Finite Group Databasebeta

← Group #84621

Character table — Group #84621

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size111111114444444444444444448888881111111144444444444444444488888811111111444444444444444444888888
order122222222244444444444444442444443666666666121212121212121212121212121212126121212121236666666661212121212121212121212121212121261212121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ3111111111111-1-11111-1-111-1-1-1-11-1-1-1-11111111111111-1-11111-1-111-1-1-1-11-1-1-1-11111111111111-1-11111-1-111-1-1-1-11-1-1-1-11
χ4111111111111-1-1-1-1-1-111-1-11111-11-1-1-11111111111111-1-1-1-1-1-111-1-11111-11-1-1-11111111111111-1-1-1-1-1-111-1-11111-11-1-1-11
χ51111111111-1-11111-1-11111-1-1-1-1-111-1-1-11111111111-1-11111-1-11111-1-1-1-1-111-1-1-11111111111-1-11111-1-11111-1-1-1-1-111-1-1-1
χ61111111111-1-111-1-111-1-1-1-111111-11-1-1-11111111111-1-111-1-111-1-1-1-111111-11-1-1-11111111111-1-111-1-111-1-1-1-111111-11-1-1-1
χ71111111111-1-1-1-111-1-1-1-1111111-1-1-111-11111111111-1-1-1-111-1-1-1-1111111-1-1-111-11111111111-1-1-1-111-1-1-1-1111111-1-1-111-1
χ81111111111-1-1-1-1-1-11111-1-1-1-1-1-111-111-11111111111-1-1-1-1-1-11111-1-1-1-1-1-111-111-11111111111-1-1-1-1-1-11111-1-1-1-1-1-111-111-1
χ911111111-1-111111111-1-1-1-111-1-1-11-11-1-111111111-1-111111111-1-1-1-111-1-1-11-11-1-111111111-1-111111111-1-1-1-111-1-1-11-11-1-1
χ1011111111-1-11111-1-1-1-11111-1-1111-1-11-1-111111111-1-11111-1-1-1-11111-1-1111-1-11-1-111111111-1-11111-1-1-1-11111-1-1111-1-11-1-1
χ1111111111-1-111-1-1111111-1-1-1-111-1-11-11-111111111-1-111-1-1111111-1-1-1-111-1-11-11-111111111-1-111-1-1111111-1-1-1-111-1-11-11-1
χ1211111111-1-111-1-1-1-1-1-1-1-11111-1-1111-11-111111111-1-111-1-1-1-1-1-1-1-11111-1-1111-11-111111111-1-111-1-1-1-1-1-1-1-11111-1-1111-11-1
χ1311111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-11111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111
χ1411111111-1-1-1-111-1-111111111-1-1-1-1-1-11111111111-1-1-1-111-1-111111111-1-1-1-1-1-11111111111-1-1-1-111-1-111111111-1-1-1-1-1-111
χ1511111111-1-1-1-1-1-111-1-111-1-111-1-11-111-1111111111-1-1-1-1-1-111-1-111-1-111-1-11-111-1111111111-1-1-1-1-1-111-1-111-1-111-1-11-111-11
χ1611111111-1-1-1-1-1-1-1-111-1-111-1-111-1111-1111111111-1-1-1-1-1-1-1-111-1-111-1-111-1111-1111111111-1-1-1-1-1-1-1-111-1-111-1-111-1111-11
χ1722-2-222-2-200002i−2i002-200002i−2i0000000022-2-222-2-200002i−2i002-200002i−2i0000000022-2-222-2-200002i−2i002-200002i−2i00000000
χ1822-2-222-2-200002i−2i00-220000−2i2i0000000022-2-222-2-200002i−2i00-220000−2i2i0000000022-2-222-2-200002i−2i00-220000−2i2i00000000
χ1922-2-222-2-20000−2i2i002-20000−2i2i0000000022-2-222-2-20000−2i2i002-20000−2i2i0000000022-2-222-2-20000−2i2i002-20000−2i2i00000000
χ2022-2-222-2-20000−2i2i00-2200002i−2i0000000022-2-222-2-20000−2i2i00-2200002i−2i0000000022-2-222-2-20000−2i2i00-2200002i−2i00000000
χ212-22-22-22-2002i−2i0000002-200002i−2i0000002-22-22-22-2002i−2i0000002-200002i−2i0000002-22-22-22-2002i−2i0000002-200002i−2i000000
χ222-22-22-22-2002i−2i000000-220000−2i2i0000002-22-22-22-2002i−2i000000-220000−2i2i0000002-22-22-22-2002i−2i000000-220000−2i2i000000
χ232-22-22-22-200−2i2i0000002-20000−2i2i0000002-22-22-22-200−2i2i0000002-20000−2i2i0000002-22-22-22-200−2i2i0000002-20000−2i2i000000
χ242-22-22-22-200−2i2i000000-2200002i−2i0000002-22-22-22-200−2i2i000000-2200002i−2i0000002-22-22-22-200−2i2i000000-2200002i−2i000000
χ252-2-22-222-22-200002i−2i00002i−2i00000000002-2-22-222-22-200002i−2i00002i−2i00000000002-2-22-222-22-200002i−2i00002i−2i0000000000
