Finite Group Databasebeta

← Group #10628857

Character table — Group #10628857

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102C103C104C105C106C107C108C109C110C111
size111111111111222222222222222222222222444444444888888888888888888888888888888888888888888888888161616161616161616161616161616161616
order1222336666662244444466661212121212121212121212124441212121212124444444488888888121212121212121212121212121212122424242424242424242424242424242422446666881212121224242424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111111111111111111-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111111111
χ5111111111111111111111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111
χ6111111111111111111111111111111111111111111111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1-1-11111-1-1-1-1
χ7111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-11111-1-1-1-1
χ8111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1111111-1-1-1-11111
χ91111−1−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+i32111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321111111111111111−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−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+i3211−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32
χ101111−1−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+i32111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i3211111111-1-1-1-1-1-1-1-1−1−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+i321+i321+i321+i321+i321−i321−i321−i321−i321+i321+i321+i321+i321−i321−i321−i321−i3211-1-1−1−i32−1−i32−1+i32−1+i32-1-11+i321−i321+i321−i321+i321+i321−i321−i32
χ111111−1−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+i32111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321111-1-1-1-111111111−1−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−i32−1−i32−1−i32−1+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−i32-1-11+i321−i321+i321−i321+i321+i321−i321−i32
χ121111−1−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+i32111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i321111-1-1-1-1-1-1-1-1-1-1-1-1−1−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+i321−i321−i321−i321−i321+i321+i321+i321+i321−i321−i321−i321−i32-1-1111+i321+i321−i321−i3211−1−i32−1+i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32
χ131111−1−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+i32111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-1-1-111111111-1-1-1-11+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−i32−1+i32−1+i32−1+i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i32-1-1-1-11+i321+i321−i321−i32111+i321−i321+i321−i32−1−i32−1−i32−1+i32−1+i32
χ141111−1−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+i32111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-1-1-11111-1-1-1-111111+i321+i321−i321−i321+i321+i321−i321−i32−1−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−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32-1-1111+i321+i321−i321−i32-1-1−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32
χ151111−1−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+i32111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-1-1-1-1-1-1-11111-1-1-1-11+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+i321+i321+i321+i321+i321−i321−i321−i321−i321111−1−i32−1−i32−1+i32−1+i32-1-1−1−i32−1+i32−1−i32−1+i321+i321+i321−i321−i32
χ161111−1−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+i32111−1−i32−1+i32−1−i32−1+i32−1−i32−1+i32-1-1-1-1-1-1-1-1-1-1-1-111111+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−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i3211-1-1−1−i32−1−i32−1+i32−1+i32111+i321−i321+i321−i32−1−i32−1−i32−1+i32−1+i32
χ171111−1+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−i32111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321111111111111111−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+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−i3211−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32
χ181111−1+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−i32111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i3211111111-1-1-1-1-1-1-1-1−1+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−i321−i321−i321−i321−i321+i321+i321+i321+i321−i321−i321−i321−i321+i321+i321+i321+i3211-1-1−1+i32−1+i32−1−i32−1−i32-1-11−i321+i321−i321+i321−i321−i321+i321+i32
