Finite Group Databasebeta

← Group #11923225

Character table — Group #11923225

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114
size111122222222223333444444444444446666666666666688888888888888888888121212121212121212121212121212121616161616161616161616161818181818181818242424242424242424242424
order122234444446664444336666661212121212122222224444444433666666121212121212121212121212661212121212121212121212121212121212121212121212121212444444446666666612121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211111111111111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i3211111111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i3211111111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32
χ3111111111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211111111111111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i3211111111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i3211111111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32
χ411111111111111-1-1-1-11111111111111111-1-1-1-11111-1-1111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ511111111111111-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211111111-1-1-1-11111-1-111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32111111111+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+i32-1-1-1-1-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i321+i321+i321−i321−i32
χ611111111111111-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211111111-1-1-1-11111-1-111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32111111111−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−i32-1-1-1-1-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i321−i321−i321+i321+i32
χ71111111-1-1-1-111111111111111111-1-1-1-1-1-111-1-111-1-1-1-11111111111-1-1-1-111-1-111-1-1-1-11111-1-111111111-1-1-1-111-1-111-1-1-1-11111-1-111-1-111-1-1-1-1-1-1
χ81111111-1-1-1-11111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211-1-1-1-1-1-111-1-111-1-1-1-111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32-1-11111-1-1−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321+i321+i321−i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32-1-11111-1-1−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i321+i321+i321−i321−i32
χ91111111-1-1-1-11111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211-1-1-1-1-1-111-1-111-1-1-1-111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32-1-11111-1-1−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321−i321−i321+i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32-1-11111-1-1−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i321−i321−i321+i321+i32
χ101111111-1-1-1-1111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1111111111111-1-1-1-111-1-111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-111-1-111-1-1111111
χ111111111-1-1-1-1111-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211-1-1-1-1-1-1-1-11111-1-11111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32-1-11111-1-11+i321+i321+i321+i321−i321−i321−i321−i321+i321+i321−i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i3211-1-1-1-1111+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32
χ121111111-1-1-1-1111-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211-1-1-1-1-1-1-1-11111-1-11111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32-1-11111-1-11−i321−i321−i321−i321+i321+i321+i321+i321−i321−i321+i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i3211-1-1-1-1111−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32
χ1311111-1-111-1-1111111111111111-1-111-1-1-1-1-1-111-1-111-1-11111111111-1-1-1-1-1-111-1-111-1-111-1-11111111111-1-1-1-1-1-111-1-111-1-111-1-111-1-111-1-111-1-1-1-1
χ1411111-1-111-1-11111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-111-1-1-1-1-1-111-1-111-1-111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32-1-111-1-111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321+i321+i321−i321−i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32-1-111-1-1111+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i321+i321+i321−i321−i32
χ1511111-1-111-1-11111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-111-1-1-1-1-1-111-1-111-1-111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32-1-111-1-111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321−i321−i321+i321+i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32-1-111-1-1111−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i321−i321−i321+i321+i32
χ1611111-1-111-1-1111-1-1-1-111111111-1-111-1-1-1-111-1-1-1-111111111111111-1-1-1-1-1-111-1-111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-111-1-111-1-111-1-11111
