Finite Group Databasebeta

← Group #11710917

Character table — Group #11710917

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size11111111111111113333333333333333666666666666666666666666666666661616161616161616161616161616161616161616161616161616161616161616
order1222222244444444222222224444444422222222222222224444444444444444336666666666666612121212121212121212121212121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111111111111111111111111−1−i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32
χ31111111111111111111111111111111111111111111111111111111111111111−1+i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32
χ411111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ511111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111−1−i32−1+i32−1−i32−1−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−i32
χ611111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111−1+i32−1−i32−1+i32−1+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+i32
χ7111-1-1-1-111111-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-1
χ8111-1-1-1-111111-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1−1−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−i32−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32
χ9111-1-1-1-111111-1-1-1-11111-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1−1+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+i32−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32
χ10111-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-11111
χ11111-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1−1−i32−1+i32−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i321−i321−i321−i321−i32−1−i32−1+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32
χ12111-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1−1+i32−1−i32−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i321+i321+i321+i321+i32−1+i32−1−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32
χ131-1-111-1-1111-1-111-1-111-1-111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-111-1-111-1-1-1-111-1-11111-1-111-1-111-1-111-1-1
χ141-1-111-1-1111-1-111-1-111-1-111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1−1−i32−1+i321+i321+i32−1−i32−1−i321+i321+i321−i321−i32−1+i32−1+i321−i321−i32−1−i32−1+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32
χ151-1-111-1-1111-1-111-1-111-1-111-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-11111-1-1-1-1−1+i32−1−i321−i321−i32−1+i32−1+i321−i321−i321+i321+i32−1−i32−1−i321+i321+i32−1+i32−1−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32
χ161-1-111-1-11-1-111-1-11111-1-111-1-1-1-111-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-111-1-111-1-1-1-111-1-111-1-111-1-111-1-111-1-111
