Finite Group Databasebeta

← Group #11923176

Character table — Group #11923176

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108
size11112222222222222222222222444444446666888888888888888888888888888888888888888888881212121212121212121212121212363636364848484848484848
order122222344446666666121212121212121233666666444433666666666666666666121212121212121212121212121212121212121212121212444444121212121212121244441212121212121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111−1−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+i32−1−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+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
χ411111111111111111111111111−1−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+i32−1−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+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32-1-111-1-111111111-1-1-1-11+i321+i321−i321−i321+i321+i321−i321−i32
χ511111111111111111111111111−1+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−i32−1+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−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
χ611111111111111111111111111−1+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−i32−1+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−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32-1-111-1-111111111-1-1-1-11−i321−i321+i321+i321−i321−i321+i321+i32
χ71111111-1-1-1-11111111-1-1-1-1-1-1-1-111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-11-11111-1-1-1-11-11-11-11-11-11-1
χ81111111-1-1-1-11111111-1-1-1-1-1-1-1-111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-111111-1-1-1-1-11-11-11-11-11-11
χ91111111-1-1-1-11111111-1-1-1-1-1-1-1-1−1−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+i32−1−i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i321+i321+i321+i321+i321+i321+i321+i321+i321−i321−i321−i321−i321−i321−i321−i321−i321-1-1-11-11111-1-1-1-11-11-1−1−i321+i32−1+i321−i32−1−i321+i32−1+i321−i32
χ101111111-1-1-1-11111111-1-1-1-1-1-1-1-1−1−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+i32−1−i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i321+i321+i321+i321+i321+i321+i321+i321+i321−i321−i321−i321−i321−i321−i321−i321−i32-11-1-1-111111-1-1-1-1-11-111+i32−1−i321−i32−1+i321+i32−1−i321−i32−1+i32
χ111111111-1-1-1-11111111-1-1-1-1-1-1-1-1−1+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−i32−1+i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i321−i321−i321−i321−i321−i321−i321−i321−i321+i321+i321+i321+i321+i321+i321+i321+i321-1-1-11-11111-1-1-1-11-11-1−1+i321−i32−1−i321+i32−1+i321−i32−1−i321+i32
χ121111111-1-1-1-11111111-1-1-1-1-1-1-1-1−1+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−i32−1+i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i321−i321−i321−i321−i321−i321−i321−i321−i321+i321+i321+i321+i321+i321+i321+i321+i32-11-1-1-111111-1-1-1-1-11-111−i32−1+i321+i32−1−i321−i32−1+i321+i32−1−i32
χ131111-1-1111-1-1-1-1-1-11111111-1-1-1-11111111111-1-111-1-1-1-111-1-1-1-111-1-1-1-11111-1-111-1-11111-1-1-1-11111-1-1-1-1111-1-1-111-1-111-1-1-1-111-1-1-1-11111
χ141111-1-1111-1-1-1-1-1-11111111-1-1-1-11111111111-1-111-1-1-1-111-1-1-1-111-1-1-1-11111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-11-11111-1-111-1-111-1-11111-1-1-1-1
χ151111-1-1111-1-1-1-1-1-11111111-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211-1-1−1−i32−1+i321+i321+i321−i321−i32−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i321−i321−i321−i321−i32−1−i32−1+i32−1−i32−1−i321+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+i321−i321−i321−i321−i32111-1-1-111-1-111-1-1-1-1111+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32
χ161111-1-1111-1-1-1-1-1-11111111-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211-1-1−1−i32−1+i321+i321+i321−i321−i32−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i321−i321−i321−i321−i32−1−i32−1+i32−1−i32−1−i321+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+i321−i321−i321−i321−i32-1-11-11111-1-111-1-111-1-1−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32
χ171111-1-1111-1-1-1-1-1-11111111-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211-1-1−1+i32−1−i321−i321−i321+i321+i32−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i321+i321+i321+i321+i32−1+i32−1−i32−1+i32−1+i321−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−i321+i321+i321+i321+i32111-1-1-111-1-111-1-1-1-1111−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32
χ181111-1-1111-1-1-1-1-1-11111111-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211-1-1−1+i32−1−i321−i321−i321+i321+i32−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i321+i321+i321+i321+i32−1+i32−1−i32−1+i32−1+i321−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−i321+i321+i321+i321+i32-1-11-11111-1-111-1-111-1-1−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32
χ191111-1-11-1-111-1-1-1-1111-1-1-1-111111111111111-1-111-1-1-1-111-1-1-1-111-1-1-1-111-1-111-1-111-1-1-1-11111-1-1-1-111111-1-11-1111-1-1-1-111-111-1-11-111-11-1
χ201111-1-11-1-111-1-1-1-1111-1-1-1-111111111111111-1-111-1-1-1-111-1-1-1-111-1-1-1-111-1-111-1-111-1-1-1-11111-1-1-1-11111-11-111-111-1-1-1-1111-1-111-11-1-11-11
