Finite Group Databasebeta

← Group #11921370

Character table — Group #11921370

Order 1152.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111C112C113C114C115C116C117C118C119C120C121C122C123C124C125C126
size111111112222222222222222222244444444444444446666666666668888888888888888888888888888888888888888121212121212121212122424242424242424242424242424242436363636
order1222222234444666666612121212121212123366666666666666444444444444336666666666666612121212121212121212121212121212121212121212121222666612121212121212121212121212121212121212124444
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111−1−i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32111111111111−1−i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321111111111−1−i32−1−i32−1−i32−1−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
χ41111111111111111111111111111−1−i32−1+i32−1−i32−1−i32−1−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−i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i3211111111111+i321+i321+i321+i321+i321+i321+i321+i321−i321−i321−i321−i321−i321−i321−i321−i32-1-1-1-1
χ51111111111111111111111111111−1+i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32111111111111−1+i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321111111111−1+i32−1+i32−1+i32−1+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
χ61111111111111111111111111111−1+i32−1−i32−1+i32−1+i32−1+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+i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i3211111111111−i321−i321−i321−i321−i321−i321−i321−i321+i321+i321+i321+i321+i321+i321+i321+i32-1-1-1-1
χ7111111111-1-1-1-11111111-1-1-1-1-1-1-1-111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-1
χ8111111111-1-1-1-11111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-111
χ9111111111-1-1-1-11111111-1-1-1-1-1-1-1-1−1−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+i321111-1-1-1-11111−1−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+i321+i321+i321+i321+i321−i321−i321−i321−i321+i321+i321+i321+i321+i321+i321+i321+i321−i321−i321−i321−i321−i321−i321−i321−i32-1-1-1-1-1-11111−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i3211-1-1
χ10111111111-1-1-1-11111111-1-1-1-1-1-1-1-1−1−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+i32-1-1-1-111111111−1−i32−1+i32−1−i32−1−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−i321+i321+i321+i321+i321+i321+i321+i321+i321−i321−i321−i321−i321−i321−i321−i321−i32-1-1-1-1-1-111111+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32-1-111
χ11111111111-1-1-1-11111111-1-1-1-1-1-1-1-1−1+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−i321111-1-1-1-11111−1+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−i321−i321−i321−i321−i321+i321+i321+i321+i321−i321−i321−i321−i321−i321−i321−i321−i321+i321+i321+i321+i321+i321+i321+i321+i32-1-1-1-1-1-11111−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i3211-1-1
χ12111111111-1-1-1-11111111-1-1-1-1-1-1-1-1−1+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−i32-1-1-1-111111111−1+i32−1−i32−1+i32−1+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+i321−i321−i321−i321−i321−i321−i321−i321−i321+i321+i321+i321+i321+i321+i321+i321+i32-1-1-1-1-1-111111−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32-1-111
χ13111-1-11-1-1111-1-111-1-1-1-111111-1-1-1-11111-1-111-1-111-1-1-1-1ii−i−iii−i−i11-1-11111-1-1-1-111-1-1-1-11111-1-111-1-11111-1-1-1-11111-1-1-1-11-111-1-111-1-1ii−i−iii−i−iii−i−iii−i−ii−ii−i
χ14111-1-11-1-1111-1-111-1-1-1-111111-1-1-1-11111-1-111-1-111-1-1-1-1−i−iii−i−iii11-1-11111-1-1-1-111-1-1-1-11111-1-111-1-11111-1-1-1-11111-1-1-1-11-111-1-111-1-1−i−iii−i−iii−i−iii−i−iii−ii−ii
