Finite Group Databasebeta

← Group #72277358

Character table — Group #72277358

Order 5376.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125
size1111224444446666777777778888881212121212121414141416161624242424242424242424242424242424282828282828282828282828484848484848565656565656565656565656565656565656565656565656112112112112112112112112112112112112112112112112112112112112112112112112
order122222222244714141433666666222244141414141414666644414141414141414141414282828282828666666661212121228282828282822446666666666661212121212121212444488121212121212121212121212121224242424
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1111111111111-1-1-1111111-1-1-1-1111111111111111111-1-1-1-1-1-111-1-11111-1-1-1-111111111-1-1-1-1-1111-1-1-1-1-1-111-1-1-1-11111-1-1-1-1
χ411111111111111111111111111-1-1111111111111-1-1-1111111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1111111111-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-111-1-111111111111-1-111-1-1-1-1111111-1-1-1-111111111111111-1-1-1-11111-1-1-1-111111111-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-111-1-111111111111-1-111-1-1-1-1111111-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-111111111
χ7111111111111111111111111-1-1-1-1-1-11111111111-11111-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-11-1-111-1-1-1-1111111-1-1-1-11111
χ8111111111111111111111111-1-1-1-1-1-11111111111-11111-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-111-1-111-1-1-1-111111111-1-1-1-1
χ91111111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32111111111111−1−i32−1+i32−1−i32−1+i321111111111111111111−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1+i321111111111−1−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+i32111111−1−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+i32111111111111−1−i32−1+i32−1−i32−1+i321111111111111111111−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1+i32111111-1-1-1-1−1−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−i32-1-1-1-1-1-11+i321−i32−1−i32−1+i321+i321−i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i321+i321+i321−i321−i32
χ111111111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211-1-111111111−1−i32−1+i32−1−i32−1+i32-1-1-1111111-1-1-1-1111111−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-1-1-1-1-111-1-1−1−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+i321+i321−i321−i32-1111-1-11+i321−i321+i321−i32−1−i32−1+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+i3211-1-111111111−1−i32−1+i32−1−i32−1+i32-1-1-1111111-1-1-1-1111111−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-1-1-1-1-1-1-111−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i321-1-1-111−1−i32−1+i321+i321−i321+i321−i321+i321+i321−i321−i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32
χ131111111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-111-1-1111111−1−i32−1+i32−1−i32−1+i321-1-111-1-1-1-1111111-1-1-1-1−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1+i3211-1-1-1-111111+i321+i321−i321−i32−1−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+i3211-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i321+i321+i321−i321−i321+i321+i321−i321−i32
χ141111111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-111-1-1111111−1−i32−1+i32−1−i32−1+i321-1-111-1-1-1-1111111-1-1-1-1−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1+i3211-1-1-1-1-1-1-1-11+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i321+i321+i321−i321−i321+i321+i321−i321−i32-1-111111+i321−i32−1−i32−1+i321+i321−i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32
χ151111111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-1-1-1-1-1111111−1−i32−1+i32−1−i32−1+i32-11111-1-1-1-1-1-1-1-111-1-1-1-1−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-1111111-1-11+i321+i321−i321−i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i321+i321+i321−i321−i32-11-1-1111+i321−i321+i321−i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+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+i32-1-1-1-1-1-1111111−1−i32−1+i32−1−i32−1+i32-11111-1-1-1-1-1-1-1-111-1-1-1-1−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-11111-1-1111+i321+i321−i321−i321+i321+i321−i321−i321+i321+i321−i321−i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i321-111-1-1−1−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
