Finite Group Databasebeta

← Group #11721396

Character table — Group #11721396

Order 864.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106
size1111222222222222222222222233333333666666666666666666666666666666666666666666666666666666666666363636363636363636363636
order1222344444466612121212121212121212121233666666999121212121212121212121212181818181818181818363636363636363636363636363636363636363636363636363636363636363636363636244466121212121212
χ11111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321−1−i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32111−1−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+i321111−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32
χ411111111111111111111111111−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321−1−i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32111−1−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+i32-1-1-1-11+i321−i321+i321+i321+i321−i321−i321−i32
χ511111111111111111111111111−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−1+i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32111−1+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−i321111−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32
χ611111111111111111111111111−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−1+i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32111−1+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−i32-1-1-1-11−i321+i321−i321−i321−i321+i321+i321+i32
χ71111111-1-1-1-11111111-1-1-1-1-1-1-1-11111111111111-1-1-1-111-1-1-1-11111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111-1-1111-1-11-1-1
χ81111111-1-1-1-11111111-1-1-1-1-1-1-1-11111111111111-1-1-1-111-1-1-1-11111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-111-111
χ91111111-1-1-1-11111111-1-1-1-1-1-1-1-1−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321−1−i32−1+i32−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i321−i321−i321−i321−i32111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321111-1-1-1-1-1-1-1-1−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i321+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i321−i321−i3211-1-1−1−i32−1+i32−1−i321+i321+i32−1+i321−i321−i32
χ101111111-1-1-1-11111111-1-1-1-1-1-1-1-1−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321−1−i32−1+i32−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i321−i321−i321−i321−i32111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321111-1-1-1-1-1-1-1-1−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i321+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i321−i321−i32-1-1111+i321−i321+i32−1−i32−1−i321−i32−1+i32−1+i32
χ111111111-1-1-1-11111111-1-1-1-1-1-1-1-1−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−1+i32−1−i32−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i321+i321+i321+i321+i32111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321111-1-1-1-1-1-1-1-1−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i321−i321−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i321+i3211-1-1−1+i32−1−i32−1+i321−i321−i32−1−i321+i321+i32
χ121111111-1-1-1-11111111-1-1-1-1-1-1-1-1−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−1+i32−1−i32−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i321+i321+i321+i321+i32111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321111-1-1-1-1-1-1-1-1−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i321−i321−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i321+i32-1-1111−i321+i321−i32−1+i32−1+i321+i32−1−i32−1−i32
χ1311111-1-111-1-1111-1-1-1-11111-1-1-1-111111111111-1-111-1-1-1-111-1-1111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-11-11-111-11-1-11-1
χ1411111-1-111-1-1111-1-1-1-11111-1-1-1-111111111111-1-111-1-1-1-111-1-1111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-11-11-1-11-111-11
χ1511111-1-111-1-1111-1-1-1-11111-1-1-1-1−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321−1−i32−1+i321+i321+i32−1−i32−1−i321+i321+i321−i321−i32−1+i32−1+i321−i321−i32111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-1-1-1-11111-1-1-1-11+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+i321−i321−i321−i321−i321-11-1−1−i32−1+i321+i32−1−i321+i321−i32−1+i321−i32
χ1611111-1-111-1-1111-1-1-1-11111-1-1-1-1−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321−1−i32−1+i321+i321+i32−1−i32−1−i321+i321+i321−i321−i32−1+i32−1+i321−i321−i32111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-1-1-1-11111-1-1-1-11+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+i321−i321−i321−i321−i32-11-111+i321−i32−1−i321+i32−1−i32−1+i321−i32−1+i32
χ1711111-1-111-1-1111-1-1-1-11111-1-1-1-1−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−1+i32−1−i321−i321−i32−1+i32−1+i321−i321−i321+i321+i32−1−i32−1−i321+i321+i32111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-1-1-1-11111-1-1-1-11−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−i321+i321+i321+i321+i321-11-1−1+i32−1−i321−i32−1+i321−i321+i32−1−i321+i32
