Finite Group Databasebeta

← Group #72341691

Character table — Group #72341691

Order 3072.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118
size1111222222444466666666121212121212121212121212121212121212121212121212121212121212121212121212161616161616161616161616161616163232323232323232323232324848484848484848646464646464646464646464646464646464646464646464
order12442224448888222244442222222244444444888888888888888888883344444444661212121266666612121212121244444444121212121212121212121212121212122424242424242424
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ31111111111111111111111111111111111111111111111111111111111−1−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+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−i32−1+i32−1+i32−1+i32−1+i32
χ41111111111111111111111111111111111111111111111111111111111−1−i32−1+i32-1-1-1-1-1-1-1-1−1−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+i32-1-1-1-1-1-1-1-11+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+i32
χ51111111111111111111111111111111111111111111111111111111111−1+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−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+i32−1−i32−1−i32−1−i32−1−i32
χ61111111111111111111111111111111111111111111111111111111111−1+i32−1−i32-1-1-1-1-1-1-1-1−1+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−i32-1-1-1-1-1-1-1-11−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−i32
χ71111111111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1
χ81111111111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1
χ91111111111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−1−i32−1+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+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321111-1-1-1-1−1−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+i321−i321−i321−i321−i32
χ101111111111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−1−i32−1+i32-1-1-1-11111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32-1-1-1-111111+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−i32
χ111111111111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−1+i32−1−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−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321111-1-1-1-1−1+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−i321+i321+i321+i321+i32
χ121111111111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−1+i32−1−i32-1-1-1-11111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32-1-1-1-111111−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+i32
χ1311111-1-1-1-1111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111ii−i−iii−i−i11111111-1-1-1-1-1-1-1-111ii−i−iii−i−iii−i−iii−i−iii−i−iii−i−i11-1-111-1-1
χ1411111-1-1-1-1111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-111−i−iii−i−iii11111111-1-1-1-1-1-1-1-111−i−iii−i−iii−i−iii−i−iii−i−iii−i−iii11-1-111-1-1
χ1511111-1-1-1-1111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1−1−i32−1+i32ii−i−iii−i−i−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−i32−1+i32ii−i−iii−i−iζ11ζ11−ζ11−ζ11ζ11ζ11−ζ11−ζ11ζ7ζ7−ζ7−ζ7ζ7ζ7−ζ7−ζ7−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32