χ15111-1-11-1-1111-1-111-1-1-1-111111-1-1-1-1−1−i32−1+i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32−1−i32−1+i321+i321+i321−i321−i32ii−i−iii−i−i11-1-1−1−i32−1+i32−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i321−i321−i321−i321−i32−1−i32−1+i32−1−i32−1−i321+i321+i32−1+i32−1+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−i321-111-1-111-1-1ζ11ζ11−ζ11−ζ11ζ11ζ11−ζ11−ζ11ζ7ζ7−ζ7−ζ7ζ7ζ7−ζ7−ζ7i−ii−i
χ16111-1-11-1-1111-1-111-1-1-1-111111-1-1-1-1−1−i32−1+i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32−1−i32−1+i321+i321+i321−i321−i32−i−iii−i−iii11-1-1−1−i32−1+i32−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i321−i321−i321−i321−i32−1−i32−1+i32−1−i32−1−i321+i321+i32−1+i32−1+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−i321-111-1-111-1-1−ζ11−ζ11ζ11ζ11−ζ11−ζ11ζ11ζ11−ζ7−ζ7ζ7ζ7−ζ7−ζ7ζ7ζ7−ii−ii
χ17111-1-11-1-1111-1-111-1-1-1-111111-1-1-1-1−1+i32−1−i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32−1+i32−1−i321−i321−i321+i321+i32ii−i−iii−i−i11-1-1−1+i32−1−i32−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i321+i321+i321+i321+i32−1+i32−1−i32−1+i32−1+i321−i321−i32−1−i32−1−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+i321-111-1-111-1-1ζ7ζ7−ζ7−ζ7ζ7ζ7−ζ7−ζ7ζ11ζ11−ζ11−ζ11ζ11ζ11−ζ11−ζ11i−ii−i
χ18111-1-11-1-1111-1-111-1-1-1-111111-1-1-1-1−1+i32−1−i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32−1+i32−1−i321−i321−i321+i321+i32−i−iii−i−iii11-1-1−1+i32−1−i32−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i321+i321+i321+i321+i32−1+i32−1−i32−1+i32−1+i321−i321−i32−1−i32−1−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+i321-111-1-111-1-1−ζ7−ζ7ζ7ζ7−ζ7−ζ7ζ7ζ7−ζ11−ζ11ζ11ζ11−ζ11−ζ11ζ11ζ11−ii−ii
χ19111-1-11-1-11-1-11111-1-1-1-11-1-1-1-111111111-1-111-1-111-1-1-1-1ii−i−i−i−iii11-1-11111-1-1-1-111-1-1-1-111-1-111-1-111-1-1-1-11111-1-1-1-11111-11-1-11111-1-1ii−i−i−i−iiiii−i−i−i−iiii−i−ii
χ20111-1-11-1-11-1-11111-1-1-1-11-1-1-1-111111111-1-111-1-111-1-1-1-1−i−iiiii−i−i11-1-11111-1-1-1-111-1-1-1-111-1-111-1-111-1-1-1-11111-1-1-1-11111-11-1-11111-1-1−i−iiiii−i−i−i−iiiii−i−i−iii−i
χ21111-1-11-1-11-1-11111-1-1-1-11-1-1-1-11111−1−i32−1+i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32−1−i32−1+i321+i321+i321−i321−i32ii−i−i−i−iii11-1-1−1−i32−1+i32−1−i32−1−i321+i321+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+i321+i321+i32−1−i32−1−i32−1−i32−1−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32-11-1-11111-1-1ζ11ζ11−ζ11−ζ11−ζ11−ζ11ζ11ζ11ζ7ζ7−ζ7−ζ7−ζ7−ζ7ζ7ζ7i−i−ii
χ22111-1-11-1-11-1-11111-1-1-1-11-1-1-1-11111−1−i32−1+i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32−1−i32−1+i321+i321+i321−i321−i32−i−iiiii−i−i11-1-1−1−i32−1+i32−1−i32−1−i321+i321+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+i321+i321+i32−1−i32−1−i32−1−i32−1−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32-11-1-11111-1-1−ζ11−ζ11ζ11ζ11ζ11ζ11−ζ11−ζ11−ζ7−ζ7ζ7ζ7ζ7ζ7−ζ7−ζ7−iii−i
χ23111-1-11-1-11-1-11111-1-1-1-11-1-1-1-11111−1+i32−1−i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32−1+i32−1−i321−i321−i321+i321+i32ii−i−i−i−iii11-1-1−1+i32−1−i32−1+i32−1+i321−i321−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−i321−i321−i32−1+i32−1+i32−1+i32−1+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32-11-1-11111-1-1ζ7ζ7−ζ7−ζ7−ζ7−ζ7ζ7ζ7ζ11ζ11−ζ11−ζ11−ζ11−ζ11ζ11ζ11i−i−ii
χ24111-1-11-1-11-1-11111-1-1-1-11-1-1-1-11111−1+i32−1−i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32−1+i32−1−i321−i321−i321+i321+i32−i−iiiii−i−i11-1-1−1+i32−1−i32−1+i32−1+i321−i321−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−i321−i321−i32−1+i32−1+i32−1+i32−1+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32-11-1-11111-1-1−ζ7−ζ7ζ7ζ7ζ7ζ7−ζ7−ζ7−ζ11−ζ11ζ11ζ11ζ11ζ11−ζ11−ζ11−iii−i
