i3−1−i3−1+i3−1−i3000002-2-200002-2-2−1+i31−i3−1−i31+i3−1+i31−i3−1−i31+i31−i31+i31−i31+i300000000000022000000000000−1+i3−1+i3−1−i3−1−i3000000000-20000001−i31+i3000000000000
χ302222222-22-2-2-22222−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i30022−1+i3−1−i3−1+i3−1−i3000002-2-200002-2-2−1+i31−i3−1−i31+i3−1+i31−i3−1−i31+i31−i31+i31−i31+i3000000000000-2-20000000000001−i31−i31+i31+i30000000002000000−1+i3−1−i3000000000000
χ31222222-22-22-2-222222222222222222222-20000-2222222-2-2-2-22-22-22-22-2-2-2-2-2-2000000000000000022220000000000000000000000-2-200000000000000
χ32222222-22-22-2-2222222222222-2-222222220000-222-2-2-2-2-2-2-2-22-22-22-22-2-2-2-2220000000000000000-2-2-2-200000000000000000000002200000000000000
χ33222222-22-22-2-22222−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i32222−1−i3−1+i3−1−i3−1+i3-20000-2222222-2-2-21+i3−1−i31−i3−1+i31+i3−1−i31−i3−1+i31+i31−i31+i31−i3-2-20000000000000000−1−i3−1−i3−1+i3−1+i300000000000000000000001+i31−i300000000000000
χ34222222-22-22-2-22222−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3-2-222−1−i3−1+i3−1−i3−1+i320000-222-2-2-2-2-2-2-21+i3−1−i31−i3−1+i31+i3−1−i31−i3−1+i31+i31−i31+i31−i32200000000000000001+i31+i31−i31−i30000000000000000000000−1−i3−1+i300000000000000
χ35222222-22-22-2-22222−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i32222−1+i3−1−i3−1+i3−1−i3-20000-2222222-2-2-21−i3−1+i31+i3−1−i31−i3−1+i31+i3−1−i31−i31+i31−i31+i3-2-20000000000000000−1+i3−1+i3−1−i3−1−i300000000000000000000001−i31+i300000000000000
χ36222222-22-22-2-22222−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3-2-222−1+i3−1−i3−1+i3−1−i320000-222-2-2-2-2-2-2-21−i3−1+i31+i3−1−i31−i3−1+i31+i3−1−i31−i31+i31−i31+i32200000000000000001−i31−i31+i31+i30000000000000000000000−1+i3−1−i300000000000000
χ37222222-2-2-2-2222222222222220022222200000-2-2-20000-222-2-2-2-2-2-2-2-2222200000000000000002200000000000000002222-2000-2-20000000000000000
χ38222222-2-2-2-2222222222222220022222200000-2-2-20000-222-2-2-2-2-2-2-2-222220000000000000000-2-20000000000000000-2-2-2-22000220000000000000000
χ39222222-2-2-2-2222222−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i30022−1−i3−1+i3−1−i3−1+i300000-2-2-20000-2221+i31+i31−i31−i31+i31+i31−i31−i3−1−i3−1+i3−1−i3−1+i30000000000000000220000000000000000−1−i3−1−i3−1+i3−1+i3-20001+i31−i30000000000000000
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Here ζ is a primitive root of unity of order 84 (ζ84 = 1); i = ζ21.