Finite Group Databasebeta

← Group #10637678

Character table — Group #10637678

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111111111111222222444444444444444444888888888888888888888888888888888888888888888888161616161616161616161616161616161616
order122233666666441212121224444466121212121212121212122244444444446666888812121212121212121212121212121212121212122424242424242424448888121212122424242424242424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111-111-1-1-1-11-1-1-111-1-111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111-111-1-1-1-11-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111
χ5111111111111111111111111111111111111-11-1-111-1-1-11-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-111111111-1-111-1-1-1-1-1-11111-1-1-1-1
χ6111111111111111111111111111111111111-11-1-111-1-1-11-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1-1-11111
χ7111111111111111111111111111111111111-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-111-1-1-1-1-1-1-1-11111
χ8111111111111111111111111111111111111-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1
χ9111111111111-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-111111111-1-11-11-11-11-1111111-1-1-1-1-1-111-1-111-1-111-1-111-1-11111-1-1-1-11-11-11-111-1-111-1-111-1-1
χ10111111111111-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-111111111-1-11-11-11-11-11111-1-111-1-1-1-111-1-111-1-111-1-111-1-1-1-1-1-11111-11-11-11-1-111-1-111-1-111
χ11111111111111-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-11111111-1-1-1-11-1111-1111-1-111-1-1-1-1-1-1-1-111-1-1111111-1-1111111-1-1-1-11-1-11-1111-1-1-1-111-1-111
χ12111111111111-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-11111111-1-1-1-11-1111-1111-1-1-1-111-1-1-1-1-1-111-1-1111111-1-111-1-1-1-11111-111-11-1-1-11111-1-111-1-1
χ13111111111111-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1111111-11111-1-11-1-1-11-1-11111-1-1111111-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-111-1-11-1-11111-1-1-1-111
χ14111111111111-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1111111-11111-1-11-1-1-11-1-111-1-111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-111111-1-111-111-1-1-1-11111-1-1
χ15111111111111-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1111111-1-111-111-1-111-1-1-1-1-111-1-11111-1-11111-1-1-1-11111-1-11111-1-1-1-1-11-111-1-1-111-1-11111-1-1
χ16111111111111-1-1-1-1-1-1-1-1-1111-1-1-1-1-1-1111111-1-111-111-1-111-1-1-1-1-1-1-1111111-1-11111-1-1-1-11111-1-1-1-1-1-111111-11-1-1111-1-111-1-1-1-111
χ171111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i3211−1−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+i32111111111111−1−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+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
χ181111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i3211−1−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+i32111111111111−1−i32−1+i32−1−i32−1+i32-1-1-1-1−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i321+i321+i321−i321−i32-1-1-1-1-1-11+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i32
χ191111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i3211−1−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+i321-111-1-1-1-11-1-1-1−1−i32−1+i321+i321−i321111−1−i32−1−i32−1+i32−1+i321+i321−i321+i321−i321+i321−i321+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+i3211-1-1-1-1−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i321+i321−i321+i321−i32
χ201111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i3211−1−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+i321-111-1-1-1-11-1-1-1−1−i32−1+i321+i321−i32-1-1-1-1−1−i32−1−i32−1+i32−1+i321+i321−i321+i321−i321+i321−i321+i321−i32−1−i32−1+i321+i321−i321+i321−i321+i321−i321+i321+i321−i321−i321+i321+i321−i321−i32-1-111111+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32
χ211111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i3211−1−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+i32-11-1-111-1-1-11-1-11+i321−i32−1−i32−1+i3211111+i321+i321−i321−i32−1−i32−1+i32−1−i32−1+i321+i321−i321+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+i32-1-111-1-11+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i32
χ221111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i3211−1−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+i32-11-1-111-1-1-11-1-11+i321−i32−1−i32−1+i32-1-1-1-11+i321+i321−i321−i32−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i321+i321−i32−1−i32−1+i321+i321−i321+i321−i321+i321+i321−i321−i321+i321+i321−i321−i3211-1-111−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i32
χ231111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i3211−1−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+i32-1-1-1-1-1-111-1-1111+i321−i321+i321−i3211111+i321+i321−i321−i321+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32-1-1-1-1111+i321−i321+i321−i321+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i32
χ241111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i3211−1−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+i32-1-1-1-1-1-111-1-1111+i321−i321+i321−i32-1-1-1-11+i321+i321−i321−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+i321+i321−i321−i321+i321+i321−i321−i321111-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i32
