Finite Group Databasebeta

← Group #72341690

Character table — Group #72341690

Order 3072.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118
size1111222222444466666666121212121212121212121212121212121212121212121212121212121212121212121212161616161616161616161616161616163232323232323232323232324848484848484848646464646464646464646464646464646464646464646464
order12224444448888224444442222444444444444888888888888888888882222334444666666121212121212121212121212444444446666666612121212121212122424242424242424
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111111111111−1−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+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
χ311111111111111111111111111111111111111111111111111111111111111−1+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−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
χ41111111111111111111111111111111111111111111111111111111111-1-1-1-111-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ51111111111111111111111111111111111111111111111111111111111-1-1-1-1−1−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+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
χ61111111111111111111111111111111111111111111111111111111111-1-1-1-1−1+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−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
χ71111111111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-11111111111111111111111-1-1-1-111-1-111-1-111-1-111-1-1-1-1-1-1-1-1-1-1
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−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−i32−1+i32−1+i321111-1-1-1-1−1−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+i321−i321−i321−i321−i32
χ91111111111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1−1+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+i32−1−i32−1−i321111-1-1-1-1−1+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−i321+i321+i321+i321+i32
χ101111111111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111111111111111-1-1-1-11111-1-111-1-111-1-111-1-111-1-1-1-1-1-1-1-1
χ111111111111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111−1−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+i32−1+i32-1-1-1-111111+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−i321−i321−i32
χ121111111111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111−1+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−i32−1−i32-1-1-1-111111−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+i321+i321+i32
χ131111-1-1-1-11111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1111111-1-1-1-1-1-1-1-1111111-1-111-1-111111111-1-1-1-1-1-1-1-111-1-111-1-1
χ141111-1-1-1-11111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111−1−i32−1+i32-1-1-1-1−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i32−1−i32−1−i32−1+i32−1+i3211-1-111-1-1−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32
χ151111-1-1-1-11111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111−1+i32−1−i32-1-1-1-1−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i32−1+i32−1+i32−1−i32−1−i3211-1-111-1-1−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32
χ161111-1-1-1-11111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-11111-1-111-1-111-1-1-1-1-1-1-1-11111111111-1-111-1-1
