Finite Group Databasebeta

← Group #72341841

Character table — Group #72341841

Order 3072.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118
size1111222222444466666666121212121212121212121212121212121212121212121212121212121212121212121212161616161616161616161616161616163232323232323232323232324848484848484848646464646464646464646464646464646464646464646464
order12442488884488224488882222444444444444448888888888888888882233446688881212121266121224242424242424244444888866661212121212121212242424242424242424242424
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111−1−i32−1+i3211−1−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+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
χ3111111111111111111111111111111111111111111111111111111111111−1+i32−1−i3211−1+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−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
χ41111111111111111111111111111111111111111111111111111111111-1-111-1-111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ51111111111111111111111111111111111111111111111111111111111-1-1−1−i32−1+i32-1-1−1−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+i32-1-1-1-1-1-1-1-11+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−i32−1−i32−1+i32−1+i32
χ61111111111111111111111111111111111111111111111111111111111-1-1−1+i32−1−i32-1-1−1+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−i32-1-1-1-1-1-1-1-11−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+i32−1+i32−1−i32−1−i32
χ71111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11-1111-11111-1-1111111111111111111-1-111-1-11-11-11-11-1-1-1-1-111-1-111-1-1-1-1-1-1
χ81111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11-1−1−i32−1+i321-1−1−i32−1+i3211-1-1−1−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+i3211-1-111-1-1−1−i321+i32−1+i321−i32−1−i321+i32−1+i321−i321+i321+i321−i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i321+i321+i321−i321−i32
χ91111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-11-1−1+i32−1−i321-1−1+i32−1−i3211-1-1−1+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−i3211-1-111-1-1−1+i321−i32−1−i321+i32−1+i321−i32−1−i321+i321−i321−i321+i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i321−i321−i321+i321+i32
χ101111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1111-1111-1-1111111111111111111-1-111-1-111-11-11-11-11-1-1-1-1-1-111-1-111-1-1-1-1
χ111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-11−1−i32−1+i32-11−1−i32−1+i32-1-111−1−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+i32-1-111-1-1111+i32−1−i321−i32−1+i321+i32−1−i321−i32−1+i321+i321+i321−i321−i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i321+i321+i321−i321−i32
χ121111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-11−1+i32−1−i32-11−1+i32−1−i32-1-111−1+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−i32-1-111-1-1111−i32−1+i321+i32−1−i321−i32−1+i321+i32−1−i321−i321−i321+i321+i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i321−i321−i321+i321+i32
χ13111111-1-1-1-111-1-11111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1111-111-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-1111-11-11-11-11111-1-111-1-111-1-1-1-1
χ14111111-1-1-1-111-1-11111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1−1−i32−1+i321-1−1−i32−1+i32-1-111−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i3211-1-1-1-111−1−i321+i32−1+i321−i32−1−i321+i32−1+i321−i32−1−i32−1−i32−1+i32−1+i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i321+i321+i321−i321−i32
