Finite Group Databasebeta

← Group #84990

Character table — Group #84990

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size111122222244444444444444448888881111222222444444444444444488888811112222224444444444444444888888
order12224444442444444444448888224488366612121212121261212121212121212121212242424246612122424366612121212121261212121212121212121212242424246612122424
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111-1-1-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-11111111111111111111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111
χ411111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1
χ51111111111-1-1-1-11111-1-1-1-111111-11-1-1-11111111111-1-1-1-11111-1-1-1-111111-11-1-1-11111111111-1-1-1-11111-1-1-1-111111-11-1-1-1
χ61111111111-1-1-1-11111-1-1-1-1-1-1-1-1-11-11111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-11-11111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-11-1111
χ71111111111-1-1-1-1-1-1-1-111111111-11-11-1-11111111111-1-1-1-1-1-1-1-111111111-11-11-1-11111111111-1-1-1-1-1-1-1-111111111-11-11-1-1
χ81111111111-1-1-1-1-1-1-1-11111-1-1-1-11-11-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-11-11-1111111111111-1-1-1-1-1-1-1-11111-1-1-1-11-11-111
χ91111-1-1-1-11111-1-111-1-111-1-111-1-11-1-111-11111-1-1-1-11111-1-111-1-111-1-111-1-11-1-111-11111-1-1-1-11111-1-111-1-111-1-111-1-11-1-111-1
χ101111-1-1-1-11111-1-111-1-111-1-1-1-111-111-1-111111-1-1-1-11111-1-111-1-111-1-1-1-111-111-1-111111-1-1-1-11111-1-111-1-111-1-1-1-111-111-1-11
χ111111-1-1-1-11111-1-1-1-111-1-11111-1-1-111-11-11111-1-1-1-11111-1-1-1-111-1-11111-1-1-111-11-11111-1-1-1-11111-1-1-1-111-1-11111-1-1-111-11-1
χ121111-1-1-1-11111-1-1-1-111-1-111-1-1111-1-11-111111-1-1-1-11111-1-1-1-111-1-111-1-1111-1-11-111111-1-1-1-11111-1-1-1-111-1-111-1-1111-1-11-11
χ131111-1-1-1-111-1-11111-1-1-1-11111-1-111-1-1-111111-1-1-1-111-1-11111-1-1-1-11111-1-111-1-1-111111-1-1-1-111-1-11111-1-1-1-11111-1-111-1-1-11
χ141111-1-1-1-111-1-11111-1-1-1-111-1-111-1-1111-11111-1-1-1-111-1-11111-1-1-1-111-1-111-1-1111-11111-1-1-1-111-1-11111-1-1-1-111-1-111-1-1111-1
χ151111-1-1-1-111-1-111-1-11111-1-111-1-1-1-111-111111-1-1-1-111-1-111-1-11111-1-111-1-1-1-111-111111-1-1-1-111-1-111-1-11111-1-111-1-1-1-111-11
χ161111-1-1-1-111-1-111-1-11111-1-1-1-11111-1-11-11111-1-1-1-111-1-111-1-11111-1-1-1-11111-1-11-11111-1-1-1-111-1-111-1-11111-1-1-1-11111-1-11-1
χ17222222-2-2-2-22-22-2000000000000000000222222-2-2-2-22-22-2000000000000000000222222-2-2-2-22-22-2000000000000000000
χ18222222-2-2-2-2-22-22000000000000000000222222-2-2-2-2-22-22000000000000000000222222-2-2-2-2-22-22000000000000000000
χ192222-2-222-2-22-2-220000000000000000002222-2-222-2-22-2-220000000000000000002222-2-222-2-22-2-22000000000000000000
χ202222-2-222-2-2-222-20000000000000000002222-2-222-2-2-222-20000000000000000002222-2-222-2-2-222-2000000000000000000
χ2122-2-22i−2i2i−2i2-2000000002-22i−2i000000000022-2-22i−2i2i−2i2-2000000002-22i−2i000000000022-2-22i−2i2i−2i2-2000000002-22i−2i0000000000
χ2222-2-22i−2i2i−2i2-200000000-22−2i2i000000000022-2-22i−2i2i−2i2-200000000-22−2i2i000000000022-2-22i−2i2i−2i2-200000000-22−2i2i0000000000
χ2322-2-22i−2i−2i2i-2200002-22i−2i0000000000000022-2-22i−2i−2i2i-2200002-22i−2i0000000000000022-2-22i−2i−2i2i-2200002-22i−2i00000000000000
χ2422-2-22i−2i−2i2i-220000-22−2i2i0000000000000022-2-22i−2i−2i2i-220000-22−2i2i0000000000000022-2-22i−2i−2i2i-220000-22−2i2i00000000000000
χ2522-2-2−2i2i2i−2i-2200002-2−2i2i0000000000000022-2-2−2i2i2i−2i-2200002-2−2i2i0000000000000022-2-2−2i2i2i−2i-2200002-2−2i2i00000000000000