χ211111-1-11-1-111-1-1-1-1111-1-1-1-11111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211-1-1−1−i32−1+i321+i321+i321−i321−i32−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i321−i321−i321−i321−i32−1−i32−1+i321+i321+i32−1−i32−1−i321−i321−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+i321-1-11-1111-1-1-1-111-111-11+i32−1−i321−i32−1+i32−1−i321+i32−1+i321−i32
χ221111-1-11-1-111-1-1-1-1111-1-1-1-11111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211-1-1−1−i32−1+i321+i321+i321−i321−i32−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i321−i321−i321−i321−i32−1−i32−1+i321+i321+i32−1−i32−1−i321−i321−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+i32-11-111-111-1-1-1-1111-1-11−1−i321+i32−1+i321−i321+i32−1−i321−i32−1+i32
χ231111-1-11-1-111-1-1-1-1111-1-1-1-11111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211-1-1−1+i32−1−i321−i321−i321+i321+i32−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i321+i321+i321+i321+i32−1+i32−1−i321−i321−i32−1+i32−1+i321+i321+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−i321-1-11-1111-1-1-1-111-111-11−i32−1+i321+i32−1−i32−1+i321−i32−1−i321+i32
χ241111-1-11-1-111-1-1-1-1111-1-1-1-11111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211-1-1−1+i32−1−i321−i321−i321+i321+i32−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i321+i321+i321+i321+i32−1+i32−1−i321−i321−i32−1+i32−1+i321+i321+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−i32-11-111-111-1-1-1-1111-1-11−1+i321−i32−1−i321+i321−i32−1+i321+i32−1−i32
χ25222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1222222222222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1002200-1-1-1-1-1-1-1-1000000000000
χ26222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i322221+i321−i32−1−i3−1−i3−1+i3−1+i31+i321+i321+i321+i321+i321+i321−i321−i321−i321−i321−i321−i321+i321−i32−1−i3−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3−1+i31+i321+i321+i321+i321+i321+i321+i321+i321−i321−i321−i321−i321−i321−i321−i321−i32002200-1-1-1-1-1-1-1-1000000000000
χ27222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i322221−i321+i32−1+i3−1+i3−1−i3−1−i31−i321−i321−i321−i321−i321−i321+i321+i321+i321+i321+i321+i321−i321+i32−1+i3−1+i3−1+i3−1+i3−1−i3−1−i3−1−i3−1−i31−i321−i321−i321−i321−i321−i321−i321−i321+i321+i321+i321+i321+i321+i321+i321+i32002200-1-1-1-1-1-1-1-1000000000000
χ28222222-1-2-2-2-2-1-1-1-1-1-1-111111111222222222222-1-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-2111111111111111100-2-200-1-1-1-11111000000000000
χ29222222-1-2-2-2-2-1-1-1-1-1-1-111111111−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i322221+i321−i32−1−i3−1−i3−1+i3−1+i31+i321+i321+i321+i321+i321+i321−i321−i321−i321−i321−i321−i321+i321−i321+i31+i31+i31+i31−i31−i31−i31−i3−1−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+i3200-2-200-1-1-1-11111000000000000
χ30222222-1-2-2-2-2-1-1-1-1-1-1-111111111−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i322221−i321+i32−1+i3−1+i3−1−i3−1−i31−i321−i321−i321−i321−i321−i321+i321+i321+i321+i321+i321+i321−i321+i321−i31−i31−i31−i31+i31+i31+i31+i3−1+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−i3200-2-200-1-1-1-11111000000000000
χ312222-2-2-122-2-21111-1-1-1-1-1-1-111112222222222-2-2-1-1-2-2-2-2-1-11111-1-11111-1-122-2-222-2-2-1-1-1-11111-1-1-1-11111002-200-1-111-1-111000000000000
χ322222-2-2-122-2-21111-1-1-1-1-1-1-11111−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i322-2-21+i321−i321+i31+i31−i31−i31+i321+i32−1−i32−1−i32−1−i32−1−i321−i321−i32−1+i32−1+i32−1+i32−1+i321+i321−i32−1−i3−1−i31+i31+i3−1+i3−1+i31−i31−i31+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32002-200-1-111-1-111000000000000
χ332222-2-2-122-2-21111-1-1-1-1-1-1-11111−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i322-2-21−i321+i321−i31−i31+i31+i31−i321−i32−1+i32−1+i32−1+i32−1+i321+i321+i32−1−i32−1−i32−1−i32−1−i321−i321+i32−1+i3−1+i31−i31−i3−1−i3−1−i31+i31+i31−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32002-200-1-111-1-111000000000000
χ342222-2-2-1-2-2221111-1-1-11111-1-1-1-12222222222-2-2-1-1-2-2-2-2-1-11111-1-11111-1-1-2-222-2-2221111-1-1-1-11111-1-1-1-100-2200-1-11111-1-1000000000000
χ352222-2-2-1-2-2221111-1-1-11111-1-1-1-1−1−i3−1+i3−1−i3−1+i3−1−i3−1+i3−1−i3−1+i322-2-21+i321−i321+i31+i31−i31−i31+i321+i32−1−i32−1−i32−1−i32−1−i321−i321−i32−1+i32−1+i32−1+i32−1+i321+i321−i321+i31+i3−1−i3−1−i31−i31−i3−1+i3−1+i3−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i3200-2200-1-11111-1-1000000000000
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χ10566-6-66-6-30000-3-3333-33−33−333333−33−33333300000000-22-22000000000000000000000000000000000000000000000000001-11-13−33−3000000000000
χ10666-6-6-6660000-6-666-66-60000000000000000-222-200000000000000000000000000000000000000000000000000-222-20000000000000000
χ10766-6-6-66-3000033-3-33-333333−33−33−33−33333300000000-222-2000000000000000000000000000000000000000000000000001-1-11−333−3000000000000
χ10866-6-6-66-3000033-3-33-33−33−3333333333−33−3300000000-222-2000000000000000000000000000000000000000000000000001-1-113−3−33000000000000

Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.