Finite Group Databasebeta

← Group #10632066

Character table — Group #10632066

Order 768.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96C97C98C99C100C101C102
size111111111111222222222222222222444444444444888888888888888888888888888888888888161616161616161616161616161616161616161616161616
order123344661212121222244466666612121212121288882424242424242424448812121212161616161616161624242424484848484848484848484848484848484444448812121212121212121212121224242424
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
χ5111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-1-1-1
χ6111111111111111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111
χ7111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-11111-1-1-1-11111-1-1-1-1
χ8111111111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1-1-11111-1-1-1-11111
χ911−1−i32−1+i3211−1−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+i321111−1−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−i32−1+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
χ1011−1−i32−1+i3211−1−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+i321111−1−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−i32−1+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
χ1111−1−i32−1+i3211−1−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+i321111−1−i32−1−i32−1+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
χ1211−1−i32−1+i3211−1−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+i321111−1−i32−1−i32−1+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
χ1311−1−i32−1+i3211−1−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+i32-1-1-1-11+i321+i321−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−i321111-1-1-1-1−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i321+i321+i321−i321−i32
χ1411−1−i32−1+i3211−1−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+i32-1-1-1-11+i321+i321−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−i32-1-1-1-111111+i321+i321−i321−i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32
χ1511−1−i32−1+i3211−1−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+i32-1-1-1-11+i321+i321−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+i3211-1-111-1-1−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32
χ1611−1−i32−1+i3211−1−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+i32-1-1-1-11+i321+i321−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+i32-1-111-1-1111+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i321+i321+i321−i321−i32−1−i32−1−i32−1+i32−1+i32
χ1711−1+i32−1−i3211−1+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−i321111−1+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+i32−1−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
χ1811−1+i32−1−i3211−1+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−i321111−1+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+i32−1−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
χ1911−1+i32−1−i3211−1+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−i321111−1+i32−1+i32−1−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
χ2011−1+i32−1−i3211−1+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−i321111−1+i32−1+i32−1−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
χ2111−1+i32−1−i3211−1+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−i32-1-1-1-11−i321−i321+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+i321111-1-1-1-1−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i321−i321−i321+i321+i32
χ2211−1+i32−1−i3211−1+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−i32-1-1-1-11−i321−i321+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+i32-1-1-1-111111−i321−i321+i321+i321−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32−1+i32−1+i32−1−i32−1−i32
χ2311−1+i32−1−i3211−1+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−i32-1-1-1-11−i321−i321+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−i3211-1-111-1-1−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32
χ2411−1+i32−1−i3211−1+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−i32-1-1-1-11−i321−i321+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−i32-1-111-1-1111−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i321−i321−i321+i321+i32−1+i32−1+i32−1−i32−1−i32
χ25222222222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-222-2-2222200000000-2-2-2-20000000000000000000000000000000000000000
χ26222222222222222222222222222222-2-2-2-2-2-2-2-2-2-2-2-2-2-222-2-2-2-20000000022220000000000000000000000000000000000000000
χ272222222222222-2-2-22-222-2-2-2-2-2-222-2-22-22-22-22-22-22-200000000000022-2-200000000000022-2-222-2-2000000000000000000000000