χ2622-2-2−2i2i2i−2i-220000-222i−2i0000000000000022-2-2−2i2i2i−2i-220000-222i−2i0000000000000022-2-2−2i2i2i−2i-220000-222i−2i00000000000000
χ2722-2-2−2i2i−2i2i2-2000000002-2−2i2i000000000022-2-2−2i2i−2i2i2-2000000002-2−2i2i000000000022-2-2−2i2i−2i2i2-2000000002-2−2i2i0000000000
χ2822-2-2−2i2i−2i2i2-200000000-222i−2i000000000022-2-2−2i2i−2i2i2-200000000-222i−2i000000000022-2-2−2i2i−2i2i2-200000000-222i−2i0000000000
χ294-44-40000000000000000002i2−2i2000000004-44-40000000000000000002i2−2i2000000004-44-40000000000000000002i2−2i200000000
χ304-44-4000000000000000000−2i22i2000000004-44-4000000000000000000−2i22i2000000004-44-4000000000000000000−2i22i200000000
χ314-4-44000000000000000000002i2−2i20000004-4-44000000000000000000002i2−2i20000004-4-44000000000000000000002i2−2i2000000
χ324-4-4400000000000000000000−2i22i20000004-4-4400000000000000000000−2i22i20000004-4-4400000000000000000000−2i22i2000000
χ3311111111111111111111111111111111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32
χ341111111111111111111111-1-1-1-1-1-1-1-1-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+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−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−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+i32
χ3511111111111111-1-1-1-1-1-1-1-11111-1-1-1-111−1+i32−1+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+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−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−i321+i321+i321+i321+i32−1−i32−1−i32
χ3611111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1−1+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+i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+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−i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32
χ371111111111-1-1-1-11111-1-1-1-111111-11-1-1-1−1+i32−1+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+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i321−i32−1+i321−i321−i321−i32−1−i32−1−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−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i321+i32−1−i321+i321+i321+i32
χ381111111111-1-1-1-11111-1-1-1-1-1-1-1-1-11-1111−1+i32−1+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+i321−i321−i321−i321−i321−i321−i321−i321−i321−i32−1+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−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i321+i321+i32−1−i321+i32−1−i32−1−i32−1−i32
χ391111111111-1-1-1-1-1-1-1-111111111-11-11-1-1−1+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+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i32−1+i321−i32−1+i321−i321−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−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i32−1−i321+i32−1−i321+i321+i32
χ401111111111-1-1-1-1-1-1-1-11111-1-1-1-11-11-111−1+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+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i321−i32−1+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−i321+i321+i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i321+i32−1−i321+i32−1−i32−1−i32
χ411111-1-1-1-11111-1-111-1-111-1-111-1-11-1-111-1−1+i32−1+i32−1+i32−1+i321−i321−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−i32−1+i321−i321−i32−1+i32−1+i321−i32−1−i32−1−i32−1−i32−1−i321+i321+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+i32−1−i321+i321+i32−1−i32−1−i321+i32
χ421111-1-1-1-11111-1-111-1-111-1-1-1-111-111-1-11−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−i32−1+i32−1+i321−i321−i32−1+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i32−1−i32−1−i321+i321+i32−1−i32