χ15111111-1-1-1-111-1-11111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1−1+i32−1−i321-1−1+i32−1−i32-1-111−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i3211-1-1-1-111−1+i321−i32−1−i321+i32−1+i321−i32−1−i321+i32−1+i32−1+i32−1−i32−1−i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i321−i321−i321+i321+i32
χ16111111-1-1-1-111-1-11111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-111111-1-111111111-1-1-1-1-1-1-1-1-1-11111-1-1-11-11-11-11111111-1-111-1-1-1-1-1-1
χ17111111-1-1-1-111-1-11111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11−1−i32−1+i32-11−1−i32−1+i3211-1-1−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i32-1-11111-1-11+i32−1−i321−i32−1+i321+i32−1−i321−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i321+i321+i321−i321−i32
χ18111111-1-1-1-111-1-11111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11−1+i32−1−i32-11−1+i32−1−i3211-1-1−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i32-1-11111-1-11−i32−1+i321+i32−1−i321−i32−1+i321+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i321−i321−i321+i321+i32
χ19111111-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111
χ20111111-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111−1−i32−1+i3211−1−i32−1+i32-1-1-1-1−1−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+i321+i321+i321−i321−i321+i321+i321+i321+i321−i321−i321−i321−i32−1−i32−1−i32−1+i32−1+i32
χ21111111-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111−1+i32−1−i3211−1+i32−1−i32-1-1-1-1−1+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−i321−i321−i321+i321+i321−i321−i321−i321−i321+i321+i321+i321+i32−1+i32−1+i32−1−i32−1−i32
χ22111111-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111111111
χ23111111-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1−1−i32−1+i32-1-1−1−i32−1+i321111−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32−1−i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i32-1-1-1-111111+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+i32−1−i32−1−i32−1+i32−1+i32
χ24111111-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1−1+i32−1−i32-1-1−1+i32−1−i321111−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32−1+i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i32-1-1-1-111111−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−i32−1+i32−1+i32−1−i32−1−i32
χ2511-1-1-11ii−i−ii−i1-1-111-1ii−i−i11-1-111-1-1iiiii−i−i−i−i−iiiii−i−i−i−i11111-1-1-1-1-11111-1-111i−ii−i-1-1-1-1-1-111ii−i−iii−i−i1-11-1i−ii−i1111-1-1-1-1i−ii−ii−ii−ii−ii−i1-11-1
χ2611-1-1-11ii−i−ii−i1-1-111-1ii−i−i11-1-111-1-1iiiii−i−i−i−i−iiiii−i−i−i−i11111-1-1-1-1-111−1−i32−1+i32-1-1−1−i32−1+i32i−ii−i1+i321+i321−i321−i321+i321−i32−1−i32−1+i32ζ11ζ11−ζ11−ζ11ζ7ζ7−ζ7−ζ71-11-1i−ii−i−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32ζ11−ζ11ζ7−ζ7ζ11−ζ11ζ11−ζ11ζ7−ζ7ζ7−ζ7−1−i321+i32−1+i321−i32
χ2711-1-1-11ii−i−ii−i1-1-111-1ii−i−i11-1-111-1-1iiiii−i−i−i−i−iiiii−i−i−i−i11111-1-1-1-1-111−1+i32−1−i32-1-1−1+i32−1−i32i−ii−i1−i321−i321+i321+i321−i321+i32−1+i32−1−i32ζ7ζ7−ζ7−ζ7ζ11ζ11−ζ11−ζ111-11-1i−ii−i−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32ζ7−ζ7ζ11−ζ11ζ7−ζ7ζ7−ζ7ζ11−ζ11ζ11−ζ11−1+i321−i32−1−i321+i32
χ2811-1-1-11ii−i−ii−i1-1-111-1ii−i−i11-1-111-1-1iiiii−i−i−i−i−iiiii−i−i−i−i11111-1-1-1-1-1-1-1111111−ii−ii-1-1-1-1-1-111ii−i−iii−i−i-11-11−ii−ii-1-1-1-11111i−ii−i−ii−ii−ii−ii1-11-1
