Finite Group Databasebeta

← Group #84591

Character table — Group #84591

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size111111114444444444444444448888881111111144444444444444444488888811111111444444444444444444888888
order12222222444444444444444444224444366666661212121212121212121212121212121212126612121212366666661212121212121212121212121212121212126612121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1
χ3111111111111-1-1-1-1-1-1111111-1-11-11-1-1-1111111111111-1-1-1-1-1-1111111-1-11-11-1-1-1111111111111-1-1-1-1-1-1111111-1-11-11-1-1-1
χ4111111111111-1-1-1-1-1-1-1-1-1-1-1-111-111-111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-111-111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-111-111
χ51111111111-1-111-1-1-1-11111-1-111-11-11-1-11111111111-1-111-1-1-1-11111-1-111-11-11-1-11111111111-1-111-1-1-1-11111-1-111-11-11-1-1
χ61111111111-1-111-1-1-1-1-1-1-1-111-1-11-1-11111111111111-1-111-1-1-1-1-1-1-1-111-1-11-1-11111111111111-1-111-1-1-1-1-1-1-1-111-1-11-1-1111
χ71111111111-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1111111111111-1-1-1-111111111-1-1-1-1-1-1-1-111
χ81111111111-1-1-1-11111-1-1-1-1111111-1-1-1-11111111111-1-1-1-11111-1-1-1-1111111-1-1-1-11111111111-1-1-1-11111-1-1-1-1111111-1-1-1-1
χ911111111-1-1111111-1-111-1-111-1-1-11-1-11-111111111-1-1111111-1-111-1-111-1-1-11-1-11-111111111-1-1111111-1-111-1-111-1-1-11-1-11-1
χ1011111111-1-1111111-1-1-1-111-1-1111-1-1-1-1111111111-1-1111111-1-1-1-111-1-1111-1-1-1-1111111111-1-1111111-1-1-1-111-1-1111-1-1-1-11
χ1111111111-1-111-1-1-1-11111-1-11111-1-1-11-1111111111-1-111-1-1-1-11111-1-11111-1-1-11-1111111111-1-111-1-1-1-11111-1-11111-1-1-11-11
χ1211111111-1-111-1-1-1-111-1-111-1-1-1-111-111-111111111-1-111-1-1-1-111-1-111-1-1-1-111-111-111111111-1-111-1-1-1-111-1-111-1-1-1-111-111-1
χ1311111111-1-1-1-111-1-11111-1-1-1-1-1-1111-1-1111111111-1-1-1-111-1-11111-1-1-1-1-1-1111-1-1111111111-1-1-1-111-1-11111-1-1-1-1-1-1111-1-11
χ1411111111-1-1-1-111-1-111-1-1111111-1-11-11-111111111-1-1-1-111-1-111-1-1111111-1-11-11-111111111-1-1-1-111-1-111-1-1111111-1-11-11-1
χ1511111111-1-1-1-1-1-111-1-111-1-1-1-1111-1111-111111111-1-1-1-1-1-111-1-111-1-1-1-1111-1111-111111111-1-1-1-1-1-111-1-111-1-1-1-1111-1111-1
χ1611111111-1-1-1-1-1-111-1-1-1-11111-1-1-1111-1111111111-1-1-1-1-1-111-1-1-1-11111-1-1-1111-1111111111-1-1-1-1-1-111-1-1-1-11111-1-1-1111-11
χ1722-22-2-2-222-2000000002i−2i2i−2i000000000022-22-2-2-222-2000000002i−2i2i−2i000000000022-22-2-2-222-2000000002i−2i2i−2i0000000000
χ1822-22-2-2-222-200000000−2i2i−2i2i000000000022-22-2-2-222-200000000−2i2i−2i2i000000000022-22-2-2-222-200000000−2i2i−2i2i0000000000
χ1922-22-2-2-22-22000000002i−2i−2i2i000000000022-22-2-2-22-22000000002i−2i−2i2i000000000022-22-2-2-22-22000000002i−2i−2i2i0000000000
χ2022-22-2-2-22-2200000000−2i2i2i−2i000000000022-22-2-2-22-2200000000−2i2i2i−2i000000000022-22-2-2-22-2200000000−2i2i2i−2i0000000000
χ2122-2-222-2-2000000002-200002i−2i2i−2i00000022-2-222-2-2000000002-200002i−2i2i−2i00000022-2-222-2-2000000002-200002i−2i2i−2i000000
χ2222-2-222-2-2000000002-20000−2i2i−2i2i00000022-2-222-2-2000000002-20000−2i2i−2i2i00000022-2-222-2-2000000002-20000−2i2i−2i2i000000
χ2322-2-222-2-200000000-2200002i−2i−2i2i00000022-2-222-2-200000000-2200002i−2i−2i2i00000022-2-222-2-200000000-2200002i−2i−2i2i000000
χ2422-2-222-2-200000000-220000−2i2i2i−2i00000022-2-222-2-200000000-220000−2i2i2i−2i00000022-2-222-2-200000000-220000−2i2i2i−2i000000
χ252-2-2-22-222002-22-22-200000000000000002-2-2-22-222002-22-22-200000000000000002-2-2-22-222002-22-22-20000000000000000
