Finite Group Databasebeta

← Group #10631663

Character table — Group #10631663

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111111111111222222444444444444444444888888888888888888888888888888888888888888888888161616161616161616161616161616161616
order1222336666662266664444441212121212121212121212122244444444444444666612121212121212121212121212121212121212121212121212121212888888242424242424242424242424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111-1-111-1-1-1-111-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111-1-11111-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111-1-1-1-1-1-11111-1-1-1-1
χ411111111111111111111111111111111111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111
χ5111111111111111111111111111111111111-1-11111-1-111111111-1-1-1-111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ6111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111111111
χ7111111111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1111111-1-1-1-11111
χ8111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-111111111-1-1-1-1
χ91111−1−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+i321111111111111111−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+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
χ101111−1−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+i321111-1-111-1-1-1-111-1-1−1−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−i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i3211-1-1-1-1−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i321+i321+i321−i321−i32
χ111111−1−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+i3211-1-11111-1-1-1-1-1-111−1−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−i321+i321+i321−i321−i321+i321+i321−i321−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
χ121111−1−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+i3211-1-1-1-1111111-1-1-1-1−1−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+i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i321+i321+i321−i321−i32-1-1-1-1111+i321+i321−i321−i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32
χ131111−1−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+i32-1-11111-1-1111111111+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+i32−1−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−i32
χ141111−1−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+i32-1-111-1-1-1-1-1-1-1-111-1-11+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i321+i321+i321−i321−i321+i321+i321−i321−i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+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
χ151111−1−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+i32-1-1-1-111-1-1-1-1-1-1-1-1111+i321+i321−i321−i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i321+i321+i321−i321−i321+i321+i321−i321−i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i3211-1-111−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32
χ161111−1−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+i32-1-1-1-1-1-1-1-11111-1-1-1-11+i321+i321−i321−i321+i321+i321−i321−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+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
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−i321111111111111111−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−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−i321111-1-111-1-1-1-111-1-1−1+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+i321−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i3211-1-1-1-1−1+i32−1+i32−1−i32−1−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−i3211-1-11111-1-1-1-1-1-111−1+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+i321−i321−i321+i321+i321−i321−i321+i321+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
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−i3211-1-1-1-1111111-1-1-1-1−1+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−i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i321−i321−i321+i321+i32-1-1-1-1111−i321−i321+i321+i321−i321−i321+i321+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−i32-1-11111-1-1111111111−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−i32−1+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+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−i32-1-111-1-1-1-1-1-1-1-111-1-11−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i321−i321−i321+i321+i321−i321−i321+i321+i321−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−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
