Finite Group Databasebeta

← Group #13047376

Character table — Group #13047376

Order 1296.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110
size11111122222222233333333333366666666666666666666999999999999999999121212181818181818181818181818181818181818181818181818181818181818181818363636363636363636
order12336644412121212121233333366666636121212121212121212121212121212121212441212121212121212121212121212121212121222236666666666666666666666666991818121212363636363636
χ111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111
χ3111111111111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3211−1−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+i321111111111111−1−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+i321−1−i32−1+i32−1−i32−1+i32111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32
χ4111111111111111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3211−1−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+i32-1-1-1-1-1-11+i321+i321+i321+i321+i321+i321−i321−i321−i321−i321−i321−i32111-1-1-11-1-1-1-1-1-11+i321+i321+i321+i321+i321+i321+i321+i321+i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−1−i32−1+i32−1−i32−1+i32111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32
χ5111111111111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3211−1+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−i321111111111111−1+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−i321−1+i32−1−i32−1+i32−1−i32111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32
χ6111111111111111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3211−1+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−i32-1-1-1-1-1-11−i321−i321−i321−i321−i321−i321+i321+i321+i321+i321+i321+i32111-1-1-11-1-1-1-1-1-11−i321−i321−i321−i321−i321−i321−i321−i321−i321+i321+i321+i321+i321+i321+i321+i321+i321+i321−1+i32−1−i32−1+i32−1−i32111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32
χ71111111-1-111-1-1-1-111111111111111111-1-1-1-1-1-1111-1-1-1-1-1-11111111111111111111-1-11-1-1111-1-1-1-1111-1-1-1-1-1-1111-1-1-1-1-1-1111111-1-11-1-11-1-1
χ81111111-1-111-1-1-1-111111111111111111-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1111-1-11111-1-1-1111111-1-1-1111111111111-1-11-1-11-1-1
χ91111111-1-111-1-1-1-1−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3211−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32111111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321-1-11-1-1111-1-1-1-1−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i321−1−i32−1+i32−1−i32−1+i321-1-1−1−i321+i321+i32−1+i321−i321−i32
χ101111111-1-111-1-1-1-1−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i3211−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32-1-1-1-1-1-11+i321+i321+i321+i321+i321+i321−i321−i321−i321−i321−i321−i321-1-1-1111-1-111111+i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−1−i32−1+i32−1−i32−1+i321-1-1−1−i321+i321+i32−1+i321−i321−i32
χ111111111-1-111-1-1-1-1−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3211−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32111111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321-1-11-1-1111-1-1-1-1−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321−1+i32−1−i32−1+i32−1−i321-1-1−1+i321−i321−i32−1−i321+i321+i32
χ121111111-1-111-1-1-1-1−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i3211−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32-1-1-1-1-1-11−i321−i321−i321−i321−i321−i321+i321+i321+i321+i321+i321+i321-1-1-1111-1-111111−i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321−1+i32−1−i32−1+i32−1−i321-1-1−1+i321−i321−i32−1−i321+i321+i32
χ13111111-11-1-1-111-1-111111111111111-1-1-1111-1-1-1-1-1-1111-1-1-1111111111111111111-11-1-11-11-1-111-1-1-1-1-1111-1-1-1-1-1-1111-1-1-111111-11-1-11-1-11-1
χ14111111-11-1-1-111-1-111111111111111-1-1-1111-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-11-11111-1-111111-1-1-1111111-1-1-111111111-11-1-11-1-11-1
χ15111111-11-1-1-111-1-1−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111+i321+i321+i32−1−i32−1−i32−1−i321+i321+i321+i321−i321−i321−i32−1+i32−1+i32−1+i321−i321−i321−i32111111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32-11-1-11-11-1-111-1-11+i321+i321+i32−1−i32−1−i32−1−i321+i321+i321+i321−i321−i321−i32−1+i32−1+i32−1+i321−i321−i321−i321−1−i32−1+i32−1−i32−1+i32-11-11+i32−1−i321+i321−i32−1+i321−i32
χ16111111-11-1-1-111-1-1−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111+i321+i321+i32−1−i32−1−i32−1−i321+i321+i321+i321−i321−i321−i32−1+i32−1+i32−1+i321−i321−i321−i32-1-1-1-1-1-11+i321+i321+i321+i321+i321+i321−i321−i321−i321−i321−i321−i32-11-11-11111-1-111−1−i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i32−1+i321−1−i32−1+i32−1−i32−1+i32-11-11+i32−1−i321+i321−i32−1+i321−i32