χ171-1-111-1-11-1-111-1-11111-1-111-1-1-1-111-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1−1−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−i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i32
χ181-1-111-1-11-1-111-1-11111-1-111-1-1-1-111-1-111-1-1-1-11111-1-1-1-111111111-1-1-1-11111-1-1-1-1−1+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+i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32
χ191-1-1-1-111111-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-111
χ201-1-1-1-111111-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111−1−i32−1+i321+i321+i321+i321+i32−1−i32−1−i321−i321−i321−i321−i32−1+i32−1+i32−1−i32−1+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
χ211-1-1-1-111111-1-1-1-11111-1-1-1-11111-1-1-1-1111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111−1+i32−1−i321−i321−i321−i321−i32−1+i32−1+i321+i321+i321+i321+i32−1−i32−1−i32−1+i32−1−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
χ221-1-1-1-1111-1-11111-1-111-1-1-1-111-1-11111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-11111-1-11111-1-1-1-11111-1-1
χ231-1-1-1-1111-1-11111-1-111-1-1-1-111-1-11111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111−1−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−i32−1−i32−1−i321+i321+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32
χ241-1-1-1-1111-1-11111-1-111-1-1-1-111-1-11111-1-1-1-1-1-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111−1+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+i32−1+i32−1+i321−i321−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32
χ2522-22-22-2-22i−2i2i−2i2i−2i2i−2i2-22-22-22-22i−2i2i−2i2i−2i2i−2i00000000000000000000000000000000-1-11-11-11-11-11-11-111i−ii−ii−ii−ii−ii−ii−ii−i
χ2622-22-22-2-22i−2i2i−2i2i−2i2i−2i2-22-22-22-22i−2i2i−2i2i−2i2i−2i000000000000000000000000000000001+i321−i32−1−i321+i32−1−i321+i32−1−i321+i32−1+i321−i32−1+i321−i32−1+i321−i32−1−i32−1+i32ζ11−ζ11ζ11−ζ11ζ11−ζ11ζ11−ζ11ζ7−ζ7ζ7−ζ7ζ7−ζ7ζ7−ζ7
χ2722-22-22-2-22i−2i2i−2i2i−2i2i−2i2-22-22-22-22i−2i2i−2i2i−2i2i−2i000000000000000000000000000000001−i321+i32−1+i321−i32−1+i321−i32−1+i321−i32−1−i321+i32−1−i321+i32−1−i321+i32−1+i32−1−i32ζ7−ζ7ζ7−ζ7ζ7−ζ7ζ7−ζ7ζ11−ζ11ζ11−ζ11ζ11−ζ11ζ11−ζ11
χ2822-22-22-2-2−2i2i−2i2i−2i2i−2i2i2-22-22-22-2−2i2i−2i2i−2i2i−2i2i00000000000000000000000000000000-1-11-11-11-11-11-11-111−ii−ii−ii−ii−ii−ii−ii−ii
χ2922-22-22-2-2−2i2i−2i2i−2i2i−2i2i2-22-22-22-2−2i2i−2i2i−2i2i−2i2i000000000000000000000000000000001+i321−i32−1−i321+i32−1−i321+i32−1−i321+i32−1+i321−i32−1+i321−i32−1+i321−i32−1−i32−1+i32−ζ11ζ11−ζ11ζ11−ζ11ζ11−ζ11ζ11−ζ7ζ7−ζ7ζ7−ζ7ζ7−ζ7ζ7
χ3022-22-22-2-2−2i2i−2i2i−2i2i−2i2i2-22-22-22-2−2i2i−2i2i−2i2i−2i2i000000000000000000000000000000001−i321+i32−1+i321−i32−1+i321−i32−1+i321−i32−1−i321+i32−1−i321+i32−1−i321+i32−1+i32−1−i32−ζ7ζ7−ζ7ζ7−ζ7ζ7−ζ7ζ7−ζ11ζ11−ζ11ζ11−ζ11ζ11−ζ11ζ11