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−i32-1-1-1-111-1-1-1-1-1-1-1-1111−i321−i321+i321+i321−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i321−i321−i321+i321+i321−i321−i321+i321+i321−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i3211-1-111−1+i32−1+i32−1−i32−1−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−i32-1-1-1-1-1-1-1-11111-1-1-1-11−i321−i321+i321+i321−i321−i321+i321+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−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
χ251-1-1111-1-1-1-1111-111-1-111-11-1-111-111-11-1-11-1-11-1i−ii−i1-11-11-1i−ii−i1-11-1i−ii−ii−ii−i1-11-11-11-11-11-1i−ii−ii−ii−ii−ii−i1-1i−ii−ii−ii−i1-11-1
χ261-1-1111-1-1-1-1111-111-1-111-11-1-111-111-11-1-11-1-11-1i−i−ii1-1-11-11i−i−ii1-11-1i−ii−i−ii−ii1-11-1-11-11-11-11i−ii−i−ii−iii−i−ii-11i−ii−i−ii−ii-11-11
χ271-1-1111-1-1-1-1111-111-1-111-11-1-111-111-11-1-11-1-11-1−iii−i1-1-11-11−iii−i1-11-1−ii−iii−ii−i1-11-1-11-11-11-11−ii−iii−ii−i−iii−i-11−ii−iii−ii−i-11-11
χ281-1-1111-1-1-1-1111-111-1-111-11-1-111-111-11-1-11-1-11-1−ii−ii1-11-11-1−ii−ii1-11-1−ii−ii−ii−ii1-11-11-11-11-11-1−ii−ii−ii−ii−ii−ii1-1−ii−ii−ii−ii1-11-1
χ291-1-1111-1-1-1-1111-111-1-111-11-1-111-111-11-1-11-1-1-11i−ii−i-111-11-1i−ii−i-11-11i−ii−ii−ii−i-11-111-11-11-11-1i−ii−ii−ii−i−ii−ii-11−ii−ii−ii−ii-11-11
χ301-1-1111-1-1-1-1111-111-1-111-11-1-111-111-11-1-11-1-1-11i−i−ii-11-11-11i−i−ii-11-11i−ii−i−ii−ii-11-11-11-11-11-11i−ii−i−ii−ii−iii−i1-1−ii−iii−ii−i1-11-1
χ311-1-1111-1-1-1-1111-111-1-111-11-1-111-111-11-1-11-1-1-11−iii−i-11-11-11−iii−i-11-11−ii−iii−ii−i-11-11-11-11-11-11−ii−iii−ii−ii−i−ii1-1i−ii−i−ii−ii1-11-1
χ321-1-1111-1-1-1-1111-111-1-111-11-1-111-111-11-1-11-1-1-11−ii−ii-111-11-1−ii−ii-11-11−ii−ii−ii−ii-11-111-11-11-11-1−ii−ii−ii−iii−ii−i-11i−ii−ii−ii−i-11-11
χ331-1-11−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i321-1−1−i32−1+i321+i321−i3211-11-1-1−1−i32−1−i321+i32−1+i32−1+i321−i32−1−i321+i321+i32−1+i321−i321−i321-1i−ii−i1-11-11-1i−ii−i−1−i321+i32−1+i321−i32ζ11−ζ11ζ7−ζ7ζ11−ζ11ζ7−ζ7−1−i321+i32−1+i321−i32−1−i321+i32−1+i321−i32−1−i321+i32−1+i321−i32ζ11−ζ11ζ7−ζ7ζ11−ζ11ζ7−ζ7i−ii−i1-1ζ11−ζ11ζ7−ζ7ζ11−ζ11ζ7−ζ7−1−i321+i32−1+i321−i32
χ341-1-11−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i321-1−1−i32−1+i321+i321−i3211-11-1-1−1−i32−1−i321+i32−1+i32−1+i321−i32−1−i321+i321+i32−1+i321−i321−i321-1i−i−ii1-1-11-11i−i−ii−1−i321+i32−1+i321−i32ζ11−ζ11ζ7−ζ7−ζ11ζ11−ζ7ζ7−1−i321+i32−1+i321−i321+i32−1−i321−i32−1+i321+i32−1−i321−i32−1+i32ζ11−ζ11ζ7−ζ7−ζ11ζ11−ζ7ζ7i−i−ii-11ζ11−ζ11ζ7−ζ7−ζ11ζ11−ζ7ζ71+i32−1−i321−i32−1+i32
χ351-1-11−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i321-1−1−i32−1+i321+i321−i3211-11-1-1−1−i32−1−i321+i32−1+i32−1+i321−i32−1−i321+i321+i32−1+i321−i321−i321-1−iii−i1-1-11-11−iii−i−1−i321+i32−1+i321−i32−ζ11ζ11−ζ7ζ7ζ11−ζ11ζ7−ζ7−1−i321+i32−1+i321−i321+i32−1−i321−i32−1+i321+i32−1−i321−i32−1+i32−ζ11ζ11−ζ7ζ7ζ11−ζ11ζ7−ζ7−iii−i-11−ζ11ζ11−ζ7ζ7ζ11−ζ11ζ7−ζ71+i32−1−i321−i32−1+i32
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χ822-2-22−1+i3−1−i31−i31−i31+i31+i3−1+i3−1−i32-2−1+i3−1−i31−i31+i3-222-22-21−i3−1+i3−1+i31+i3−1−i3−1−i31−i3−1+i31−i31+i3−1−i31+i300−2i2i000000002i−2i000000−2ζ72ζ7−2ζ112ζ1100000000000000002ζ7−2ζ72ζ11−2ζ110000000000000000000000
χ832-2-22−1+i3−1−i31−i31−i31+i31+i3−1+i3−1−i32-2−1+i3−1−i31−i31+i3-2-2-22221−i31−i31−i31+i31+i31+i3−1+i3−1+i3−1+i3−1−i3−1−i3−1−i3000000002-2-2200000000000000000000−1+i31−i3−1−i31+i31−i3−1+i31+i3−1−i300000000000000000000000000
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χ904444−2+2i3−2−2i3−2+2i3−2+2i3−2−2i3−2−2i3−2+2i3−2−2i3-4-42−2i32+2i32−2i32+2i3000000000000000000-2-2000022000000001−i31−i31+i31+i300000000−1+i3−1+i3−1−i3−1−i30000000000000000000000000000000000
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χ934-4-44−2−2i3−2+2i32+2i32+2i32−2i32−2i3−2−2i3−2+2i3-442+2i32−2i3−2−2i3−2+2i30000000000000000002-20000-2200000000−1−i31+i3−1+i31−i3000000001+i3−1−i31−i3−1+i30000000000000000000000000000000000
χ944-4-44−2−2i3−2+2i32+2i32+2i32−2i32−2i3−2−2i3−2+2i3-442+2i32−2i3−2−2i3−2+2i3000000000000000000-2200002-2000000001+i3−1−i31−i3−1+i300000000−1−i31+i3−1+i31−i30000000000000000000000000000000000
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χ964-4-44−2+2i3−2−2i32−2i32−2i32+2i32+2i3−2+2i3−2−2i3-442−2i32+2i3−2+2i3−2−2i3000000000000000000-2200002-2000000001−i3−1+i31+i3−1−i300000000−1+i31−i3−1−i31+i30000000000000000000000000000000000
χ9788-8-8888-88-8-8-8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9888-8-8−4−4i3−4+4i3−4−4i34+4i3−4+4i34−4i34+4i34−4i3000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
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.