χ282222222222222-2-2-22-222-2-2-2-2-2-222-2-22-22-22-22-22-22-2000000000000-2-222000000000000-2-222-2-222000000000000000000000000
χ292222222222222-2-2-22-222-2-2-2-2-2-222-2-2-22-22-22-22-22-220000000022-2-20000000022-2-222-2-200000000000000000000000000000000
χ302222222222222-2-2-22-222-2-2-2-2-2-222-2-2-22-22-22-22-22-2200000000-2-22200000000-2-222-2-22200000000000000000000000000000000
χ31222222222222-22-2-2-22-2-222-2-2-2-2-2-222000000000000002-20000−i2i2−i2i2−i2i2−i2i22-22-2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2000000000000000000000000
χ32222222222222-22-2-2-22-2-222-2-2-2-2-2-222000000000000002-20000i2−i2i2−i2i2−i2i2−i22-22-2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2i2−i2000000000000000000000000
χ33222222222222-22-2-2-22-2-222-2-2-2-2-2-22200000000000000-220000−i2i2−i2i2i2−i2i2−i2-22-22−i2i2−i2i2−i2i2−i2i2i2−i2i2−i2i2−i2i2−i2000000000000000000000000
χ34222222222222-22-2-2-22-2-222-2-2-2-2-2-22200000000000000-220000i2−i2i2−i2−i2i2−i2i2-22-22i2−i2i2−i2i2−i2i2−i2−i2i2−i2i2−i2i2−i2i2000000000000000000000000
χ35222222222222-2-222-2-2-2-2-2-22222-2-2-2-20000000000002-2002-22-2−i2i2i2−i2−i2i2i2−i20000−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2000000000000000000000000
χ36222222222222-2-222-2-2-2-2-2-22222-2-2-2-20000000000002-2002-22-2i2−i2−i2i2i2−i2−i2i20000i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2i2−i2−i2i2000000000000000000000000
χ37222222222222-2-222-2-2-2-2-2-22222-2-2-2-2000000000000-2200-22-22−i2i2i2−i2i2−i2−i2i20000−i2i2i2−i2−i2i2i2−i2i2−i2−i2i2i2−i2−i2i2000000000000000000000000
χ38222222222222-2-222-2-2-2-2-2-22222-2-2-2-2000000000000-2200-22-22i2−i2−i2i2−i2i2i2−i20000i2−i2−i2i2i2−i2−i2i2−i2i2i2−i2−i2i2i2−i2000000000000000000000000
χ392222-2-222-2-2-2-2-22-222-2-2-222-2-22222-2-222-2-22222-2-2-2-20000000000000000000000000000000000002-20000002-22-2000000000000
χ402222-2-222-2-2-2-2-22-222-2-2-222-2-22222-2-222-2-22222-2-2-2-2000000000000000000000000000000000000-22000000-22-22000000000000
χ412222-2-222-2-2-2-2-22-222-2-2-222-2-22222-2-2-2-222-2-2-2-222220000000000000000000000000000000000000000002i−2i0000000000002i−2i2i−2i
χ422222-2-222-2-2-2-2-22-222-2-2-222-2-22222-2-2-2-222-2-2-2-22222000000000000000000000000000000000000000000−2i2i000000000000−2i2i−2i2i
χ432222-2-222-2-2-2-2-2-22-222-2-2-2-222-2-222222-2-222-22-2-22-2200000000000000000000000000000000000000002-200000000002-22-20000
χ442222-2-222-2-2-2-2-2-22-222-2-2-2-222-2-222222-2-222-22-2-22-220000000000000000000000000000000000000000-220000000000-22-220000
χ452222-2-222-2-2-2-2-2-22-222-2-2-2-222-2-22222-222-2-22-222-22-2000000000000000000000000000000000000002-2000000002-22-200000000
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χ9022−1+i3−1−i3-2-2−1+i3−1−i31−i31−i31+i31+i3-2-22-2221−i31+i31−i31+i3−1+i3−1−i31−i31+i3−1+i3−1−i3−1+i3−1−i3-222-21−i3−1+i31+i3−1−i3−1+i31−i3−1−i31+i300000000000000000000000000000000000000-22000000001−i3−1+i31+i3−1−i300000000
χ914444-4-444-4-4-4-4444-4-4-4444444-4-4-4-4-4-4000000000000000000000000000000000000000000000000000000000000000000000000
χ924444-4-444-4-4-4-44-4-44-4444-4-4-4-444-4-444000000000000000000000000000000000000000000000000000000000000000000000000
χ9344−2−2i3−2+2i3-4-4−2−2i3−2+2i32+2i32+2i32−2i32−2i3444-4-4-4−2−2i3−2+2i3−2−2i3−2+2i3−2−2i3−2+2i32+2i32−2i32+2i32−2i32+2i32−2i3000000000000000000000000000000000000000000000000000000000000000000000000
χ9444−2−2i3−2+2i3-4-4−2−2i3−2+2i32+2i32+2i32−2i32−2i34-4-44-44−2−2i3−2+2i32+2i32−2i32+2i32−2i3−2−2i3−2+2i32+2i32−2i3−2−2i3−2+2i3000000000000000000000000000000000000000000000000000000000000000000000000
χ9544−2+2i3−2−2i3-4-4−2+2i3−2−2i32−2i32−2i32+2i32+2i3444-4-4-4−2+2i3−2−2i3−2+2i3−2−2i3−2+2i3−2−2i32−2i32+2i32−2i32+2i32−2i32+2i3000000000000000000000000000000000000000000000000000000000000000000000000
χ9644−2+2i3−2−2i3-4-4−2+2i3−2−2i32−2i32−2i32+2i32+2i34-4-44-44−2+2i3−2−2i32−2i32+2i32−2i32+2i3−2+2i3−2−2i32−2i32+2i3−2+2i3−2−2i3000000000000000000000000000000000000000000000000000000000000000000000000
χ978-8888i−8i-8-88i−8i8i−8i000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ988-888−8i8i-8-8−8i8i−8i8i000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ998-8−4−4i3−4+4i38i−8i4+4i34−4i38ζ22−8ζ228ζ14−8ζ14000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1008-8−4−4i3−4+4i3−8i8i4+4i34−4i3−8ζ228ζ22−8ζ148ζ14000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1018-8−4+4i3−4−4i38i−8i4−4i34+4i38ζ14−8ζ148ζ22−8ζ22000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000
χ1028-8−4+4i3−4−4i3−8i8i4−4i34+4i3−8ζ148ζ14−8ζ228ζ22000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

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