χ171111111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32111111111111−1+i32−1−i32−1+i32−1−i321111111111111111111−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1−i321111111111−1+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−i32111111−1+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−i32111111111111−1+i32−1−i32−1+i32−1−i321111111111111111111−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1−i32111111-1-1-1-1−1+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+i32-1-1-1-1-1-11−i321+i32−1+i32−1−i321−i321+i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i321−i321−i321+i321+i32
χ191111111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211-1-111111111−1+i32−1−i32−1+i32−1−i32-1-1-1111111-1-1-1-1111111−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-1-1-1-1-111-1-1−1+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−i321−i321+i321+i32-1111-1-11−i321+i321−i321+i32−1+i32−1−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−i3211-1-111111111−1+i32−1−i32−1+i32−1−i32-1-1-1111111-1-1-1-1111111−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-1-1-1-1-1-1-111−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i321−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i321-1-1-111−1+i32−1−i321−i321+i321−i321+i321−i321−i321+i321+i321−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32
χ211111111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-111-1-1111111−1+i32−1−i32−1+i32−1−i321-1-111-1-1-1-1111111-1-1-1-1−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1−i3211-1-1-1-111111−i321−i321+i321+i32−1+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−i3211-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i321−i321−i321+i321+i321−i321−i321+i321+i32
χ221111111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-111-1-1111111−1+i32−1−i32−1+i32−1−i321-1-111-1-1-1-1111111-1-1-1-1−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1−i3211-1-1-1-1-1-1-1-11−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i321−i321−i321+i321+i321−i321−i321+i321+i32-1-111111−i321+i32−1+i32−1−i321−i321+i321−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32
χ231111111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-1-1-1-1-1111111−1+i32−1−i32−1+i32−1−i32-11111-1-1-1-1-1-1-1-111-1-1-1-1−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-1111111-1-11−i321−i321+i321+i321−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i321−i321−i321+i321+i32-11-1-1111−i321+i321−i321+i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−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−i32-1-1-1-1-1-1111111−1+i32−1−i32−1+i32−1−i32-11111-1-1-1-1-1-1-1-111-1-1-1-1−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-11111-1-1111−i321−i321+i321+i321−i321−i321+i321+i321−i321−i321+i321+i321−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i321-111-1-1−1+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
χ252222222-22-2-2-22222222222220022002222222222-200-2-200002222-2-200002-22-22-22-2-2-2-2-2-2-2000000000000222200000000000000000000-2-200000000000000
χ262222222-22-2-2-222222222222200-2-2002222222222200-2-20000-2-2-2-2-2-200002-22-22-22-2-2-2-2-222000000000000-2-2-2-2000000000000000000002200000000000000
χ272222222-22-2-2-22222−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3002200222222−1−i3−1+i3−1−i3−1+i3-200-2-200002222-2-20000−1−i31+i3−1+i31−i3−1−i31+i3−1+i31−i31+i31−i31+i31−i3-2-2000000000000−1−i3−1−i3−1+i3−1+i3000000000000000000001+i31−i300000000000000
χ282222222-22-2-2-22222−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i300-2-200222222−1−i3−1+i3−1−i3−1+i3200-2-20000-2-2-2-2-2-20000−1−i31+i3−1+i31−i3−1−i31+i3−1+i31−i31+i31−i31+i31−i3220000000000001+i31+i31−i31−i300000000000000000000−1−i3−1+i300000000000000
χ292222222-22-2-2-22222−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3002200222222−1+i3−1−i3−1+i3−1−i3-200-2-200002222-2-20000−1+i31−i3−1−i31+i3−1+i31−i3−1−i31+i31−i31+i31−i31+i3-2-2000000000000−1+i3−1+i3−1−i3−1−i3000000000000000000001−i31+i300000000000000
χ302222222-22-2-2-22222−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i300-2-200222222−1+i3−1−i3−1+i3−1−i3200-2-20000-2-2-2-2-2-20000−1+i31−i3−1−i31+i3−1+i31−i3−1−i31+i31−i31+i31−i31+i3220000000000001−i31−i31+i31+i300000000000000000000−1+i3−1−i300000000000000