χ2522222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-12222222222222222000000002222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-122-1-1-1-1-1-1-1-100000000000000000000
χ2622222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−1−i3−1+i3−1−i3−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3−1+i3−1−i3−1+i3−1−i3−1−i3−1+i3−1+i30000000022221+i321−i321+i321+i321+i321+i321+i321+i321−i321−i321−i321−i321−i321−i321+i321−i32−1−i3−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3−1+i31+i321+i321+i321+i321+i321+i321+i321+i321−i321−i321−i321−i321−i321−i321−i321−i3222-1-1-1-1-1-1-1-100000000000000000000
χ2722222222-12222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1−1+i3−1−i3−1+i3−1+i3−1+i3−1+i3−1−i3−1−i3−1−i3−1−i3−1+i3−1−i3−1+i3−1+i3−1−i3−1−i30000000022221−i321+i321−i321−i321−i321−i321−i321−i321+i321+i321+i321+i321+i321+i321−i321+i32−1+i3−1+i3−1+i3−1+i3−1−i3−1−i3−1−i3−1−i31−i321−i321−i321−i321−i321−i321−i321−i321+i321+i321+i321+i321+i321+i321+i321+i3222-1-1-1-1-1-1-1-100000000000000000000
χ2822222222-1-2-2-2-2-1-1-1-1-1-1-1111111112222222222222222000000002222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-2-2-2-2-2-2-2-21111111111111111-2-21111-1-1-1-100000000000000000000
χ2922222222-1-2-2-2-2-1-1-1-1-1-1-111111111−1−i3−1+i3−1−i3−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3−1+i3−1−i3−1+i3−1−i3−1−i3−1+i3−1+i30000000022221+i321−i321+i321+i321+i321+i321+i321+i321−i321−i321−i321−i321−i321−i321+i321−i321+i31+i31+i31+i31−i31−i31−i31−i3−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32-2-21111-1-1-1-100000000000000000000
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χ34222-2-22-2-2-1-2-222-1-11111-11111-1-1-1-12222-2-222-2-222-2-2-2-20000000022-2-2-1-1-1-11111-1-11111-1-1-2-222-2-2221111-1-1-1-11111-1-1-1-1-2211-1-1-1-11100000000000000000000
χ35222-2-22-2-2-1-2-222-1-11111-11111-1-1-1-1−1−i3−1+i3−1−i3−1−i31+i31+i3−1+i3−1+i31−i31−i3−1−i3−1+i31+i31+i31−i31−i30000000022-2-21+i321−i321+i321+i32−1−i32−1−i32−1−i32−1−i321−i321−i32−1+i32−1+i32−1+i32−1+i321+i321−i321+i31+i3−1−i3−1−i31−i31−i3−1+i3−1+i3−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32-2211-1-1-1-11100000000000000000000
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χ1114-44-4-4-444-200002-22-2-22223−23−2323−232323−23-2-2-22-2-2-22-2-2222222000000000000111-11-1-111-11-1-11-1-1000000003−3−33−333−33−3−33−333−3000000000000000000000000000000
χ1124-44-4-4-444-200002-22-2-22223−23−2323−232323−231+i31−i31+i3−1−i31+i31+i31−i3−1+i31−i31−i3−1−i3−1+i3−1−i3−1−i3−1+i3−1+i3000000000000−1−i32−1+i32−1−i321+i32−1−i321+i321+i32−1−i32−1+i321−i32−1+i321−i321−i32−1+i321+i321−i32000000002ζ7+ζ11−2ζ7−ζ11−2ζ7−ζ112ζ7+ζ11−2ζ7−ζ112ζ7+ζ112ζ7+ζ11−2ζ7−ζ11−ζ7−2ζ11ζ7+2ζ11ζ7+2ζ11−ζ7−2ζ11ζ7+2ζ11−ζ7−2ζ11−ζ7−2ζ11ζ7+2ζ11000000000000000000000000000000
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χ1216-6-66-66-6660000-6-66-66-6600000000000000000000000000000000-22-220000000000000000000000000000000000000000000000-22-2200000000000000000000
χ1226-6-66-66-66-3000033-33-33-3−3i33i3−3i33i3−3i33i3−3i33i3000000000000000000000000-22-22000000000000000000000000000000000000000000i3−i3i3−i31-11-100000000000000000000
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χ1246-6-6-6666-660000-6-6-66-66600000000000000000000000000000000-222-20000000000000000000000000000000000000000000000-222-200000000000000000000
χ1256-6-6-6666-6-30000333-33-3-3−3i33i3−3i33i33i3−3i33i3−3i3000000000000000000000000-222-2000000000000000000000000000000000000000000i3−i3−i3i31-1-1100000000000000000000
χ1266-6-6-6666-6-30000333-33-3-33i3−3i33i3−3i3−3i33i3−3i33i3000000000000000000000000-222-2000000000000000000000000000000000000000000−i3i3i3−i31-1-1100000000000000000000

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