Finite Group Databasebeta

← Group #84656

Character table — Group #84656

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size111111114444444444444444448888881111111144444444444444444488888811111111444444444444444444888888
order122222224444444444444444444444443666666612121212121212121212121212121212121212121212121236666666121212121212121212121212121212121212121212121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111-1-1-1-1-1-111-1-11-11-1-1-11111111111111111-1-1-1-1-1-111-1-11-11-1-1-11111111111111111-1-1-1-1-1-111-1-11-11-1-1-1
χ3111111111111-1-1-1-11111-1-1-1-111-111-1-1-1111111111111-1-1-1-11111-1-1-1-111-111-1-1-1111111111111-1-1-1-11111-1-1-1-111-111-1-1-1
χ4111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111
χ51111111111-1-1111111-1-111-1-1-1-1-11-11-1-11111111111-1-1111111-1-111-1-1-1-1-11-11-1-11111111111-1-1111111-1-111-1-1-1-1-11-11-1-1
χ61111111111-1-11111-1-111-1-1-1-111-1-1-1-1111111111111-1-11111-1-111-1-1-1-111-1-1-1-1111111111111-1-11111-1-111-1-1-1-111-1-1-1-111
χ71111111111-1-1-1-1-1-111-1-1-1-111-1-111-1-1111111111111-1-1-1-1-1-111-1-1-1-111-1-111-1-1111111111111-1-1-1-1-1-111-1-1-1-111-1-111-1-111
χ81111111111-1-1-1-1-1-1-1-1111111111-1-11-1-11111111111-1-1-1-1-1-1-1-1111111111-1-11-1-11111111111-1-1-1-1-1-1-1-1111111111-1-11-1-1
χ911111111-1-11111-1-1111111-1-1-1-11-1-1-11-111111111-1-11111-1-1111111-1-1-1-11-1-1-11-111111111-1-11111-1-1111111-1-1-1-11-1-1-11-1
χ1011111111-1-11111-1-1-1-1-1-1-1-1-1-11111-11-1111111111-1-11111-1-1-1-1-1-1-1-1-1-11111-11-1111111111-1-11111-1-1-1-1-1-1-1-1-1-11111-11-11
χ1111111111-1-111-1-1111111-1-111-1-1-1-1-11-1111111111-1-111-1-1111111-1-111-1-1-1-1-11-1111111111-1-111-1-1111111-1-111-1-1-1-1-11-11
χ1211111111-1-111-1-111-1-1-1-1111111-11-1-11-111111111-1-111-1-111-1-1-1-1111111-11-1-11-111111111-1-111-1-111-1-1-1-1111111-11-1-11-1
χ1311111111-1-1-1-111-1-111-1-1111111-1-11-1-1111111111-1-1-1-111-1-111-1-1111111-1-11-1-1111111111-1-1-1-111-1-111-1-1111111-1-11-1-11
χ1411111111-1-1-1-111-1-1-1-111-1-111-1-1-11111-111111111-1-1-1-111-1-1-1-111-1-111-1-1-11111-111111111-1-1-1-111-1-1-1-111-1-111-1-1-11111-1
χ1511111111-1-1-1-1-1-11111-1-1-1-1-1-1111-1111-111111111-1-1-1-1-1-11111-1-1-1-1-1-1111-1111-111111111-1-1-1-1-1-11111-1-1-1-1-1-1111-1111-1
χ1611111111-1-1-1-1-1-111-1-11111-1-1-1-1111-1-1111111111-1-1-1-1-1-111-1-11111-1-1-1-1111-1-1111111111-1-1-1-1-1-111-1-11111-1-1-1-1111-1-11
χ17222-22-2-2-2002-200002-22-2000000000000222-22-2-2-2002-200002-22-2000000000000222-22-2-2-2002-200002-22-2000000000000
χ18222-22-2-2-2002-20000-22-22000000000000222-22-2-2-2002-20000-22-22000000000000222-22-2-2-2002-20000-22-22000000000000
χ19222-22-2-2-200-2200002-2-22000000000000222-22-2-2-200-2200002-2-22000000000000222-22-2-2-200-2200002-2-22000000000000
χ20222-22-2-2-200-220000-222-2000000000000222-22-2-2-200-220000-222-2000000000000222-22-2-2-200-220000-222-2000000000000
χ2122-22-22-2-22-2002-22-2000000000000000022-22-22-2-22-2002-22-2000000000000000022-22-22-2-22-2002-22-20000000000000000
χ2222-22-22-2-22-200-22-22000000000000000022-22-22-2-22-200-22-22000000000000000022-22-22-2-22-200-22-220000000000000000
χ2322-22-22-2-2-22002-2-22000000000000000022-22-22-2-2-22002-2-22000000000000000022-22-22-2-2-22002-2-220000000000000000
χ2422-22-22-2-2-2200-222-2000000000000000022-22-22-2-2-2200-222-2000000000000000022-22-22-2-2-2200-222-20000000000000000
