Finite Group Databasebeta

← Group #10631923

Character table — Group #10631923

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111111111111222222222222222222444444444444888888888888888888888888888888888888161616161616161616161616161616161616161616161616
order12223366666622444466661212121212121212888824242424242424242466881212161616161616161624242424484848484848484848484848484848482224444466666612121212121212121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111-1-1-1-1-1-1-1-11111
χ411111111111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-1
χ5111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1111-1-11-1-1111111-1-1-1-111-1-1-1-1
χ6111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-111-111-1-1-1-1-1-11111-1-11111
χ7111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111-111-1-1-11111-1-11111-1-1-1-1-1-1
χ8111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-11-1-1111-1-1-1-111-1-1-1-1111111
χ91111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32111111−1−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+i3211−1−i32−1+i3211−1−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+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
χ101111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32111111−1−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+i3211−1−i32−1+i3211−1−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+i32-1-1-1-1-1-1-1-11+i321+i321−i321−i321+i321−i321+i321+i321−i321−i321+i321−i321+i321+i321−i321−i32
χ111111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32111111−1−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+i3211−1−i32−1+i3211−1−i32−1+i32-1-1-1-1-1-1-1-1−1−i32−1−i32−1+i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i321+i321+i321+i321+i321−i321−i321−i321−i3211-1-1-1-111−1−i32−1−i32−1+i32−1+i321+i321−i321+i321+i321−i321−i321+i321−i32−1−i32−1−i32−1+i32−1+i32
χ121111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32111111−1−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+i3211−1−i32−1+i3211−1−i32−1+i32-1-1-1-1-1-1-1-1−1−i32−1−i32−1+i32−1+i321+i321+i321+i321+i321−i321−i321−i321−i321+i321+i321+i321+i321−i321−i321−i321−i32-1-11111-1-11+i321+i321−i321−i32−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321+i321+i321−i321−i32
χ131111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32111111−1−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+i32-1-11+i321−i32-1-11+i321−i321111-1-1-1-11+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−i32111-1-11-1-1−1−i32−1−i32−1+i32−1+i32−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+i321+i321+i321−i321−i32
χ141111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32111111−1−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+i32-1-11+i321−i32-1-11+i321−i321111-1-1-1-11+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−i32-1-1-111-1111+i321+i321−i321−i321+i321−i32−1−i32−1−i32−1+i32−1+i321+i321−i32−1−i32−1−i32−1+i32−1+i32
χ151111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32111111−1−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+i32-1-11+i321−i32-1-11+i321−i32-1-1-1-111111+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+i3211-111-1-1-1−1−i32−1−i32−1+i32−1+i321+i321−i32−1−i32−1−i32−1+i32−1+i321+i321−i321+i321+i321−i321−i32