χ251111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32-1-11+i321+i321−i321−i32-1-1-11111+i321−i321+i321−i321+i321−i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i3211-1-11-11-11-11-1−1−i32−1+i32−1−i32−1+i3211-1-11+i321+i321−i321−i32−1−i32−1+i321+i321−i32−1−i32−1+i321+i321−i32−1−i32−1+i321+i321−i32−1−i32−1+i321+i321−i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i321-11-11-1−1−i32−1+i321+i321−i32−1−i32−1+i321+i321−i32−1−i32−1+i321+i321−i32
χ261111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32-1-11+i321+i321−i321−i32-1-1-11111+i321−i321+i321−i321+i321−i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i3211-1-11-11-11-11-1−1−i32−1+i32−1−i32−1+i32-1-1111+i321+i321−i321−i32−1−i32−1+i321+i321−i32−1−i32−1+i321+i321−i32−1−i32−1+i321+i321−i32−1−i32−1+i321+i321−i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32-11-11-111+i321−i32−1−i32−1+i321+i321−i32−1−i32−1+i321+i321−i32−1−i32−1+i32
χ271111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32-1-11+i321+i321−i321−i32-1-1-11111+i321−i321+i321−i321+i321−i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321-1-1-1-11-1111-11−1−i32−1+i321+i321−i3211-1-11+i321+i321−i321−i321+i321−i32−1−i32−1+i321+i321−i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321+i321−i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i321-1-11-11−1−i32−1+i321+i321−i321+i321−i32−1−i32−1+i321+i321−i32−1−i32−1+i32
χ281111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32-1-11+i321+i321−i321−i32-1-1-11111+i321−i321+i321−i321+i321−i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321-1-1-1-11-1111-11−1−i32−1+i321+i321−i32-1-1111+i321+i321−i321−i321+i321−i32−1−i32−1+i321+i321−i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321+i321−i32−1−i32−1+i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32-111-11-11+i321−i32−1−i32−1+i32−1−i32−1+i321+i321−i32−1−i32−1+i321+i321−i32
χ291111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32-1-11+i321+i321−i321−i32-1-1-11111+i321−i321+i321−i321+i321−i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32-11111-1-11-1-1-111+i321−i32−1−i32−1+i3211-1-1−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321+i321−i321+i321−i32−1−i32−1+i321+i321−i321+i321−i321+i321−i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32-111-1-111+i321−i32−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i32−1−i32−1+i32
χ301111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32-1-11+i321+i321−i321−i32-1-1-11111+i321−i321+i321−i321+i321−i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32-11111-1-11-1-1-111+i321−i32−1−i32−1+i32-1-111−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321+i321−i321+i321−i32−1−i32−1+i321+i321−i321+i321−i321+i321−i32−1−i32−1+i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i321-1-111-1−1−i32−1+i321+i321−i321+i321−i32−1−i32−1+i32−1−i32−1+i321+i321−i32
χ311111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32-1-11+i321+i321−i321−i32-1-1-11111+i321−i321+i321−i321+i321−i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32-1-111-111-1-111-11+i321−i321+i321−i3211-1-1−1−i32−1−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−i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32-11-111-11+i321−i32−1−i32−1+i321+i321−i32−1−i32−1+i32−1−i32−1+i321+i321−i32
χ321111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32-1-11+i321+i321−i321−i32-1-1-11111+i321−i321+i321−i321+i321−i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32-1-111-111-1-111-11+i321−i321+i321−i32-1-111−1−i32−1−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+i321−i321−i32−1−i32−1−i32−1+i32−1+i321-11-1-11−1−i32−1+i321+i321−i32−1−i32−1+i321+i321−i321+i321−i32−1−i32−1+i32
χ331111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i3211−1+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−i32111111111111−1+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−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
χ341111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i3211−1+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−i32111111111111−1+i32−1−i32−1+i32−1−i32-1-1-1-1−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i321−i321−i321+i321+i32-1-1-1-1-1-11−i321+i321−i321+i321−i321+i321−i321+i321−i321+i321−i321+i32
χ351111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i3211−1+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−i321-111-1-1-1-11-1-1-1−1+i32−1−i321−i321+i321111−1+i32−1+i32−1−i32−1−i321−i321+i321−i321+i321−i321+i321−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−i3211-1-1-1-1−1+i32−1−i32−1+i32−1−i321−i321+i321−i321+i321−i321+i321−i321+i32
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χ9988-8-8−4+4i3−4−4i3−4+4i34−4i3−4−4i34+4i34−4i34+4i3000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1008-88-888-88-88-8-8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1018-88-8−4−4i3−4+4i34+4i3−4−4i34−4i3−4+4i34+4i34−4i3000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1028-88-8−4+4i3−4−4i34−4i3−4+4i34+4i3−4−4i34−4i34+4i3000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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