χ252-2-2-2222-20000000000002-22i−2i2i−2i0000002-2-2-2222-20000000000002-22i−2i2i−2i0000002-2-2-2222-20000000000002-22i−2i2i−2i000000
χ262-2-2-2222-20000000000002-2−2i2i−2i2i0000002-2-2-2222-20000000000002-2−2i2i−2i2i0000002-2-2-2222-20000000000002-2−2i2i−2i2i000000
χ272-2-2-2222-2000000000000-222i−2i−2i2i0000002-2-2-2222-2000000000000-222i−2i−2i2i0000002-2-2-2222-2000000000000-222i−2i−2i2i000000
χ282-2-2-2222-2000000000000-22−2i2i2i−2i0000002-2-2-2222-2000000000000-22−2i2i2i−2i0000002-2-2-2222-2000000000000-22−2i2i2i−2i000000
χ2944-4-4-4-44400000000000000000000000044-4-4-4-44400000000000000000000000044-4-4-4-444000000000000000000000000
χ304-444-4-44-40000000000000000000000004-444-4-44-40000000000000000000000004-444-4-44-4000000000000000000000000
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
χ341111111111111111-1-1-1-1-1-111-1-11-11-1-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−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−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i321+i32−1−i321+i321+i321+i32
χ35111111111111-1-1-1-11111-1-1-1-111-111-1-1-1−1+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−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+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−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+i32−1−i32−1−i321+i321+i321+i32
χ36111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i321−i321−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−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+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32
χ371111111111-1-1111111-1-111-1-1-1-1-11-11-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−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−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+i321+i321+i321+i32−1−i321+i32−1−i321+i321+i32
χ381111111111-1-11111-1-111-1-1-1-111-1-1-1-111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−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−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−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32
χ391111111111-1-1-1-1-1-111-1-1-1-111-1-111-1-111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−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−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−i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32
χ401111111111-1-1-1-1-1-1-1-1111111111-1-11-1-1−1+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+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−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−i321+i321+i32−1−i321+i321+i32
χ4111111111-1-11111-1-1111111-1-1-1-11-1-1-11-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i321−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−i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i321+i321+i321+i32−1−i321+i32
χ4211111111-1-11111-1-1-1-1-1-1-1-1-1-11111-11-11−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i321−i321−i321−i321−i32−1+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−i32−1−i321+i321+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−i321+i32−1−i321+i32−1−i32
χ4311111111-1-111-1-1111111-1-111-1-1-1-1-11-11−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+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−i321+i321+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+i321+i321+i321+i32−1−i321+i32−1−i32