χ31222222-22-22-2-22222222222220000002-2-22-2-222220002200000000-2-20000-22-22-22-22-2-2-2-20000002200000000002222000000000-200000000-2-2000000000000
χ32222222-22-22-2-22222222222220000002-2-22-2-222220002200000000-2-20000-22-22-22-22-2-2-2-2000000-2-20000000000-2-2-2-200000000020000000022000000000000
χ33222222-22-22-2-22222−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i30000002-2-22-2-2−1−i3−1+i3−1−i3−1+i30002200000000-2-200001+i3−1−i31−i3−1+i31+i3−1−i31−i3−1+i31+i31−i31+i31−i3000000220000000000−1−i3−1−i3−1+i3−1+i3000000000-2000000001+i31−i3000000000000
χ34222222-22-22-2-22222−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i30000002-2-22-2-2−1−i3−1+i3−1−i3−1+i30002200000000-2-200001+i3−1−i31−i3−1+i31+i3−1−i31−i3−1+i31+i31−i31+i31−i3000000-2-200000000001+i31+i31−i31−i3000000000200000000−1−i3−1+i3000000000000
χ35222222-22-22-2-22222−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i30000002-2-22-2-2−1+i3−1−i3−1+i3−1−i30002200000000-2-200001−i3−1+i31+i3−1−i31−i3−1+i31+i3−1−i31−i31+i31−i31+i3000000220000000000−1+i3−1+i3−1−i3−1−i3000000000-2000000001−i31+i3000000000000
χ36222222-22-22-2-22222−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i30000002-2-22-2-2−1+i3−1−i3−1+i3−1−i30002200000000-2-200001−i3−1+i31+i3−1−i31−i3−1+i31+i3−1−i31−i31+i31−i31+i3000000-2-200000000001−i31−i31+i31+i3000000000200000000−1+i3−1−i3000000000000
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χ10988-8-8000000008-88-8−4+4i3−4−4i3−4+4i3−4−4i34−4i34+4i34−4i34+4i300000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ110121212121212-1212-1212-12-12-2-2-2-200000000000000-222-2220000000-2-200000000220000000000000000000000000000000000000000000000000000000000000000000000
χ111121212121212-12-12-12-121212-2-2-2-200000000000000-222-22200000002200000000-2-20000000000000000000000000000000000000000000000000000000000000000000000
χ11212121212-12-12000000-2-2-2-2000000006600-6-62−2i72i72−2i72i7000000000−1−i7−1+i7−1−i7−1+i70000001+i71−i71+i71−i7000000000000000000000000000000000000000000000000000000000000000000
χ11312121212-12-12000000-2-2-2-2000000006600-6-622i7−2i722i7−2i7000000000−1+i7−1−i7−1+i7−1−i70000001−i71+i71−i71+i7000000000000000000000000000000000000000000000000000000000000000000
χ11412121212-12-12000000-2-2-2-200000000-6-600662−2i72i72−2i72i70000000001+i71−i71+i71−i7000000−1−i7−1+i7−1−i7−1+i7000000000000000000000000000000000000000000000000000000000000000000
χ11512121212-12-12000000-2-2-2-200000000-6-6006622i7−2i722i7−2i70000000001−i71+i71−i71+i7000000−1+i7−1−i7−1+i7−1−i7000000000000000000000000000000000000000000000000000000000000000000
χ11612-1212-1212-12000000-222-2000000006-600-66-2−2i72i722i7−2i7000000000−1+i7−1−i71−i71+i70000001−i71+i7−1+i7−1−i7000000000000000000000000000000000000000000000000000000000000000000
χ11712-1212-1212-12000000-222-2000000006-600-66-22i7−2i72−2i72i7000000000−1−i7−1+i71+i71−i70000001+i71−i7−1−i7−1+i7000000000000000000000000000000000000000000000000000000000000000000
χ11812-1212-1212-12000000-222-200000000-66006-6-2−2i72i722i7−2i70000000001−i71+i7−1+i7−1−i7000000−1+i7−1−i71−i71+i7000000000000000000000000000000000000000000000000000000000000000000
χ11912-1212-1212-12000000-222-200000000-66006-6-22i7−2i72−2i72i70000000001+i71−i7−1−i7−1+i7000000−1−i7−1+i71+i71−i7000000000000000000000000000000000000000000000000000000000000000000
χ12012-1212-12-12121212-12-1212-12-222-2000000000000002-2-2-2220000000-2200000000-220000000000000000000000000000000000000000000000000000000000000000000000
χ12112-1212-12-121212-12-1212-1212-222-2000000000000002-2-2-22200000002-2000000002-20000000000000000000000000000000000000000000000000000000000000000000000
χ1222424-24-2400000000-44-44000000000000000000000000000000000−2i72i72i7−2i7000000000000000000000000000000000000000000000000000000000000000000000000
χ1232424-24-2400000000-44-440000000000000000000000000000000002i7−2i7−2i72i7000000000000000000000000000000000000000000000000000000000000000000000000
χ12424-24-242400000000-4-444000000000012-12000000000000000000000-2-222000000000000000000000000000000000000000000000000000000000000000000000000
χ12524-24-242400000000-4-4440000000000-121200000000000000000000022-2-2000000000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 84 (ζ84 = 1); i = ζ21.