χ262-2-2-22-222002-2-22-2200000000000000002-2-2-22-222002-2-22-2200000000000000002-2-2-22-222002-2-22-220000000000000000
χ272-2-2-22-22200-222-2-2200000000000000002-2-2-22-22200-222-2-2200000000000000002-2-2-22-22200-222-2-220000000000000000
χ282-2-2-22-22200-22-222-200000000000000002-2-2-22-22200-22-222-200000000000000002-2-2-22-22200-22-222-20000000000000000
χ29444-4-4-44-4000000000000000000000000444-4-4-44-4000000000000000000000000444-4-4-44-4000000000000000000000000
χ304-4444-4-4-40000000000000000000000004-4444-4-4-40000000000000000000000004-4444-4-4-4000000000000000000000000
χ314-44-4-44-440000000000000000000000004-44-4-44-440000000000000000000000004-44-4-44-44000000000000000000000000
χ324-4-44-444-40000000000000000000000004-4-44-444-40000000000000000000000004-4-44-444-4000000000000000000000000
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
χ34111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1−1+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+i321−i321−i321−i321−i321−i321−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−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−i321+i321+i32
χ35111111111111-1-1-1-1-1-1111111-1-11-11-1-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−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−i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i32−1−i321+i321+i321+i32
χ36111111111111-1-1-1-1-1-1-1-1-1-1-1-111-111-111−1+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+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−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i321+i32−1−i32−1−i321+i32−1−i32−1−i321+i32−1−i32−1−i32
χ371111111111-1-111-1-1-1-11111-1-111-11-11-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−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+i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i32−1−i321+i32−1−i321+i321+i32
χ381111111111-1-111-1-1-1-1-1-1-1-111-1-11-1-1111−1+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−i321−i321−i321−i321−i321−i321−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−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−i321+i321+i32−1−i321+i321+i32−1−i32−1−i32−1−i32
χ391111111111-1-1-1-111111111-1-1-1-1-1-1-1-111−1+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+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−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
χ401111111111-1-1-1-11111-1-1-1-1111111-1-1-1-1−1+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+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−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−i321+i321+i321+i321+i32
χ4111111111-1-1111111-1-111-1-111-1-1-11-1-11-1−1+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+i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i321−i32−1+i321−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−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i321+i32−1−i321+i321+i32−1−i321+i32
χ4211111111-1-1111111-1-1-1-111-1-1111-1-1-1-11−1+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+i321−i321−i321−i321−i32−1+i32−1+i321−i321−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−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−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32
χ4311111111-1-111-1-1-1-11111-1-11111-1-1-11-11−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i32−1+i321−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+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i32−1−i321+i32−1−i32