χ17111111-11-1-1-111-1-1−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111−i321−i321−i32−1+i32−1+i32−1+i321−i321−i321−i321+i321+i321+i32−1−i32−1−i32−1−i321+i321+i321+i32111111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32-11-1-11-11-1-111-1-11−i321−i321−i32−1+i32−1+i32−1+i321−i321−i321−i321+i321+i321+i32−1−i32−1−i32−1−i321+i321+i321+i321−1+i32−1−i32−1+i32−1−i32-11-11−i32−1+i321−i321+i32−1−i321+i32
χ18111111-11-1-1-111-1-1−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111−i321−i321−i32−1+i32−1+i32−1+i321−i321−i321−i321+i321+i321+i32−1−i32−1−i32−1−i321+i321+i321+i32-1-1-1-1-1-11−i321−i321−i321−i321−i321−i321+i321+i321+i321+i321+i321+i32-11-11-11111-1-111−1+i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i32−1−i321−1+i32−1−i32−1+i32−1−i32-11-11−i32−1+i321−i321+i32−1−i321+i32
χ19111111-1-11-1-1-1-11111111111111111-1-1-1-1-1-1111-1-1-1-1-1-1111111111111111111111-1-11-1-111-1-1-1-111-1-1-1-1-1-1111-1-1-1-1-1-111111111-1-11-1-11-1-11
χ20111111-1-11-1-1-1-11111111111111111-1-1-1-1-1-1111-1-1-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-111111-1-1111111-1-1-1111111-1-1-111111-1-11-1-11-1-11
χ21111111-1-11-1-1-1-111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i321−i321−i321−i321−i321−i321−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+i32-1-11-1-111-1-1-1-1111+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i321−1−i32−1+i32−1−i32−1+i32-1-111+i321+i32−1−i321−i321−i32−1+i32
χ22111111-1-11-1-1-1-111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32111+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32-1-1-1-1-1-11+i321+i321+i321+i321+i321+i321−i321−i321−i321−i321−i321−i32-1-1111-111111-1-1−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−1−i32−1+i32−1−i32−1+i32-1-111+i321+i32−1−i321−i321−i32−1+i32
χ23111111-1-11-1-1-1-111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i321+i321+i321+i321+i321+i321+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−i32-1-11-1-111-1-1-1-1111−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i321−1+i32−1−i32−1+i32−1−i32-1-111−i321−i32−1+i321+i321+i32−1−i32
χ24111111-1-11-1-1-1-111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32111−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32-1-1-1-1-1-11−i321−i321−i321−i321−i321−i321+i321+i321+i321+i321+i321+i32-1-1111-111111-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321−1+i32−1−i32−1+i32−1−i32-1-111−i321−i32−1+i321+i321+i32−1−i32
χ2522222222222222222222222222222222222222222222222000000000000000000222000-1000000000000000000000000-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ26222222222222222−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3−1−i3−1−i3−1−i3−1+i3−1+i3−1+i322−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3000000000000000000222000-1000000000000000000000000-11+i321−i321+i321−i32-1-1-11+i321+i321+i321−i321−i321−i32
χ27222222222222222−1+i3−1+i3−1+i3−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3−1−i3−1−i3−1−i322−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3000000000000000000222000-1000000000000000000000000-11−i321+i321−i321+i32-1-1-11−i321−i321−i321+i321+i321+i32
χ282222222-2-222-2-2-2-222222222222222222-2-2-2-2-2-2222-2-2-2-2-2-20000000000000000002-2-2000-1000000000000000000000000-1-1-1-1-1-111-111-111
χ292222222-2-222-2-2-2-2−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3−1−i3−1−i3−1−i3−1+i3−1+i3−1+i322−1−i3−1−i3−1−i31+i31+i31+i31+i31+i31+i3−1+i3−1+i3−1+i31−i31−i31−i31−i31−i31−i30000000000000000002-2-2000-1000000000000000000000000-11+i321−i321+i321−i32-1111+i32−1−i32−1−i321−i32−1+i32−1+i32
χ302222222-2-222-2-2-2-2−1+i3−1+i3−1+i3−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3−1−i3−1−i3−1−i322−1+i3−1+i3−1+i31−i31−i31−i31−i31−i31−i3−1−i3−1−i3−1−i31+i31+i31+i31+i31+i31+i30000000000000000002-2-2000-1000000000000000000000000-11−i321+i321−i321+i32-1111−i32−1+i32−1+i321+i32−1−i32−1−i32
χ31222222-22-2-2-222-2-222222222222222-2-2-2222-2-2-2-2-2-2222-2-2-2000000000000000000-22-2000-1000000000000000000000000-1-1-1-1-11-111-111-11
χ32222222-22-2-2-222-2-2−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3221+i31+i31+i3−1−i3−1−i3−1−i31+i31+i31+i31−i31−i31−i3−1+i3−1+i3−1+i31−i31−i31−i3000000000000000000-22-2000-1000000000000000000000000-11+i321−i321+i321−i321-11−1−i321+i32−1−i32−1+i321−i32−1+i32
χ33222222-22-2-2-222-2-2−1+i3−1+i3−1+i3−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3−1−i3−1−i3−1−i3221−i31−i31−i3−1+i3−1+i3−1+i31−i31−i31−i31+i31+i31+i3−1−i3−1−i3−1−i31+i31+i31+i3000000000000000000-22-2000-1000000000000000000000000-11−i321+i321−i321+i321-11−1+i321−i32−1+i32−1−i321+i32−1−i32
χ34222222-2-22-2-2-2-22222222222222222-2-2-2-2-2-2222-2-2-2-2-2-2222000000000000000000-2-22000-1000000000000000000000000-1-1-1-1-111-111-111-1
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.