χ171111-1-1-1-11111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1−1−i32−1+i321111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i32−1−i32−1−i32−1+i32−1+i32-1-111-1-1111+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−i321+i321+i32−1+i32−1+i321−i321−i32
χ181111-1-1-1-11111-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1−1+i32−1−i321111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i32−1+i32−1+i32−1−i32−1−i32-1-111-1-1111−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+i321−i321−i32−1−i32−1−i321+i321+i32
χ191111-1-1-1-111-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-111-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-111-1-1-1-111-1-111-1-111-1-111
χ201111-1-1-1-111-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1−1−i32−1+i32-1-111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i32−1−i32−1−i32−1+i32−1+i3211-1-1-1-111−1−i32−1−i321+i321+i32−1+i32−1+i321−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+i32
χ211111-1-1-1-111-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1−1+i32−1−i32-1-111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i32−1+i32−1+i32−1−i32−1−i3211-1-1-1-111−1+i32−1+i321−i321−i32−1−i32−1−i321+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−i32
χ221111-1-1-1-111-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1111111-1-1111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111-1-11111-1-111-1-1-1-111-1-111
χ231111-1-1-1-111-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111−1−i32−1+i3211-1-1−1−i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i32−1−i32−1−i32−1+i32−1+i32-1-11111-1-11+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32
χ241111-1-1-1-111-1-1111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111−1+i32−1−i3211-1-1−1+i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i32−1+i32−1+i32−1−i32−1−i32-1-11111-1-11−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32
χ2511-1-1ii−i−i1-11-1i−i1-11-1ii−i−i11-1-111-1-1iiii−i−i−i−i11111-1-1-1-1-1iiiii−i−i−i−i−i1-11-111i−ii−i11-1-1-1-1ii−i−iii−i−i1-11-11-1i−i1-1i−i1-11-11-11-1i−ii−ii−ii−i1-1i−i1-1i−i
χ2611-1-1ii−i−i1-11-1i−i1-11-1ii−i−i11-1-111-1-1iiii−i−i−i−i11111-1-1-1-1-1iiiii−i−i−i−i−i1-11-1−1−i32−1+i32i−ii−i−1−i32−1+i321+i321+i321−i321−i32ζ11ζ11−ζ11−ζ11ζ7ζ7−ζ7−ζ7−1−i321+i32−1+i321−i321-1i−i1-1i−i−1−i321+i32−1−i321+i32−1+i321−i32−1+i321−i32ζ11−ζ11ζ11−ζ11ζ7−ζ7ζ7−ζ7−1−i321+i32ζ11−ζ11−1+i321−i32ζ7−ζ7
χ2711-1-1ii−i−i1-11-1i−i1-11-1ii−i−i11-1-111-1-1iiii−i−i−i−i11111-1-1-1-1-1iiiii−i−i−i−i−i1-11-1−1+i32−1−i32i−ii−i−1+i32−1−i321−i321−i321+i321+i32ζ7ζ7−ζ7−ζ7ζ11ζ11−ζ11−ζ11−1+i321−i32−1−i321+i321-1i−i1-1i−i−1+i321−i32−1+i321−i32−1−i321+i32−1−i321+i32ζ7−ζ7ζ7−ζ7ζ11−ζ11ζ11−ζ11−1+i321−i32ζ7−ζ7−1−i321+i32ζ11−ζ11
χ2811-1-1ii−i−i1-11-1i−i1-11-1ii−i−i11-1-111-1-1iiii−i−i−i−i11111-1-1-1-1-1iiiii−i−i−i−i−i-11-1111−ii−ii11-1-1-1-1ii−i−iii−i−i1-11-1-11−ii-11−ii-11-11-11-11−ii−ii−ii−ii1-1i−i1-1i−i
χ2911-1-1ii−i−i1-11-1i−i1-11-1ii−i−i11-1-111-1-1iiii−i−i−i−i11111-1-1-1-1-1iiiii−i−i−i−i−i-11-11−1−i32−1+i32−ii−ii−1−i32−1+i321+i321+i321−i321−i32ζ11ζ11−ζ11−ζ11ζ7ζ7−ζ7−ζ7−1−i321+i32−1+i321−i32-11−ii-11−ii1+i32−1−i321+i32−1−i321−i32−1+i321−i32−1+i32−ζ11ζ11−ζ11ζ11−ζ7ζ7−ζ7ζ7−1−i321+i32ζ11−ζ11−1+i321−i32ζ7−ζ7