χ1811111-1-111-1-1111-1-1-1-11111-1-1-1-1−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−1+i32−1−i321−i321−i32−1+i32−1+i321−i321−i321+i321+i32−1−i32−1−i321+i321+i32111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-1-1-1-11111-1-1-1-11−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−i321+i321+i321+i321+i32-11-111−i321+i32−1+i321−i32−1+i32−1−i321+i32−1−i32
χ1911111-1-1-1-111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-111-1-1-1-111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111-1-1111-1-11-1-11
χ2011111-1-1-1-111111-1-1-1-1-1-1-1-1111111111111111-1-1-1-111-1-1-1-111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-111-1-1-111-111-1
χ2111111-1-1-1-111111-1-1-1-1-1-1-1-11111−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321−1−i32−1+i321+i321+i321+i321+i32−1−i32−1−i321−i321−i321−i321−i32−1+i32−1+i32111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-1-1-1-1-1-1-1-111111+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+i321-1-11−1−i32−1+i321+i321+i32−1−i321−i321−i32−1+i32
χ2211111-1-1-1-111111-1-1-1-1-1-1-1-11111−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321−1−i32−1+i321+i321+i321+i321+i32−1−i32−1−i321−i321−i321−i321−i32−1+i32−1+i32111−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32-1-1-1-1-1-1-1-111111+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+i32-111-11+i321−i32−1−i32−1−i321+i32−1+i32−1+i321−i32
χ2311111-1-1-1-111111-1-1-1-1-1-1-1-11111−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−1+i32−1−i321−i321−i321−i321−i32−1+i32−1+i321+i321+i321+i321+i32−1−i32−1−i32111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-1-1-1-1-1-1-1-111111−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−i321-1-11−1+i32−1−i321−i321−i32−1+i321+i321+i32−1−i32
χ2411111-1-1-1-111111-1-1-1-1-1-1-1-11111−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321−1+i32−1−i321−i321−i321−i321−i32−1+i32−1+i321+i321+i321+i321+i32−1−i32−1−i32111−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32-1-1-1-1-1-1-1-111111−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−i32-111-11−i321+i32−1+i32−1+i321−i32−1−i32−1−i321+i32
χ252222222222222222222222222222222222-1-1-1222222222222-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000
χ2622222222222222222222222222−1−i3−1+i3−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3-11+i321−i32−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3-1-1-11+i321+i321+i321−i321−i321−i32-1-1-1-1-1-1-1-1-1-1-1-11+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i32000000000000
χ2722222222222222222222222222−1+i3−1−i3−1+i3−1+i3−1+i3−1−i3−1−i3−1−i3-11−i321+i32−1+i3−1+i3−1+i3−1+i3−1+i3−1+i3−1−i3−1−i3−1−i3−1−i3−1−i3−1−i3-1-1-11−i321−i321−i321+i321+i321+i32-1-1-1-1-1-1-1-1-1-1-1-11−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i32000000000000
χ282222222-2-2-2-22222222-2-2-2-2-2-2-2-222222222-1-1-122-2-2-2-222-2-2-2-2-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-111111111000000000000
χ292222222-2-2-2-22222222-2-2-2-2-2-2-2-2−1−i3−1+i3−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3-11+i321−i32−1−i3−1−i31+i31+i31+i31+i3−1+i3−1+i31−i31−i31−i31−i3-1-1-11+i321+i321+i321−i321−i321−i32-1-1-1-1111111111+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32000000000000
χ302222222-2-2-2-22222222-2-2-2-2-2-2-2-2−1+i3−1−i3−1+i3−1+i3−1+i3−1−i3−1−i3−1−i3-11−i321+i32−1+i3−1+i31−i31−i31−i31−i3−1−i3−1−i31+i31+i31+i31+i3-1-1-11−i321−i321−i321+i321+i321+i32-1-1-1-1111111111−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32000000000000
χ3122222-2-222-2-2222-2-2-2-22222-2-2-2-222222222-1-1-1-2-222-2-2-2-222-2-2-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-111111111-1-1-1-11111000000000000
χ3222222-2-222-2-2222-2-2-2-22222-2-2-2-2−1−i3−1+i3−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3-11+i321−i321+i31+i3−1−i3−1−i31+i31+i31−i31−i3−1+i3−1+i31−i31−i3-1-1-11+i321+i321+i321−i321−i321−i321111-1-1-1-11111−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32000000000000
χ3322222-2-222-2-2222-2-2-2-22222-2-2-2-2−1+i3−1−i3−1+i3−1+i3−1+i3−1−i3−1−i3−1−i3-11−i321+i321−i31−i3−1+i3−1+i31−i31−i31+i31+i3−1−i3−1−i31+i31+i3-1-1-11−i321−i321−i321+i321+i321+i321111-1-1-1-11111−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32000000000000
χ3422222-2-2-2-222222-2-2-2-2-2-2-2-2222222222222-1-1-1-2-2-2-222-2-2-2-222-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-111111111-1-1-1-1000000000000
χ3522222-2-2-2-222222-2-2-2-2-2-2-2-22222−1−i3−1+i3−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3-11+i321−i321+i31+i31+i31+i3−1−i3−1−i31−i31−i31−i31−i3−1+i3−1+i3-1-1-11+i321+i321+i321−i321−i321−i3211111111-1-1-1-1−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32000000000000
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Here ζ is a primitive root of unity of order 12 (ζ12 = 1); i = ζ3.