χ161111−1−i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1+i32111111−1−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+i32-1-11+i321−i32-1-11+i321−i32-1-1-1-111111+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+i32-1-11-1-11111+i321+i321−i321−i32−1−i32−1+i321+i321+i321−i321−i32−1−i32−1+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−i32111111−1+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−i3211−1+i32−1−i3211−1+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−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
χ181111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32111111−1+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−i3211−1+i32−1−i3211−1+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−i32-1-1-1-1-1-1-1-11−i321−i321+i321+i321−i321+i321−i321−i321+i321+i321−i321+i321−i321−i321+i321+i32
χ191111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32111111−1+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−i3211−1+i32−1−i3211−1+i32−1−i32-1-1-1-1-1-1-1-1−1+i32−1+i32−1−i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i321−i321−i321−i321−i321+i321+i321+i321+i3211-1-1-1-111−1+i32−1+i32−1−i32−1−i321−i321+i321−i321−i321+i321+i321−i321+i32−1+i32−1+i32−1−i32−1−i32
χ201111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32111111−1+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−i3211−1+i32−1−i3211−1+i32−1−i32-1-1-1-1-1-1-1-1−1+i32−1+i32−1−i32−1−i321−i321−i321−i321−i321+i321+i321+i321+i321−i321−i321−i321−i321+i321+i321+i321+i32-1-11111-1-11−i321−i321+i321+i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−i321−i321+i321+i32
χ211111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32111111−1+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−i32-1-11−i321+i32-1-11−i321+i321111-1-1-1-11−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+i32111-1-11-1-1−1+i32−1+i32−1−i32−1−i32−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i321−i321−i321+i321+i32
χ221111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32111111−1+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−i32-1-11−i321+i32-1-11−i321+i321111-1-1-1-11−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+i32-1-1-111-1111−i321−i321+i321+i321−i321+i32−1+i32−1+i32−1−i32−1−i321−i321+i32−1+i32−1+i32−1−i32−1−i32
χ231111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32111111−1+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−i32-1-11−i321+i32-1-11−i321+i32-1-1-1-111111−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−i3211-111-1-1-1−1+i32−1+i32−1−i32−1−i321−i321+i32−1+i32−1+i32−1−i32−1−i321−i321+i321−i321−i321+i321+i32
χ241111−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1−i32111111−1+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−i32-1-11−i321+i32-1-11−i321+i32-1-1-1-111111−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−i32-1-11-1-11111−i321−i321+i321+i32−1+i32−1−i321−i321−i321+i321+i32−1+i32−1−i32−1+i32−1+i32−1−i32−1−i32
χ25222222222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-22222-2-22200000000-2-2-2-20000000000000000000000000000000000000000
χ26222222222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-2-2-222-2-20000000022220000000000000000000000000000000000000000
χ2722222222222222-2-2-2-22222-2-2-2-2-2-2-2-20000000000002-22200-2-222−2−222−2−2000022−2−222−2−222−2−222−2−2000000000000000000000000
χ2822222222222222-2-2-2-22222-2-2-2-2-2-2-2-20000000000002-22200-2-2−2−222−2−2220000−2−222−2−222−2−222−2−222000000000000000000000000
χ2922222222222222-2-2-2-22222-2-2-2-2-2-2-2-2000000000000-22-2-2002222−2−2−2−222000022−2−222−2−2−2−222−2−222000000000000000000000000