χ3011-1-1ii−i−i1-11-1i−i1-11-1ii−i−i11-1-111-1-1iiii−i−i−i−i11111-1-1-1-1-1iiiii−i−i−i−i−i-11-11−1+i32−1−i32−ii−ii−1+i32−1−i321−i321−i321+i321+i32ζ7ζ7−ζ7−ζ7ζ11ζ11−ζ11−ζ11−1+i321−i32−1−i321+i32-11−ii-11−ii1−i32−1+i321−i32−1+i321+i32−1−i321+i32−1−i32−ζ7ζ7−ζ7ζ7−ζ11ζ11−ζ11ζ11−1+i321−i32ζ7−ζ7−1−i321+i32ζ11−ζ11
χ3111-1-1ii−i−i1-1-11−ii1-11-1ii−i−i11-1-111-1-1iiii−i−i−i−i-1-1-1-1-111111−i−i−i−i−iiiiii1-1-1111i−i−ii11-1-1-1-1ii−i−iii−i−i1-11-11-1i−i-11−ii1-1-111-1-11i−i−iii−i−ii-11−ii-11−ii
χ3211-1-1ii−i−i1-1-11−ii1-11-1ii−i−i11-1-111-1-1iiii−i−i−i−i-1-1-1-1-111111−i−i−i−i−iiiiii1-1-11−1−i32−1+i32i−i−ii−1−i32−1+i321+i321+i321−i321−i32ζ11ζ11−ζ11−ζ11ζ7ζ7−ζ7−ζ7−1−i321+i32−1+i321−i321-1i−i-11−ii−1−i321+i321+i32−1−i32−1+i321−i321−i32−1+i32ζ11−ζ11−ζ11ζ11ζ7−ζ7−ζ7ζ71+i32−1−i32−ζ11ζ111−i32−1+i32−ζ7ζ7
χ3311-1-1ii−i−i1-1-11−ii1-11-1ii−i−i11-1-111-1-1iiii−i−i−i−i-1-1-1-1-111111−i−i−i−i−iiiiii1-1-11−1+i32−1−i32i−i−ii−1+i32−1−i321−i321−i321+i321+i32ζ7ζ7−ζ7−ζ7ζ11ζ11−ζ11−ζ11−1+i321−i32−1−i321+i321-1i−i-11−ii−1+i321−i321−i32−1+i32−1−i321+i321+i32−1−i32ζ7−ζ7−ζ7ζ7ζ11−ζ11−ζ11ζ111−i32−1+i32−ζ7ζ71+i32−1−i32−ζ11ζ11
χ3411-1-1ii−i−i1-1-11−ii1-11-1ii−i−i11-1-111-1-1iiii−i−i−i−i-1-1-1-1-111111−i−i−i−i−iiiiii-111-111−iii−i11-1-1-1-1ii−i−iii−i−i1-11-1-11−ii1-1i−i-111-1-111-1−iii−i−iii−i-11−ii-11−ii
χ3511-1-1ii−i−i1-1-11−ii1-11-1ii−i−i11-1-111-1-1iiii−i−i−i−i-1-1-1-1-111111−i−i−i−i−iiiiii-111-1−1−i32−1+i32−iii−i−1−i32−1+i321+i321+i321−i321−i32ζ11ζ11−ζ11−ζ11ζ7ζ7−ζ7−ζ7−1−i321+i32−1+i321−i32-11−ii1-1i−i1+i32−1−i32−1−i321+i321−i32−1+i32−1+i321−i32−ζ11ζ11ζ11−ζ11−ζ7ζ7ζ7−ζ71+i32−1−i32−ζ11ζ111−i32−1+i32−ζ7ζ7
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χ10966-6-6−6i−6i6i6i6-66-6−6i6i-22-222i2i−2i−2i2-2-22-222-2−2i2i−2i2i2i−2i2i−2i-222-2-22-2-2222i−2i−2i2i2i−2i2i2i−2i−2i000000000000000000000000000000000000000000000000000000000000
χ11066-6-6−6i−6i6i6i6-66-6−6i6i-22-222i2i−2i−2i-222-22-2-222i−2i2i−2i−2i2i−2i2i-2-2-222222-2-22i2i2i−2i−2i−2i−2i−2i2i2i000000000000000000000000000000000000000000000000000000000000
χ11166-6-6−6i−6i6i6i6-6-666i−6i-22-222i2i−2i−2i2-2-22-222-2−2i2i−2i2i2i−2i2i−2i2-2-222-222-2-2−2i2i2i−2i−2i2i−2i−2i2i2i000000000000000000000000000000000000000000000000000000000000
χ11266-6-6−6i−6i6i6i6-6-666i−6i-22-222i2i−2i−2i-222-22-2-222i−2i2i−2i−2i2i−2i2i222-2-2-2-2-222−2i−2i−2i2i2i2i2i2i−2i−2i000000000000000000000000000000000000000000000000000000000000
χ11316-1616-160000000000000000000000000000000000000000000000000000000000440000-4-44-44-400000000000000000000000000000000000000000000
χ11416-1616-160000000000000000000000000000000000000000000000000000000000−2−2i3−2+2i300002+2i32−2i3−2−2i32+2i3−2+2i32−2i300000000000000000000000000000000000000000000
χ11516-1616-160000000000000000000000000000000000000000000000000000000000−2+2i3−2−2i300002−2i32+2i3−2+2i32−2i3−2−2i32+2i300000000000000000000000000000000000000000000
χ11616-16-16160000000000000000000000000000000000000000000000000000000000440000-4-4-44-4400000000000000000000000000000000000000000000
χ11716-16-16160000000000000000000000000000000000000000000000000000000000−2−2i3−2+2i300002+2i32−2i32+2i3−2−2i32−2i3−2+2i300000000000000000000000000000000000000000000
χ11816-16-16160000000000000000000000000000000000000000000000000000000000−2+2i3−2−2i300002−2i32+2i32−2i3−2+2i32+2i3−2−2i300000000000000000000000000000000000000000000

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