χ2911-1-1-11ii−i−ii−i1-1-111-1ii−i−i11-1-111-1-1iiiii−i−i−i−i−iiiii−i−i−i−i11111-1-1-1-1-1-1-1−1−i32−1+i3211−1−i32−1+i32−ii−ii1+i321+i321−i321−i321+i321−i32−1−i32−1+i32ζ11ζ11−ζ11−ζ11ζ7ζ7−ζ7−ζ7-11-11−ii−ii1+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32ζ11−ζ11ζ7−ζ7−ζ11ζ11−ζ11ζ11−ζ7ζ7−ζ7ζ7−1−i321+i32−1+i321−i32
χ3011-1-1-11ii−i−ii−i1-1-111-1ii−i−i11-1-111-1-1iiiii−i−i−i−i−iiiii−i−i−i−i11111-1-1-1-1-1-1-1−1+i32−1−i3211−1+i32−1−i32−ii−ii1−i321−i321+i321+i321−i321+i32−1+i32−1−i32ζ7ζ7−ζ7−ζ7ζ11ζ11−ζ11−ζ11-11-11−ii−ii1−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32ζ7−ζ7ζ11−ζ11−ζ7ζ7−ζ7ζ7−ζ11ζ11−ζ11ζ11−1+i321−i32−1−i321+i32
χ3111-1-1-11ii−i−i−ii-11-111-1ii−i−i11-1-111-1-1−i−i−i−i−iiiiiiiiii−i−i−i−i-1-1-1-1-1111111-111-1111i−i−ii-1-1-1-1-1-111ii−i−iii−i−i1-1-11i−i−ii1-11-1-11-11−ii−iii−i−iii−i−ii-11-11
χ3211-1-1-11ii−i−i−ii-11-111-1ii−i−i11-1-111-1-1−i−i−i−i−iiiiiiiiii−i−i−i−i-1-1-1-1-1111111-1−1−i32−1+i32-11−1−i32−1+i32i−i−ii1+i321+i321−i321−i321+i321−i32−1−i32−1+i32ζ11ζ11−ζ11−ζ11ζ7ζ7−ζ7−ζ71-1-11i−i−ii−1−i321+i32−1+i321−i321+i32−1−i321−i32−1+i32−ζ11ζ11−ζ7ζ7ζ11−ζ11−ζ11ζ11ζ7−ζ7−ζ7ζ71+i32−1−i321−i32−1+i32
χ3311-1-1-11ii−i−i−ii-11-111-1ii−i−i11-1-111-1-1−i−i−i−i−iiiiiiiiii−i−i−i−i-1-1-1-1-1111111-1−1+i32−1−i32-11−1+i32−1−i32i−i−ii1−i321−i321+i321+i321−i321+i32−1+i32−1−i32ζ7ζ7−ζ7−ζ7ζ11ζ11−ζ11−ζ111-1-11i−i−ii−1+i321−i32−1−i321+i321−i32−1+i321+i32−1−i32−ζ7ζ7−ζ11ζ11ζ7−ζ7−ζ7ζ7ζ11−ζ11−ζ11ζ111−i32−1+i321+i32−1−i32
χ3411-1-1-11ii−i−i−ii-11-111-1ii−i−i11-1-111-1-1−i−i−i−i−iiiiiiiiii−i−i−i−i-1-1-1-1-111111-11111-111−iii−i-1-1-1-1-1-111ii−i−iii−i−i-111-1−iii−i-11-111-11-1−ii−ii−iii−i−iii−i-11-11
χ3511-1-1-11ii−i−i−ii-11-111-1ii−i−i11-1-111-1-1−i−i−i−i−iiiiiiiiii−i−i−i−i-1-1-1-1-111111-11−1−i32−1+i321-1−1−i32−1+i32−iii−i1+i321+i321−i321−i321+i321−i32−1−i32−1+i32ζ11ζ11−ζ11−ζ11ζ7ζ7−ζ7−ζ7-111-1−iii−i1+i32−1−i321−i32−1+i32−1−i321+i32−1+i321−i32−ζ11ζ11−ζ7ζ7−ζ11ζ11ζ11−ζ11−ζ7ζ7ζ7−ζ71+i32−1−i321−i32−1+i32
χ3611-1-1-11ii−i−i−ii-11-111-1ii−i−i11-1-111-1-1−i−i−i−i−iiiiiiiiii−i−i−i−i-1-1-1-1-111111-11−1+i32−1−i321-1−1+i32−1−i32−iii−i1−i321−i321+i321+i321−i321+i32−1+i32−1−i32ζ7ζ7−ζ7−ζ7ζ11ζ11−ζ11−ζ11-111-1−iii−i1−i32−1+i321+i32−1−i32−1+i321−i32−1−i321+i32−ζ7ζ7−ζ11ζ11−ζ7ζ7ζ7−ζ7−ζ11ζ11ζ11−ζ111−i32−1+i321+i32−1−i32
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χ11266-6-6-66−6i−6i6i6i−6i6i6-62-2-222i2i−2i−2i-22-222-22-22i2i2i−2i−2i−2i−2i−2i2i2i2i−2i2i−2i−2i2i−2i2i-2-2-222222-2-2000000000000000000000000000000000000000000000000000000000000
χ11316-1616i−16i000000000000000000000000000000000000000000000000000000004400-4-400004i−4i4i−4i00000000000000000000000000000000000000000000
χ11416-1616i−16i00000000000000000000000000000000000000000000000000000000−2−2i3−2+2i3002+2i32−2i300004ζ11−4ζ114ζ7−4ζ700000000000000000000000000000000000000000000
χ11516-1616i−16i00000000000000000000000000000000000000000000000000000000−2+2i3−2−2i3002−2i32+2i300004ζ7−4ζ74ζ11−4ζ1100000000000000000000000000000000000000000000
χ11616-16−16i16i000000000000000000000000000000000000000000000000000000004400-4-40000−4i4i−4i4i00000000000000000000000000000000000000000000
χ11716-16−16i16i00000000000000000000000000000000000000000000000000000000−2−2i3−2+2i3002+2i32−2i30000−4ζ114ζ11−4ζ74ζ700000000000000000000000000000000000000000000
χ11816-16−16i16i00000000000000000000000000000000000000000000000000000000−2+2i3−2−2i3002−2i32+2i30000−4ζ74ζ7−4ζ114ζ1100000000000000000000000000000000000000000000

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