χ3022222222222222-2-2-2-22222-2-2-2-2-2-2-2-2000000000000-22-2-20022−2−22222−2−20000−2−222−2−22222−2−222−2−2000000000000000000000000
χ31222222222222-2-22-2-22-2-2-2-22-2-22-2-2222-22-22-22-22-22-200000000000000000000000000000000000000200-2000000220000-2-20000
χ32222222222222-2-22-2-22-2-2-2-22-2-22-2-2222-22-22-22-22-22-200000000000000000000000000000000000000-2002000000-2-20000220000
χ33222222222222-2-22-2-22-2-2-2-22-2-22-2-222-22-22-22-22-22-220000000000000000000000000000000000000002-20000000002-22-2000000
χ34222222222222-2-22-2-22-2-2-2-22-2-22-2-222-22-22-22-22-22-22000000000000000000000000000000000000000-22000000000-22-22000000
χ352222−1−i3−1+i3−1−i3−1−i3−1+i3−1+i3−1−i3−1+i3222222−1−i3−1+i3−1−i3−1+i3−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3−1−i3−1+i3-2-2-2-21+i31+i31−i31−i31+i31+i31−i31−i322−1−i3−1+i3-2-2−1−i3−1+i3000000001+i31+i31−i31−i30000000000000000000000000000000000000000
χ362222−1−i3−1+i3−1−i3−1−i3−1+i3−1+i3−1−i3−1+i3222222−1−i3−1+i3−1−i3−1+i3−1−i3−1−i3−1−i3−1+i3−1+i3−1+i3−1−i3−1+i3-2-2-2-21+i31+i31−i31−i31+i31+i31−i31−i3-2-21+i31−i3221+i31−i300000000−1−i3−1−i3−1+i3−1+i30000000000000000000000000000000000000000
χ372222−1−i3−1+i3−1−i3−1−i3−1+i3−1+i3−1−i3−1+i322-2-2-2-2−1−i3−1+i3−1−i3−1+i31+i31+i31+i31−i31−i31−i31+i31−i30000000000002-2−1−i3−1+i3001+i31−i322−2−222−2−20000−ζ7+ζ13−ζ7+ζ13ζ7−ζ13ζ7−ζ13ζ5−ζ23ζ5−ζ23−ζ5+ζ23−ζ5+ζ23−ζ7+ζ13−ζ7+ζ13ζ7−ζ13ζ7−ζ13ζ5−ζ23ζ5−ζ23−ζ5+ζ23−ζ5+ζ23000000000000000000000000
χ382222−1−i3−1+i3−1−i3−1−i3−1+i3−1+i3−1−i3−1+i322-2-2-2-2−1−i3−1+i3−1−i3−1+i31+i31+i31+i31−i31−i31−i31+i31−i30000000000002-2−1−i3−1+i3001+i31−i3−2−222−2−2220000ζ7−ζ13ζ7−ζ13−ζ7+ζ13−ζ7+ζ13−ζ5+ζ23−ζ5+ζ23ζ5−ζ23ζ5−ζ23ζ7−ζ13ζ7−ζ13−ζ7+ζ13−ζ7+ζ13−ζ5+ζ23−ζ5+ζ23ζ5−ζ23ζ5−ζ23000000000000000000000000
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χ91444444444444-4-4-444-4-4-4-4-4-444-444-4-4000000000000000000000000000000000000000000000000000000000000000000000000
χ924444−2−2i3−2+2i3−2−2i3−2−2i3−2+2i3−2+2i3−2−2i3−2+2i3-4-4-444-42+2i32−2i32+2i32−2i32+2i3−2−2i3−2−2i32−2i3−2+2i3−2+2i32+2i32−2i3000000000000000000000000000000000000000000000000000000000000000000000000
χ934444−2+2i3−2−2i3−2+2i3−2+2i3−2−2i3−2−2i3−2+2i3−2−2i3-4-4-444-42−2i32+2i32−2i32+2i32−2i3−2+2i3−2+2i32+2i3−2−2i3−2−2i32−2i32+2i3000000000000000000000000000000000000000000000000000000000000000000000000
χ944-4-4444-4-4-4-444-444-44-4-4-4444-444-44-4-4000000000000000000000000000000000000000000000000000000000000000000000000
χ954-4-44−2−2i3−2+2i32+2i32+2i32−2i32−2i3−2−2i3−2+2i3-444-44-42+2i32−2i3−2−2i3−2+2i3−2−2i32+2i3−2−2i3−2+2i32−2i3−2+2i32+2i32−2i3000000000000000000000000000000000000000000000000000000000000000000000000
χ964-4-44−2+2i3−2−2i32−2i32−2i32+2i32+2i3−2+2i3−2−2i3-444-44-42−2i32+2i3−2+2i3−2−2i3−2+2i32−2i3−2+2i3−2−2i32+2i3−2−2i32−2i32+2i3000000000000000000000000000000000000000000000000000000000000000000000000
χ9788-8-8888-88-8-8-8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9888-8-8−4−4i3−4+4i3−4−4i34+4i3−4+4i34−4i34+4i34−4i3000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ9988-8-8−4+4i3−4−4i3−4+4i34−4i3−4−4i34+4i34−4i34+4i3000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1008-88-888-88-88-8-8000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1018-88-8−4−4i3−4+4i34+4i3−4−4i34−4i3−4+4i34+4i34−4i3000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1028-88-8−4+4i3−4−4i34−4i3−4+4i34+4i3−4−4i34−4i34+4i3000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 24 (ζ24 = 1); i = ζ6.