χ431111-1-1-1-11111-1-1-1-111-1-11111-1-1-111-11-1−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i321−i32−1+i321−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−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i321+i32−1−i321+i32
χ441111-1-1-1-11111-1-1-1-111-1-111-1-1111-1-11-11−1+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+i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i321−i32−1+i321−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−i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i32−1−i32
χ451111-1-1-1-111-1-11111-1-1-1-11111-1-111-1-1-11−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−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−i32−1+i32−1+i321−i321−i321−i32−1+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+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+i32−1−i32−1−i321+i321+i321+i32−1−i32
χ461111-1-1-1-111-1-11111-1-1-1-111-1-111-1-1111-1−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i32
χ471111-1-1-1-111-1-111-1-11111-1-111-1-1-1-111-11−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−i32−1+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i32−1−i32
χ481111-1-1-1-111-1-111-1-11111-1-1-1-11111-1-11-1−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−i321−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−i32−1+i321−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i321+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+i32−1−i321+i32
χ49222222-2-2-2-22-22-2000000000000000000−1+i3−1+i3−1+i3−1+i3−1+i3−1+i31−i31−i31−i31−i3−1+i31−i3−1+i31−i3000000000000000000−1−i3−1−i3−1−i3−1−i3−1−i3−1−i31+i31+i31+i31+i3−1−i31+i3−1−i31+i3000000000000000000
χ50222222-2-2-2-2-22-22000000000000000000−1+i3−1+i3−1+i3−1+i3−1+i3−1+i31−i31−i31−i31−i31−i3−1+i31−i3−1+i3000000000000000000−1−i3−1−i3−1−i3−1−i3−1−i3−1−i31+i31+i31+i31+i31+i3−1−i31+i3−1−i3000000000000000000
χ512222-2-222-2-22-2-22000000000000000000−1+i3−1+i3−1+i3−1+i31−i31−i3−1+i3−1+i31−i31−i3−1+i31−i31−i3−1+i3000000000000000000−1−i3−1−i3−1−i3−1−i31+i31+i3−1−i3−1−i31+i31+i3−1−i31+i31+i3−1−i3000000000000000000
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χ8922-2-2−2i2i2i−2i-2200002-2−2i2i00000000000000−1−i3−1−i31+i31+i3−2ζ222ζ222ζ22−2ζ221+i3−1−i30000−1−i31+i3−2ζ222ζ2200000000000000−1+i3−1+i31−i31−i3−2ζ142ζ142ζ14−2ζ141−i3−1+i30000−1+i31−i3−2ζ142ζ1400000000000000
χ9022-2-2−2i2i2i−2i-220000-222i−2i00000000000000−1−i3−1−i31+i31+i3−2ζ222ζ222ζ22−2ζ221+i3−1−i300001+i3−1−i32ζ22−2ζ2200000000000000−1+i3−1+i31−i31−i3−2ζ142ζ142ζ14−2ζ141−i3−1+i300001−i3−1+i32ζ14−2ζ1400000000000000
χ9122-2-2−2i2i−2i2i2-2000000002-2−2i2i0000000000−1−i3−1−i31+i31+i3−2ζ222ζ22−2ζ222ζ22−1−i31+i300000000−1−i31+i3−2ζ222ζ220000000000−1+i3−1+i31−i31−i3−2ζ142ζ14−2ζ142ζ14−1+i31−i300000000−1+i31−i3−2ζ142ζ140000000000
χ9222-2-2−2i2i−2i2i2-200000000-222i−2i0000000000−1−i3−1−i31+i31+i3−2ζ222ζ22−2ζ222ζ22−1−i31+i3000000001+i3−1−i32ζ22−2ζ220000000000−1+i3−1+i31−i31−i3−2ζ142ζ14−2ζ142ζ14−1+i31−i3000000001−i3−1+i32ζ14−2ζ140000000000
χ934-44-40000000000000000002i2−2i200000000−2−2i32+2i3−2−2i32+2i3000000000000000000−2ζ7−2ζ132ζ7+2ζ1300000000−2+2i32−2i3−2+2i32−2i3000000000000000000−2ζ5−2ζ232ζ5+2ζ2300000000
χ944-44-4000000000000000000−2i22i200000000−2−2i32+2i3−2−2i32+2i30000000000000000002ζ7+2ζ13−2ζ7−2ζ1300000000−2+2i32−2i3−2+2i32−2i30000000000000000002ζ5+2ζ23−2ζ5−2ζ2300000000
χ954-4-44000000000000000000002i2−2i2000000−2−2i32+2i32+2i3−2−2i300000000000000000000−2ζ7−2ζ132ζ7+2ζ13000000−2+2i32−2i32−2i3−2+2i300000000000000000000−2ζ5−2ζ232ζ5+2ζ23000000
χ964-4-4400000000000000000000−2i22i2000000−2−2i32+2i32+2i3−2−2i3000000000000000000002ζ7+2ζ13−2ζ7−2ζ13000000−2+2i32−2i32−2i3−2+2i3000000000000000000002ζ5+2ζ23−2ζ5−2ζ23000000

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