χ262-2-22-222-22-20000−2i2i0000−2i2i00000000002-2-22-222-22-20000−2i2i0000−2i2i00000000002-2-22-222-22-20000−2i2i0000−2i2i0000000000
χ272-2-22-222-2-2200002i−2i0000−2i2i00000000002-2-22-222-2-2200002i−2i0000−2i2i00000000002-2-22-222-2-2200002i−2i0000−2i2i0000000000
χ282-2-22-222-2-220000−2i2i00002i−2i00000000002-2-22-222-2-220000−2i2i00002i−2i00000000002-2-22-222-2-220000−2i2i00002i−2i0000000000
χ294444-4-4-4-40000000000000000000000004444-4-4-4-40000000000000000000000004444-4-4-4-4000000000000000000000000
χ3044-4-4-4-44400000000000000000000000044-4-4-4-44400000000000000000000000044-4-4-4-444000000000000000000000000
χ314-44-4-44-440000000000000000000000004-44-4-44-440000000000000000000000004-44-4-44-44000000000000000000000000
χ324-4-444-4-440000000000000000000000004-4-444-4-440000000000000000000000004-4-444-4-44000000000000000000000000
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
χ3411111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−1+i32−1+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−i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−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+i32−1−i32−1−i32−1−i32−1−i32
χ35111111111111-1-11111-1-111-1-1-1-11-1-1-1-11−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i321−i321−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−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i321+i321+i32−1−i321+i321+i321+i321+i32−1−i32
χ36111111111111-1-1-1-1-1-111-1-11111-11-1-1-11−1+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−i32−1+i32−1+i321−i321−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−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i32−1−i321+i321+i321+i32−1−i32
χ371111111111-1-11111-1-11111-1-1-1-1-111-1-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i32−1+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+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i32−1−i32−1−i321+i321+i321+i32
χ381111111111-1-111-1-111-1-1-1-111111-11-1-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−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+i32−1−i32−1−i321+i321+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
χ391111111111-1-1-1-111-1-1-1-1111111-1-1-111-1−1+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+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i32−1+i32−1+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−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i321+i32
χ401111111111-1-1-1-1-1-11111-1-1-1-1-1-111-111-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1+i32−1+i321−i32−1+i32−1+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+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i32−1−i321+i32−1−i32−1−i321+i32
χ4111111111-1-111111111-1-1-1-111-1-1-11-11-1-1−1+i32−1+i32−1+i32−1+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+i321−i321−i321−i321−i32−1+i32−1+i321−i321−i321−i32−1+i321−i32−1+i321−i321−i32−1−i32−1−i32−1−i32−1−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−i321+i321+i321+i321+i32−1−i32−1−i321+i321+i321+i32−1−i321+i32−1−i321+i321+i32
χ4211111111-1-11111-1-1-1-11111-1-1111-1-11-1-1−1+i32−1+i32−1+i32−1+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−i32−1+i32−1+i32−1+i321−i321−i32−1+i321−i321−i32−1−i32−1−i32−1−i32−1−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+i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i321+i32
χ4311111111-1-111-1-1111111-1-1-1-111-1-11-11-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−i321−i32−1+i321−i32−1+i321−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i321+i32−1−i321+i32
χ4411111111-1-111-1-1-1-1-1-1-1-11111-1-1111-11-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i32−1+i321−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i32−1−i321+i32