χ1611111-1-1-1-1111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1−1−i32−1+i32−i−iii−i−iii−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−i32−1+i32−i−iii−i−iii−ζ11−ζ11ζ11ζ11−ζ11−ζ11ζ11ζ11−ζ7−ζ7ζ7ζ7−ζ7−ζ7ζ7ζ7−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32
χ1711111-1-1-1-1111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1−1+i32−1−i32ii−i−iii−i−i−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+i32−1−i32ii−i−iii−i−iζ7ζ7−ζ7−ζ7ζ7ζ7−ζ7−ζ7ζ11ζ11−ζ11−ζ11ζ11ζ11−ζ11−ζ11−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32
χ1811111-1-1-1-1111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1−1+i32−1−i32−i−iii−i−iii−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+i32−1−i32−i−iii−i−iii−ζ7−ζ7ζ7ζ7−ζ7−ζ7ζ7ζ7−ζ11−ζ11ζ11ζ11−ζ11−ζ11ζ11ζ11−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32
χ1911111-1-1-1-11-1-11111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111ii−i−i−i−iii11111111-1-1-1-1-1-1-1-111ii−i−i−i−iiiii−i−i−i−iiiii−i−i−i−iii-1-111-1-111
χ2011111-1-1-1-11-1-11111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111−i−iiiii−i−i11111111-1-1-1-1-1-1-1-111−i−iiiii−i−i−i−iiiii−i−i−i−iiiii−i−i-1-111-1-111
χ2111111-1-1-1-11-1-11111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111−1−i32−1+i32ii−i−i−i−iii−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−i32−1+i32ii−i−i−i−iiiζ11ζ11−ζ11−ζ11−ζ11−ζ11ζ11ζ11ζ7ζ7−ζ7−ζ7−ζ7−ζ7ζ7ζ71+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32
χ2211111-1-1-1-11-1-11111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111−1−i32−1+i32−i−iiiii−i−i−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−i32−1+i32−i−iiiii−i−i−ζ11−ζ11ζ11ζ11ζ11ζ11−ζ11−ζ11−ζ7−ζ7ζ7ζ7ζ7ζ7−ζ7−ζ71+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32
χ2311111-1-1-1-11-1-11111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111−1+i32−1−i32ii−i−i−i−iii−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+i32−1−i32ii−i−i−i−iiiζ7ζ7−ζ7−ζ7−ζ7−ζ7ζ7ζ7ζ11ζ11−ζ11−ζ11−ζ11−ζ11ζ11ζ111−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32
χ2411111-1-1-1-11-1-11111-1-111-1-11111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111−1+i32−1−i32−i−iiiii−i−i−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+i32−1−i32−i−iiiii−i−i−ζ7−ζ7ζ7ζ7ζ7ζ7−ζ7−ζ7−ζ11−ζ11ζ11ζ11ζ11ζ11−ζ11−ζ111−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32
χ251111-11-11-1-1i−ii−i1-11-11-11-111-1-111-1-111-1-111-1-1iiiii−i−i−i−i−iiiiii−i−i−i−i−i111-11-1i−ii−i111111-1-11-11-11-11-1-1-11-11-1i−ii−i1-11-1i−ii−i1-11-1i−ii−ii−ii−ii−ii−i
χ261111-11-11-1-1i−ii−i1-11-11-11-111-1-111-1-111-1-111-1-1iiiii−i−i−i−i−iiiiii−i−i−i−i−i11-11-11−ii−ii111111-1-11-11-11-11-1-1-1-11-11−ii−ii-11-11−ii−ii-11-11−ii−iii−ii−ii−ii−i
χ271111-11-11-1-1i−ii−i1-11-11-11-111-1-111-1-111-1-111-1-1iiiii−i−i−i−i−iiiiii−i−i−i−i−i−1−i32−1+i321-11-1i−ii−i−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321−i32−1−i321+i32−1+i321−i32−1−i321+i32−1+i321−i321+i321−i321-11-1i−ii−i−1−i321+i32−1−i321+i32ζ11−ζ11ζ11−ζ11−1+i321−i32−1+i321−i32ζ7−ζ7ζ7−ζ7ζ11−ζ11ζ11−ζ11ζ7−ζ7ζ7−ζ7
χ281111-11-11-1-1i−ii−i1-11-11-11-111-1-111-1-111-1-111-1-1iiiii−i−i−i−i−iiiiii−i−i−i−i−i−1−i32−1+i32-11-11−ii−ii−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321−i32−1−i321+i32−1+i321−i32−1−i321+i32−1+i321−i321+i321−i32-11-11−ii−ii1+i32−1−i321+i32−1−i32−ζ11ζ11−ζ11ζ111−i32−1+i321−i32−1+i32−ζ7ζ7−ζ7ζ7ζ11−ζ11ζ11−ζ11ζ7−ζ7ζ7−ζ7