χ191111−1+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−i32111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321111-1-1-1-111111111−1+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+i32−1+i32−1+i32−1−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+i32-1-11−i321+i321−i321+i321−i321−i321+i321+i32
χ201111−1+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−i32111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i321111-1-1-1-1-1-1-1-1-1-1-1-1−1+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−i321+i321+i321+i321+i321−i321−i321−i321−i321+i321+i321+i321+i32-1-1111−i321−i321+i321+i3211−1+i32−1−i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32
χ211111−1+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−i32111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-1-1-111111111-1-1-1-11−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+i32−1−i32−1−i32−1−i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i32-1-1-1-11−i321−i321+i321+i32111−i321+i321−i321+i32−1+i32−1+i32−1−i32−1−i32
χ221111−1+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−i32111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-1-1-11111-1-1-1-111111−i321−i321+i321+i321−i321−i321+i321+i32−1+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+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32-1-1111−i321−i321+i321+i32-1-1−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32
χ231111−1+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−i32111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-1-1-1-1-1-1-11111-1-1-1-11−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−i321−i321−i321−i321−i321+i321+i321+i321+i321111−1+i32−1+i32−1−i32−1−i32-1-1−1+i32−1−i32−1+i32−1−i321−i321−i321+i321+i32
χ241111−1+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−i32111−1+i32−1−i32−1+i32−1−i32−1+i32−1−i32-1-1-1-1-1-1-1-1-1-1-1-111111−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+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i3211-1-1−1+i32−1+i32−1−i32−1−i32111−i321+i321−i321+i32−1+i32−1+i32−1−i32−1−i32
χ2522222222222222222-2-222222222222-2-2-2-222-2-2-2-2-2-2-2-2-222-2-20000000000002222-2-2-2-2000000000000000000000000000000000000000000
χ2622222222222222222-2-222222222222-2-2-2-222-2-2-2-2-2-2-2-2-2-2-222000000000000-2-2-2-22222000000000000000000000000000000000000000000
χ2722222222222222-2-2-222-22222-2-2-2-2-2-22222-2-22-2-222-2-2-2-20000000000000000000000000000000000000000000000002-2002-22-20000000000
χ2822222222222222-2-2-222-22222-2-2-2-2-2-22222-2-22-2-222-2-2-2-2000000000000000000000000000000000000000000000000-2200-22-220000000000
χ2922222222222222-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-2-222-2-22222000022-2-2000000000000000022-2-222-2-20000000000000000000000000000000000
χ3022222222222222-2-2-2-2-2-22222-2-2-2-2-2-2-2-2-2-2-2-2-222-2-222220000-2-2220000000000000000-2-222-2-2220000000000000000000000000000000000
χ31222222222222-2-222-222-2-2-2-2-222-222-22222-2-2-2-22-2-2-2-2220000000022-2-20000000000000000000022-2-222-2-200000000000000000000000000
χ32222222222222-2-222-222-2-2-2-2-222-222-22222-2-2-2-22-2-2-2-22200000000-2-22200000000000000000000-2-222-2-22200000000000000000000000000
χ33222222222222-2-222-2-2-2-2-2-2-2-222-222-2-2-2-2-2-2-222-22222-2-20000000000002i2i−2i−2i0000000000000000000000002i2i−2i−2i2i2i−2i−2i000000000000000000
χ34222222222222-2-222-2-2-2-2-2-2-2-222-222-2-2-2-2-2-2-222-22222-2-2000000000000−2i−2i2i2i000000000000000000000000−2i−2i2i2i−2i−2i2i2i000000000000000000
χ35222222222222-2-2-2-22222-2-2-2-2-2-22-2-22222222-22-2-2-222-2-2000000000000000000000000000000000000000000000000002-200000022-2-20000
χ36222222222222-2-2-2-22222-2-2-2-2-2-22-2-22222222-22-2-2-222-2-200000000000000000000000000000000000000000000000000-22000000-2-2220000
χ37222222222222-2-2-2-22-2-22-2-2-2-2-2-22-2-22-2-2-2-2222-2222-2-222000000000000000000000000000000000000000000000000000000002-200002-22-2
χ38222222222222-2-2-2-22-2-22-2-2-2-2-2-22-2-22-2-2-2-2222-2222-2-22200000000000000000000000000000000000000000000000000000000-220000-22-22
χ392222−1−i3−1+i3−1−i3−1−i3−1+i3−1+i3−1−i3−1+i322222-2-22−1−i3−1+i3−1−i3−1+i3−1−i3−1−i3−1−i3−1+i3−1+i3−1+i31+i31+i31−i31−i3−1−i3−1+i3-2-2-21+i31−i31+i31−i31+i31−i322-2-2000000000000−1−i3−1−i3−1+i3−1+i31+i31+i31−i31−i3000000000000000000000000000000000000000000
χ402222−1−i3−1+i3−1−i3−1−i3−1+i3−1+i3−1−i3−1+i322222-2-22−1−i3−1+i3−1−i3−1+i3−1−i3−1−i3−1−i3−1+i3−1+i3−1+i31+i31+i31−i31−i3−1−i3−1+i3-2-2-21+i31−i31+i31−i31+i31−i3-2-2220000000000001+i31+i31−i31−i3−1−i3−1−i3−1+i3−1+i3000000000000000000000000000000000000000000
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Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.