χ3122-2-22-22-22i−2i2i−2i−2i2i−2i2i2-22-2-22-222i−2i2i−2i−2i2i−2i2i00000000000000000000000000000000-1-11-1-11-111-1-11-1111i−ii−i−ii−iii−ii−i−ii−ii
χ3222-2-22-22-22i−2i2i−2i−2i2i−2i2i2-22-2-22-222i−2i2i−2i−2i2i−2i2i000000000000000000000000000000001+i321−i32−1−i321+i321+i32−1−i321+i32−1−i32−1+i321−i321−i32−1+i321−i32−1+i32−1−i32−1+i32ζ11−ζ11ζ11−ζ11−ζ11ζ11−ζ11ζ11ζ7−ζ7ζ7−ζ7−ζ7ζ7−ζ7ζ7
χ3322-2-22-22-22i−2i2i−2i−2i2i−2i2i2-22-2-22-222i−2i2i−2i−2i2i−2i2i000000000000000000000000000000001−i321+i32−1+i321−i321−i32−1+i321−i32−1+i32−1−i321+i321+i32−1−i321+i32−1−i32−1+i32−1−i32ζ7−ζ7ζ7−ζ7−ζ7ζ7−ζ7ζ7ζ11−ζ11ζ11−ζ11−ζ11ζ11−ζ11ζ11
χ3422-2-22-22-2−2i2i−2i2i2i−2i2i−2i2-22-2-22-22−2i2i−2i2i2i−2i2i−2i00000000000000000000000000000000-1-11-1-11-111-1-11-1111−ii−iii−ii−i−ii−iii−ii−i
χ3522-2-22-22-2−2i2i−2i2i2i−2i2i−2i2-22-2-22-22−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000001+i321−i32−1−i321+i321+i32−1−i321+i32−1−i32−1+i321−i321−i32−1+i321−i32−1+i32−1−i32−1+i32−ζ11ζ11−ζ11ζ11ζ11−ζ11ζ11−ζ11−ζ7ζ7−ζ7ζ7ζ7−ζ7ζ7−ζ7
χ3622-2-22-22-2−2i2i−2i2i2i−2i2i−2i2-22-2-22-22−2i2i−2i2i2i−2i2i−2i000000000000000000000000000000001−i321+i32−1+i321−i321−i32−1+i321−i32−1+i32−1−i321+i321+i32−1−i321+i32−1−i32−1+i32−1−i32−ζ7ζ7−ζ7ζ7ζ7−ζ7ζ7−ζ7−ζ11ζ11−ζ11ζ11ζ11−ζ11ζ11−ζ11
χ372-222-2-22-22i−2i−2i2i2i−2i−2i2i2-2-222-2-222i−2i−2i2i2i−2i−2i2i00000000000000000000000000000000-1-1-111-1-11-111-1-1111i−i−iii−i−iii−i−iii−i−ii
χ382-222-2-22-22i−2i−2i2i2i−2i−2i2i2-2-222-2-222i−2i−2i2i2i−2i−2i2i000000000000000000000000000000001+i321−i321+i32−1−i32−1−i321+i321+i32−1−i321−i32−1+i32−1+i321−i321−i32−1+i32−1−i32−1+i32ζ11−ζ11−ζ11ζ11ζ11−ζ11−ζ11ζ11ζ7−ζ7−ζ7ζ7ζ7−ζ7−ζ7ζ7
χ392-222-2-22-22i−2i−2i2i2i−2i−2i2i2-2-222-2-222i−2i−2i2i2i−2i−2i2i000000000000000000000000000000001−i321+i321−i32−1+i32−1+i321−i321−i32−1+i321+i32−1−i32−1−i321+i321+i32−1−i32−1+i32−1−i32ζ7−ζ7−ζ7ζ7ζ7−ζ7−ζ7ζ7ζ11−ζ11−ζ11ζ11ζ11−ζ11−ζ11ζ11
χ402-222-2-22-2−2i2i2i−2i−2i2i2i−2i2-2-222-2-22−2i2i2i−2i−2i2i2i−2i00000000000000000000000000000000-1-1-111-1-11-111-1-1111−iii−i−iii−i−iii−i−iii−i
χ412-222-2-22-2−2i2i2i−2i−2i2i2i−2i2-2-222-2-22−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000001+i321−i321+i32−1−i32−1−i321+i321+i32−1−i321−i32−1+i32−1+i321−i321−i32−1+i32−1−i32−1+i32−ζ11ζ11ζ11−ζ11−ζ11ζ11ζ11−ζ11−ζ7ζ7ζ7−ζ7−ζ7ζ7ζ7−ζ7
χ422-222-2-22-2−2i2i2i−2i−2i2i2i−2i2-2-222-2-22−2i2i2i−2i−2i2i2i−2i000000000000000000000000000000001−i321+i321−i32−1+i32−1+i321−i321−i32−1+i321+i32−1−i32−1−i321+i321+i32−1−i32−1+i32−1−i32−ζ7ζ7ζ7−ζ7−ζ7ζ7ζ7−ζ7−ζ11ζ11ζ11−ζ11−ζ11ζ11ζ11−ζ11
χ432-22-222-2-22i−2i−2i2i−2i2i2i−2i2-2-22-222-22i−2i−2i2i−2i2i2i−2i00000000000000000000000000000000-1-1-11-111-1-11-111-111i−i−ii−iii−ii−i−ii−iii−i
χ442-22-222-2-22i−2i−2i2i−2i2i2i−2i2-2-22-222-22i−2i−2i2i−2i2i2i−2i000000000000000000000000000000001+i321−i321+i32−1−i321+i32−1−i32−1−i321+i321−i32−1+i321−i32−1+i32−1+i321−i32−1−i32−1+i32ζ11−ζ11−ζ11ζ11−ζ11ζ11ζ11−ζ11ζ7−ζ7−ζ7ζ7−ζ7ζ7ζ7−ζ7