χ291111-11-11-1-1i−ii−i1-11-11-11-111-1-111-1-111-1-111-1-1iiiii−i−i−i−i−iiiiii−i−i−i−i−i−1+i32−1−i321-11-1i−ii−i−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321+i32−1+i321−i32−1−i321+i32−1+i321−i32−1−i321+i321−i321+i321-11-1i−ii−i−1+i321−i32−1+i321−i32ζ7−ζ7ζ7−ζ7−1−i321+i32−1−i321+i32ζ11−ζ11ζ11−ζ11ζ7−ζ7ζ7−ζ7ζ11−ζ11ζ11−ζ11
χ301111-11-11-1-1i−ii−i1-11-11-11-111-1-111-1-111-1-111-1-1iiiii−i−i−i−i−iiiiii−i−i−i−i−i−1+i32−1−i32-11-11−ii−ii−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321+i32−1+i321−i32−1−i321+i32−1+i321−i32−1−i321+i321−i321+i32-11-11−ii−ii1−i32−1+i321−i32−1+i32−ζ7ζ7−ζ7ζ71+i32−1−i321+i32−1−i32−ζ11ζ11−ζ11ζ11ζ7−ζ7ζ7−ζ7ζ11−ζ11ζ11−ζ11
χ311111-11-11-1-1−ii−ii1-11-11-11-111-1-111-1-111-1-111-1-1−i−i−i−i−iiiiii−i−i−i−i−iiiiii111-11-1−ii−ii111111-1-11-11-11-11-1-1-11-11-1−ii−ii1-11-1−ii−ii1-11-1−ii−ii−ii−ii−ii−ii
χ321111-11-11-1-1−ii−ii1-11-11-11-111-1-111-1-111-1-111-1-1−i−i−i−i−iiiiii−i−i−i−i−iiiiii11-11-11i−ii−i111111-1-11-11-11-11-1-1-1-11-11i−ii−i-11-11i−ii−i-11-11i−ii−i−ii−ii−ii−ii
χ331111-11-11-1-1−ii−ii1-11-11-11-111-1-111-1-111-1-111-1-1−i−i−i−i−iiiiii−i−i−i−i−iiiiii−1−i32−1+i321-11-1−ii−ii−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321−i32−1−i321+i32−1+i321−i32−1−i321+i32−1+i321−i321+i321−i321-11-1−ii−ii−1−i321+i32−1−i321+i32−ζ11ζ11−ζ11ζ11−1+i321−i32−1+i321−i32−ζ7ζ7−ζ7ζ7−ζ11ζ11−ζ11ζ11−ζ7ζ7−ζ7ζ7
χ341111-11-11-1-1−ii−ii1-11-11-11-111-1-111-1-111-1-111-1-1−i−i−i−i−iiiiii−i−i−i−i−iiiiii−1−i32−1+i32-11-11i−ii−i−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321−i32−1−i321+i32−1+i321−i32−1−i321+i32−1+i321−i321+i321−i32-11-11i−ii−i1+i32−1−i321+i32−1−i32ζ11−ζ11ζ11−ζ111−i32−1+i321−i32−1+i32ζ7−ζ7ζ7−ζ7−ζ11ζ11−ζ11ζ11−ζ7ζ7−ζ7ζ7
χ351111-11-11-1-1−ii−ii1-11-11-11-111-1-111-1-111-1-111-1-1−i−i−i−i−iiiiii−i−i−i−i−iiiiii−1+i32−1−i321-11-1−ii−ii−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321+i32−1+i321−i32−1−i321+i32−1+i321−i32−1−i321+i321−i321+i321-11-1−ii−ii−1+i321−i32−1+i321−i32−ζ7ζ7−ζ7ζ7−1−i321+i32−1−i321+i32−ζ11ζ11−ζ11ζ11−ζ7ζ7−ζ7ζ7−ζ11ζ11−ζ11ζ11
χ361111-11-11-1-1−ii−ii1-11-11-11-111-1-111-1-111-1-111-1-1−i−i−i−i−iiiiii−i−i−i−i−iiiiii−1+i32−1−i32-11-11i−ii−i−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321+i32−1+i321−i32−1−i321+i32−1+i321−i32−1−i321+i321−i321+i32-11-11i−ii−i1−i32−1+i321−i32−1+i32ζ7−ζ7ζ7−ζ71+i32−1−i321+i32−1−i32ζ11−ζ11ζ11−ζ11−ζ7ζ7−ζ7ζ7−ζ11ζ11−ζ11ζ11
χ371111-1-11-11-1i−i−ii1-1-111-1-1111-1-1-1-11111-1-1-1-111iiiii−i−i−i−i−i−i−i−i−i−iiiiii11i−i−ii-111-1111111-1-1-11-11-11-11-1-1i−i−ii-111-1i−i−ii-111-1i−i−ii-111-1i−i−iii−i−ii
χ381111-1-11-11-1i−i−ii1-1-111-1-1111-1-1-1-11111-1-1-1-111iiiii−i−i−i−i−i−i−i−i−i−iiiiii11−iii−i1-1-11111111-1-1-11-11-11-11-1-1−iii−i1-1-11−iii−i1-1-11−iii−i1-1-11i−i−iii−i−ii
χ391111-1-11-11-1i−i−ii1-1-111-1-1111-1-1-1-11111-1-1-1-111iiiii−i−i−i−i−i−i−i−i−i−iiiiii−1−i32−1+i32i−i−ii-111-1−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321−i321+i32−1−i321−i32−1+i321+i32−1−i321−i32−1+i321+i321−i32i−i−ii-111-1ζ11−ζ11−ζ11ζ111+i32−1−i32−1−i321+i32ζ7−ζ7−ζ7ζ71−i32−1+i32−1+i321−i32ζ11−ζ11−ζ11ζ11ζ7−ζ7−ζ7ζ7
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.