χ4511111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-111−1+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−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−i321+i321+i321+i321+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+i32−1−i32−1−i32
χ4611111111-1-1-1-111-1-111111111-1-1-1-1-1-111−1+i32−1+i32−1+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+i32−1+i32−1+i32−1+i32−1+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−i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32
χ4711111111-1-1-1-1-1-111-1-111-1-111-1-11-111-11−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i321−i32−1+i32−1+i321−i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i321+i32−1−i32−1−i321+i32−1−i32
χ4811111111-1-1-1-1-1-1-1-111-1-111-1-111-1111-11−1+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+i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i32−1+i32−1+i32−1+i321−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−i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i32−1−i32−1−i32−1−i321+i32−1−i32
χ4922-2-222-2-200002i−2i002-200002i−2i00000000−1+i3−1+i31−i31−i3−1+i3−1+i31−i31−i300002ζ7−2ζ700−1+i31−i300002ζ7−2ζ700000000−1−i3−1−i31+i31+i3−1−i3−1−i31+i31+i300002ζ11−2ζ1100−1−i31+i300002ζ11−2ζ1100000000
χ5022-2-222-2-200002i−2i00-220000−2i2i00000000−1+i3−1+i31−i31−i3−1+i3−1+i31−i31−i300002ζ7−2ζ7001−i3−1+i30000−2ζ72ζ700000000−1−i3−1−i31+i31+i3−1−i3−1−i31+i31+i300002ζ11−2ζ11001+i3−1−i30000−2ζ112ζ1100000000
χ5122-2-222-2-20000−2i2i002-20000−2i2i00000000−1+i3−1+i31−i31−i3−1+i3−1+i31−i31−i30000−2ζ72ζ700−1+i31−i30000−2ζ72ζ700000000−1−i3−1−i31+i31+i3−1−i3−1−i31+i31+i30000−2ζ112ζ1100−1−i31+i30000−2ζ112ζ1100000000
χ5222-2-222-2-20000−2i2i00-2200002i−2i00000000−1+i3−1+i31−i31−i3−1+i3−1+i31−i31−i30000−2ζ72ζ7001−i3−1+i300002ζ7−2ζ700000000−1−i3−1−i31+i31+i3−1−i3−1−i31+i31+i30000−2ζ112ζ11001+i3−1−i300002ζ11−2ζ1100000000
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χ892-2-22-222-22-200002i−2i00002i−2i0000000000−1−i31+i31+i3−1−i31+i3−1−i3−1−i31+i3−1−i31+i300002ζ11−2ζ1100002ζ11−2ζ110000000000−1+i31−i31−i3−1+i31−i3−1+i3−1+i31−i3−1+i31−i300002ζ7−2ζ700002ζ7−2ζ70000000000
χ902-2-22-222-22-20000−2i2i0000−2i2i0000000000−1−i31+i31+i3−1−i31+i3−1−i3−1−i31+i3−1−i31+i30000−2ζ112ζ110000−2ζ112ζ110000000000−1+i31−i31−i3−1+i31−i3−1+i3−1+i31−i3−1+i31−i30000−2ζ72ζ70000−2ζ72ζ70000000000
χ912-2-22-222-2-2200002i−2i0000−2i2i0000000000−1−i31+i31+i3−1−i31+i3−1−i3−1−i31+i31+i3−1−i300002ζ11−2ζ110000−2ζ112ζ110000000000−1+i31−i31−i3−1+i31−i3−1+i3−1+i31−i31−i3−1+i300002ζ7−2ζ70000−2ζ72ζ70000000000
χ922-2-22-222-2-220000−2i2i00002i−2i0000000000−1−i31+i31+i3−1−i31+i3−1−i3−1−i31+i31+i3−1−i30000−2ζ112ζ1100002ζ11−2ζ110000000000−1+i31−i31−i3−1+i31−i3−1+i3−1+i31−i31−i3−1+i30000−2ζ72ζ700002ζ7−2ζ70000000000
χ934444-4-4-4-4000000000000000000000000−2−2i3−2−2i3−2−2i3−2−2i32+2i32+2i32+2i32+2i3000000000000000000000000−2+2i3−2+2i3−2+2i3−2+2i32−2i32−2i32−2i32−2i3000000000000000000000000
χ9444-4-4-4-444000000000000000000000000−2−2i3−2−2i32+2i32+2i32+2i32+2i3−2−2i3−2−2i3000000000000000000000000−2+2i3−2+2i32−2i32−2i32−2i32−2i3−2+2i3−2+2i3000000000000000000000000
χ954-44-4-44-44000000000000000000000000−2−2i32+2i3−2−2i32+2i32+2i3−2−2i32+2i3−2−2i3000000000000000000000000−2+2i32−2i3−2+2i32−2i32−2i3−2+2i32−2i3−2+2i3000000000000000000000000
χ964-4-444-4-44000000000000000000000000−2−2i32+2i32+2i3−2−2i3−2−2i32+2i32+2i3−2−2i3000000000000000000000000−2+2i32−2i32−2i3−2+2i3−2+2i32−2i32−2i3−2+2i3000000000000000000000000

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