χ452-22-222-2-22i−2i−2i2i−2i2i2i−2i2-2-22-222-22i−2i−2i2i−2i2i2i−2i000000000000000000000000000000001−i321+i321−i32−1+i321−i32−1+i32−1+i321−i321+i32−1−i321+i32−1−i32−1−i321+i32−1+i32−1−i32ζ7−ζ7−ζ7ζ7−ζ7ζ7ζ7−ζ7ζ11−ζ11−ζ11ζ11−ζ11ζ11ζ11−ζ11
χ462-22-222-2-2−2i2i2i−2i2i−2i−2i2i2-2-22-222-2−2i2i2i−2i2i−2i−2i2i00000000000000000000000000000000-1-1-11-111-1-11-111-111−iii−ii−i−ii−iii−ii−i−ii
χ472-22-222-2-2−2i2i2i−2i2i−2i−2i2i2-2-22-222-2−2i2i2i−2i2i−2i−2i2i000000000000000000000000000000001+i321−i321+i32−1−i321+i32−1−i32−1−i321+i321−i32−1+i321−i32−1+i32−1+i321−i32−1−i32−1+i32−ζ11ζ11ζ11−ζ11ζ11−ζ11−ζ11ζ11−ζ7ζ7ζ7−ζ7ζ7−ζ7−ζ7ζ7
χ482-22-222-2-2−2i2i2i−2i2i−2i−2i2i2-2-22-222-2−2i2i2i−2i2i−2i−2i2i000000000000000000000000000000001−i321+i321−i32−1+i321−i32−1+i32−1+i321−i321+i32−1−i321+i32−1−i32−1−i321+i32−1+i32−1−i32−ζ7ζ7ζ7−ζ7ζ7−ζ7−ζ7ζ7−ζ11ζ11ζ11−ζ11ζ11−ζ11−ζ11ζ11
χ4933333333333333333333333333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-100000000000000000000000000000000
χ503333333333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-13-1-1-13-1-1-13-1-1-13-1-1-13-1-1-13-1-1-13-1-1-13-1-1-100000000000000000000000000000000
χ513333333333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-13-1-1-13-1-1-13-1-1-13-1-1-13-1-1-13-1-1-13-1-1-13-1-100000000000000000000000000000000
χ523333333333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-13-1-1-13-1-1-13-1-1-13-1-1-13-1-1-13-1-1-13-1-1-13-100000000000000000000000000000000
χ533333333333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-13-1-1-13-1-1-13-1-1-13-1-1-13-1-1-13-1-1-13-1-1-1300000000000000000000000000000000
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χ8966-66-66-6-66i−6i6i−6i6i−6i6i−6i-22-22-22-22−2i2i−2i2i−2i2i−2i2i0000000000000000000000000000000000000000000000000000000000000000
χ9066-66-66-6-6−6i6i−6i6i−6i6i−6i6i-22-22-22-222i−2i2i−2i2i−2i2i−2i0000000000000000000000000000000000000000000000000000000000000000
χ9166-6-66-66-66i−6i6i−6i−6i6i−6i6i-22-222-22-2−2i2i−2i2i2i−2i2i−2i0000000000000000000000000000000000000000000000000000000000000000
χ9266-6-66-66-6−6i6i−6i6i6i−6i6i−6i-22-222-22-22i−2i2i−2i−2i2i−2i2i0000000000000000000000000000000000000000000000000000000000000000
χ936-666-6-66-66i−6i−6i6i6i−6i−6i6i-222-2-222-2−2i2i2i−2i−2i2i2i−2i0000000000000000000000000000000000000000000000000000000000000000
χ946-666-6-66-6−6i6i6i−6i−6i6i6i−6i-222-2-222-22i−2i−2i2i2i−2i−2i2i0000000000000000000000000000000000000000000000000000000000000000
χ956-66-666-6-66i−6i−6i6i−6i6i6i−6i-222-22-2-22−2i2i2i−2i2i−2i−2i2i0000000000000000000000000000000000000000000000000000000000000000
χ966-66-666-6-6−6i6i6i−6i6i−6i−6i6i-222-22-2-222i−2i−2i2i−2i2i2i−2i0000000000000000000000000000000000000000000000000000000000000000

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