χ1711111-1-111-1-1111-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-111-1-1-1-111-1-1-1-1111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32-1-111-1-1111+i321+i321+i321+i321−i321−i321−i321−i321+i321+i321−i321−i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i3211-1-111-1-1−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i32−1+i32−1+i32
χ1811111-1-111-1-1111-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-111-1-1-1-111-1-1-1-1111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32-1-111-1-1111−i321−i321−i321−i321+i321+i321+i321+i321−i321−i321+i321+i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i3211-1-111-1-1−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i32−1−i32−1−i32
χ1911111-1-1-1-111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111
χ2011111-1-1-1-1111111111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-1-1-11111-1-1-1-1-1-1-1-11111−1−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−i321111-1-1-1-1−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i321111-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i32−1−i32−1−i32−1+i32−1+i32
χ2111111-1-1-1-1111111111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-1-1-11111-1-1-1-1-1-1-1-11111−1+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+i321111-1-1-1-1−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i321111-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i32−1+i32−1+i32−1−i32−1−i32
χ2211111-1-1-1-111111-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1
χ2311111-1-1-1-111111-1-1-1-1−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-1-1-111111111-1-1-1-1-1-111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i321111-1-1-1-11+i321+i321+i321+i321−i321−i321−i321−i32−1−i32−1−i32−1+i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i32-1-1-1-11111−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321+i321+i321−i321−i32
χ2411111-1-1-1-111111-1-1-1-1−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-1-1-111111111-1-1-1-1-1-111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i321111-1-1-1-11−i321−i321−i321−i321+i321+i321+i321+i32−1+i32−1+i32−1−i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i32-1-1-1-11111−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321−i321−i321+i321+i32
χ251-1-111i−ii−i1-1-11-1ii−i−i1111-1-1-1-1i−ii−i1-11-11-11-1i−ii−ii−i1-111-1-111-1-11-11-1i−ii−ii−ii−i1-11-1i−ii−iii−i−iii−i−i1-11-1i−ii−ii−ii−ii−ii−i1-11-11-11-11-11-1i−ii−i
χ261-1-111i−ii−i1-1-11-1ii−i−i−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i32i−ii−i1-11-11-11-1i−ii−ii−i1-1−1−i32−1+i321+i321−i32−1−i32−1+i321+i321−i32−1−i321+i32−1+i321−i32ζ11−ζ11ζ11−ζ11ζ7−ζ7ζ7−ζ71-11-1i−ii−iζ11ζ11−ζ11−ζ11ζ7ζ7−ζ7−ζ7−1−i321+i32−1+i321−i32ζ11−ζ11ζ11−ζ11ζ7−ζ7ζ7−ζ7i−ii−i1-11-1−1−i321+i32−1−i321+i32−1+i321−i32−1+i321−i32ζ11−ζ11ζ7−ζ7
χ271-1-111i−ii−i1-1-11-1ii−i−i−1+i32−1−i32−1+i32−1−i321−i321+i321−i321+i32i−ii−i1-11-11-11-1i−ii−ii−i1-1−1+i32−1−i321−i321+i32−1+i32−1−i321−i321+i32−1+i321−i32−1−i321+i32ζ7−ζ7ζ7−ζ7ζ11−ζ11ζ11−ζ111-11-1i−ii−iζ7ζ7−ζ7−ζ7ζ11ζ11−ζ11−ζ11−1+i321−i32−1−i321+i32ζ7−ζ7ζ7−ζ7ζ11−ζ11ζ11−ζ11i−ii−i1-11-1−1+i321−i32−1+i321−i32−1−i321+i32−1−i321+i32ζ7−ζ7ζ11−ζ11
χ281-1-111i−ii−i1-1-11-1−i−iii1111-1-1-1-1i−ii−i1-11-1-11-11i−ii−i−ii1-111-1-111-1-11-11-1i−ii−ii−ii−i1-11-1i−ii−i−i−iii−i−iii1-11-1i−ii−ii−ii−i−ii−ii-11-11-11-11-11-11−ii−ii
χ291-1-111i−ii−i1-1-11-1−i−iii−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i32i−ii−i1-11-1-11-11i−ii−i−ii1-1−1−i32−1+i321+i321−i32−1−i32−1+i321+i321−i32−1−i321+i32−1+i321−i32ζ11−ζ11ζ11−ζ11ζ7−ζ7ζ7−ζ71-11-1i−ii−i−ζ11−ζ11ζ11ζ11−ζ7−ζ7ζ7ζ7−1−i321+i32−1+i321−i32ζ11−ζ11ζ11−ζ11ζ7−ζ7ζ7−ζ7−ii−ii-11-111+i32−1−i321+i32−1−i321−i32−1+i321−i32−1+i32−ζ11ζ11−ζ7ζ7
χ301-1-111i−ii−i1-1-11-1−i−iii−1+i32−1−i32−1+i32−1−i321−i321+i321−i321+i32i−ii−i1-11-1-11-11i−ii−i−ii1-1−1+i32−1−i321−i321+i32−1+i32−1−i321−i321+i32−1+i321−i32−1−i321+i32ζ7−ζ7ζ7−ζ7ζ11−ζ11ζ11−ζ111-11-1i−ii−i−ζ7−ζ7ζ7ζ7−ζ11−ζ11ζ11ζ11−1+i321−i32−1−i321+i32ζ7−ζ7ζ7−ζ7ζ11−ζ11ζ11−ζ11−ii−ii-11-111−i32−1+i321−i32−1+i321+i32−1−i321+i32−1−i32−ζ7ζ7−ζ11ζ11
χ311-1-111i−i−ii-11-11-1ii−i−i1111-1-1-1-1i−i−ii-11-111-1-11i−i−ii−ii1-111-1-111-1-1-11-11i−i−iii−i−ii-111-1i−i−iiii−i−iii−i−i-11-11i−i−iii−i−ii−iii−i1-1-111-1-111-1-11−ii−ii
χ321-1-111i−i−ii-11-11-1ii−i−i−1−i32−1+i32−1−i32−1+i321+i321−i321+i321−i32i−i−ii-11-111-1-11i−i−ii−ii1-1−1−i32−1+i321+i321−i32−1−i32−1+i321+i321−i321+i32−1−i321−i32−1+i32ζ11−ζ11−ζ11ζ11ζ7−ζ7−ζ7ζ7-111-1i−i−iiζ11ζ11−ζ11−ζ11ζ7ζ7−ζ7−ζ71+i32−1−i321−i32−1+i32ζ11−ζ11−ζ11ζ11ζ7−ζ7−ζ7ζ7−iii−i1-1-11−1−i321+i321+i32−1−i32−1+i321−i321−i32−1+i32−ζ11ζ11−ζ7ζ7
χ331-1-111i−i−ii-11-11-1ii−i−i−1+i32−1−i32−1+i32−1−i321−i321+i321−i321+i32i−i−ii-11-111-1-11i−i−ii−ii1-1−1+i32−1−i321−i321+i32−1+i32−1−i321−i321+i321−i32−1+i321+i32−1−i32ζ7−ζ7−ζ7ζ7ζ11−ζ11−ζ11ζ11-111-1i−i−iiζ7ζ7−ζ7−ζ7ζ11ζ11−ζ11−ζ111−i32−1+i321+i32−1−i32ζ7−ζ7−ζ7ζ7ζ11−ζ11−ζ11ζ11−iii−i1-1-11−1+i321−i321−i32−1+i32−1−i321+i321+i32−1−i32−ζ7ζ7−ζ11ζ11
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.