χ4411111111-1-111-1-111-1-1-1-1111111-11-1-11-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+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−i321+i321+i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i32−1−i321+i321+i32−1−i321+i32
χ4511111111-1-1-1-111-1-111-1-1111111-1-11-1-11−1+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+i321−i321−i32−1+i32−1+i32−1+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−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+i321+i32−1−i32
χ4611111111-1-1-1-111-1-1-1-111-1-111-1-1-11111-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i321−i32−1+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+i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i32
χ4711111111-1-1-1-1-1-11111-1-1-1-1-1-1111-1111-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−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−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i321+i32−1−i32−1−i32−1−i321+i32
χ4811111111-1-1-1-1-1-111-1-11111-1-1-1-1111-1-11−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−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+i321−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−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i321+i321+i32−1−i32
χ49222-22-2-2-2002-200002-22-2000000000000−1+i3−1+i3−1+i31−i3−1+i31−i31−i31−i300−1+i31−i30000−1+i31−i3−1+i31−i3000000000000−1−i3−1−i3−1−i31+i3−1−i31+i31+i31+i300−1−i31+i30000−1−i31+i3−1−i31+i3000000000000
χ50222-22-2-2-2002-20000-22-22000000000000−1+i3−1+i3−1+i31−i3−1+i31−i31−i31−i300−1+i31−i300001−i3−1+i31−i3−1+i3000000000000−1−i3−1−i3−1−i31+i3−1−i31+i31+i31+i300−1−i31+i300001+i3−1−i31+i3−1−i3000000000000
χ51222-22-2-2-200-2200002-2-22000000000000−1+i3−1+i3−1+i31−i3−1+i31−i31−i31−i3001−i3−1+i30000−1+i31−i31−i3−1+i3000000000000−1−i3−1−i3−1−i31+i3−1−i31+i31+i31+i3001+i3−1−i30000−1−i31+i31+i3−1−i3000000000000
χ52222-22-2-2-200-220000-222-2000000000000−1+i3−1+i3−1+i31−i3−1+i31−i31−i31−i3001−i3−1+i300001−i3−1+i3−1+i31−i3000000000000−1−i3−1−i3−1−i31+i3−1−i31+i31+i31+i3001+i3−1−i300001+i3−1−i3−1−i31+i3000000000000
χ5322-22-22-2-22-2002-22-20000000000000000−1+i3−1+i31−i3−1+i31−i3−1+i31−i31−i3−1+i31−i300−1+i31−i3−1+i31−i30000000000000000−1−i3−1−i31+i3−1−i31+i3−1−i31+i31+i3−1−i31+i300−1−i31+i3−1−i31+i30000000000000000
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χ912-2-2-2222-2000000000000-222i−2i−2i2i000000−1−i31+i31+i31+i3−1−i3−1−i3−1−i31+i30000000000001+i3−1−i32ζ11−2ζ11−2ζ112ζ11000000−1+i31−i31−i31−i3−1+i3−1+i3−1+i31−i30000000000001−i3−1+i32ζ7−2ζ7−2ζ72ζ7000000
χ922-2-2-2222-2000000000000-22−2i2i2i−2i000000−1−i31+i31+i31+i3−1−i3−1−i3−1−i31+i30000000000001+i3−1−i3−2ζ112ζ112ζ11−2ζ11000000−1+i31−i31−i31−i3−1+i3−1+i3−1+i31−i30000000000001−i3−1+i3−2ζ72ζ72ζ7−2ζ7000000
χ9344-4-4-4-444000000000000000000000000−2−2i3−2−2i32+2i32+2i32+2i32+2i3−2−2i3−2−2i3000000000000000000000000−2+2i3−2+2i32−2i32−2i32−2i32−2i3−2+2i3−2+2i3000000000000000000000000
χ944-444-4-44-4000000000000000000000000−2−2i32+2i3−2−2i3−2−2i32+2i32+2i3−2−2i32+2i3000000000000000000000000−2+2i32−2i3−2+2i3−2+2i32−2i32−2i3−2+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
χ964-4-444-4-44000000000000000000000000−2−2i32+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.