χ4411111111-1-111-1-1-1-111-1-111-1-1-1-111-111-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+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−i321+i321+i32−1−i32−1−i321+i321+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+i32
χ4511111111-1-1-1-111-1-11111-1-1-1-1-1-1111-1-11−1+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+i321−i321−i321−i321−i321−i321−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−i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i321+i321+i32−1−i32
χ4611111111-1-1-1-111-1-111-1-1111111-1-11-11-1−1+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+i321−i321−i32−1+i32−1+i32−1+i32−1+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+i321+i321+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+i32−1−i321+i32−1−i321+i32
χ4711111111-1-1-1-1-1-111-1-111-1-1-1-1111-1111-1−1+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−i321−i321−i32−1+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−i321+i321+i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i321+i32−1−i32−1−i32−1−i321+i32
χ4811111111-1-1-1-1-1-111-1-1-1-11111-1-1-1111-11−1+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−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−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+i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i32−1−i321+i32−1−i32
χ4922-22-2-2-222-2000000002i−2i2i−2i0000000000−1+i3−1+i31−i3−1+i31−i31−i31−i3−1+i3−1+i31−i3000000002ζ7−2ζ72ζ7−2ζ70000000000−1−i3−1−i31+i3−1−i31+i31+i31+i3−1−i3−1−i31+i3000000002ζ11−2ζ112ζ11−2ζ110000000000
χ5022-22-2-2-222-200000000−2i2i−2i2i0000000000−1+i3−1+i31−i3−1+i31−i31−i31−i3−1+i3−1+i31−i300000000−2ζ72ζ7−2ζ72ζ70000000000−1−i3−1−i31+i3−1−i31+i31+i31+i3−1−i3−1−i31+i300000000−2ζ112ζ11−2ζ112ζ110000000000
χ5122-22-2-2-22-22000000002i−2i−2i2i0000000000−1+i3−1+i31−i3−1+i31−i31−i31−i3−1+i31−i3−1+i3000000002ζ7−2ζ7−2ζ72ζ70000000000−1−i3−1−i31+i3−1−i31+i31+i31+i3−1−i31+i3−1−i3000000002ζ11−2ζ11−2ζ112ζ110000000000
χ5222-22-2-2-22-2200000000−2i2i2i−2i0000000000−1+i3−1+i31−i3−1+i31−i31−i31−i3−1+i31−i3−1+i300000000−2ζ72ζ72ζ7−2ζ70000000000−1−i3−1−i31+i3−1−i31+i31+i31+i3−1−i31+i3−1−i300000000−2ζ112ζ112ζ11−2ζ110000000000
χ5322-2-222-2-2000000002-200002i−2i2i−2i000000−1+i3−1+i31−i31−i3−1+i3−1+i31−i31−i300000000−1+i31−i300002ζ7−2ζ72ζ7−2ζ7000000−1−i3−1−i31+i31+i3−1−i3−1−i31+i31+i300000000−1−i31+i300002ζ11−2ζ112ζ11−2ζ11000000
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χ912-2-2-22-22200-222-2-220000000000000000−1−i31+i31+i31+i3−1−i31+i3−1−i3−1−i3001+i3−1−i3−1−i31+i31+i3−1−i30000000000000000−1+i31−i31−i31−i3−1+i31−i3−1+i3−1+i3001−i3−1+i3−1+i31−i31−i3−1+i30000000000000000
χ922-2-2-22-22200-22-222-20000000000000000−1−i31+i31+i31+i3−1−i31+i3−1−i3−1−i3001+i3−1−i31+i3−1−i3−1−i31+i30000000000000000−1+i31−i31−i31−i3−1+i31−i3−1+i3−1+i3001−i3−1+i31−i3−1+i3−1+i31−i30000000000000000
χ93444-4-4-44-4000000000000000000000000−2−2i3−2−2i3−2−2i32+2i32+2i32+2i3−2−2i32+2i3000000000000000000000000−2+2i3−2+2i3−2+2i32−2i32−2i32−2i3−2+2i32−2i3000000000000000000000000
χ944-4444-4-4-4000000000000000000000000−2−2i32+2i3−2−2i3−2−2i3−2−2i32+2i32+2i32+2i3000000000000000000000000−2+2i32−2i3−2+2i3−2+2i3−2+2i32−2i32−2i32−2i3000000000000000000000000
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
χ964-4-44-444-4000000000000000000000000−2−2i32+2i32+2i3−2−2i32+2i3−2−2i3−2−2i32+2i3000000000000000000000000−2+2i32−2i32−2i3−2+2i32−2i3−2+2i3−2+2i32−2i3000000000000000000000000

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