Finite Group Databasebeta

← Group #84652

Character table — Group #84652

Order 384.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72C73C74C75C76C77C78C79C80C81C82C83C84C85C86C87C88C89C90C91C92C93C94C95C96
size111111114444444444444444448888881111111144444444444444444488888811111111444444444444444444888888
order12222222224444444444444444444444366666666612121212121212121212121212121212121212121212366666666612121212121212121212121212121212121212121212
χ1111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111-1-111-1-1-1-1-1-11-11-1-1-11111111111111111-1-111-1-1-1-1-1-11-11-1-1-11111111111111111-1-111-1-1-1-1-1-11-11-1-1-1
χ311111111111111-1-111-1-111-1-1-1-1-11-11-1-111111111111111-1-111-1-111-1-1-1-1-11-11-1-111111111111111-1-111-1-111-1-1-1-1-11-11-1-1
χ411111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111111111111111-1-1-1-1-1-1-1-11111-1-1-1-111
χ51111111111-1-1-1-11111-1-1-1-11111-1-111-1-11111111111-1-1-1-11111-1-1-1-11111-1-111-1-11111111111-1-1-1-11111-1-1-1-11111-1-111-1-1
χ61111111111-1-1-1-111-1-1-1-111-1-1-1-1-111-1111111111111-1-1-1-111-1-1-1-111-1-1-1-1-111-1111111111111-1-1-1-111-1-1-1-111-1-1-1-1-111-111
χ71111111111-1-1-1-1-1-11111-1-1-1-1-1-11-1-11111111111111-1-1-1-1-1-11111-1-1-1-1-1-11-1-11111111111111-1-1-1-1-1-11111-1-1-1-1-1-11-1-1111
χ81111111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1
χ911111111-1-111-1-1111111-1-111-1-1-11-1-11-111111111-1-111-1-1111111-1-111-1-1-11-1-11-111111111-1-111-1-1111111-1-111-1-1-11-1-11-1
χ1011111111-1-111-1-111-1-11111-1-111-1-1-11-1111111111-1-111-1-111-1-11111-1-111-1-1-11-1111111111-1-111-1-111-1-11111-1-111-1-1-11-11
χ1111111111-1-111-1-1-1-111-1-1-1-1-1-111111-1-1111111111-1-111-1-1-1-111-1-1-1-1-1-111111-1-1111111111-1-111-1-1-1-111-1-1-1-1-1-111111-1-11
χ1211111111-1-111-1-1-1-1-1-1-1-11111-1-11-1111-111111111-1-111-1-1-1-1-1-1-1-11111-1-11-1111-111111111-1-111-1-1-1-1-1-1-1-11111-1-11-1111-1
χ1311111111-1-1-1-1111111-1-11111-1-11-1-1-1-1111111111-1-1-1-1111111-1-11111-1-11-1-1-1-1111111111-1-1-1-1111111-1-11111-1-11-1-1-1-11
χ1411111111-1-1-1-11111-1-1-1-1-1-1-1-11111-111-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-111-111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-111-1
χ1511111111-1-1-1-111-1-1111111-1-111-1-11-11-111111111-1-1-1-111-1-1111111-1-111-1-11-11-111111111-1-1-1-111-1-1111111-1-111-1-11-11-1
χ1611111111-1-1-1-111-1-1-1-111-1-111-1-1-1111-1111111111-1-1-1-111-1-1-1-111-1-111-1-1-1111-1111111111-1-1-1-111-1-1-1-111-1-111-1-1-1111-11
χ172222-2-2-2-22-22-22-20000000000000000002222-2-2-2-22-22-22-20000000000000000002222-2-2-2-22-22-22-2000000000000000000
χ182222-2-2-2-22-2-22-220000000000000000002222-2-2-2-22-2-22-220000000000000000002222-2-2-2-22-2-22-22000000000000000000
χ192222-2-2-2-2-222-2-220000000000000000002222-2-2-2-2-222-2-220000000000000000002222-2-2-2-2-222-2-22000000000000000000
χ202222-2-2-2-2-22-222-20000000000000000002222-2-2-2-2-22-222-20000000000000000002222-2-2-2-2-22-222-2000000000000000000
χ212-22-22-22-20000002i−2i2i−2i00002-2000000002-22-22-22-20000002i−2i2i−2i00002-2000000002-22-22-22-20000002i−2i2i−2i00002-200000000
χ222-22-22-22-20000002i−2i−2i2i0000-22000000002-22-22-22-20000002i−2i−2i2i0000-22000000002-22-22-22-20000002i−2i−2i2i0000-2200000000
χ232-22-22-22-2000000−2i2i2i−2i0000-22000000002-22-22-22-2000000−2i2i2i−2i0000-22000000002-22-22-22-2000000−2i2i2i−2i0000-2200000000
χ242-22-22-22-2000000−2i2i−2i2i00002-2000000002-22-22-22-2000000−2i2i−2i2i00002-2000000002-22-22-22-2000000−2i2i−2i2i00002-200000000
χ252-2-222-2-2200000000002-22i−2i002i−2i0000002-2-222-2-2200000000002-22i−2i002i−2i0000002-2-222-2-2200000000002-22i−2i002i−2i000000
χ262-2-222-2-2200000000002-2−2i2i00−2i2i0000002-2-222-2-2200000000002-2−2i2i00−2i2i0000002-2-222-2-2200000000002-2−2i2i00−2i2i000000
χ272-2-222-2-220000000000-222i−2i00−2i2i0000002-2-222-2-220000000000-222i−2i00−2i2i0000002-2-222-2-220000000000-222i−2i00−2i2i000000
χ282-2-222-2-220000000000-22−2i2i002i−2i0000002-2-222-2-220000000000-22−2i2i002i−2i0000002-2-222-2-220000000000-22−2i2i002i−2i000000
χ2944-4-444-4-400000000000000000000000044-4-444-4-400000000000000000000000044-4-444-4-4000000000000000000000000
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
χ324-4-44-444-40000000000000000000000004-4-44-444-40000000000000000000000004-4-44-444-4000000000000000000000000
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
χ341111111111111111-1-111-1-1-1-1-1-11-11-1-1-1−1+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−i32−1+i32−1+i321−i321−i321−i321−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+i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i321+i32−1−i321+i321+i321+i32
χ3511111111111111-1-111-1-111-1-1-1-1-11-11-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−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−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i321+i321+i321+i32−1−i321+i32−1−i321+i321+i32
χ3611111111111111-1-1-1-1-1-1-1-11111-1-1-1-111−1+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
χ371111111111-1-1-1-11111-1-1-1-11111-1-111-1-1−1+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+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−i321+i321+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+i32
χ381111111111-1-1-1-111-1-1-1-111-1-1-1-1-111-111−1+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+i321−i321−i321−i321−i32−1+i32−1+i321−i321−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−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i321+i321+i321+i321+i32−1−i32−1−i321+i32−1−i32−1−i32
χ391111111111-1-1-1-1-1-11111-1-1-1-1-1-11-1-1111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−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+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i321+i321+i32−1−i32−1−i32−1−i32
χ401111111111-1-1-1-1-1-1-1-11111111111-1-1-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−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−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−i321+i321+i321+i321+i32
χ4111111111-1-111-1-1111111-1-111-1-1-11-1-11-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+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−i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i321+i32−1−i321+i321+i32−1−i321+i32
χ4211111111-1-111-1-111-1-11111-1-111-1-1-11-11−1+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+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−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+i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i321+i32−1−i321+i32−1−i32
χ4311111111-1-111-1-1-1-111-1-1-1-1-1-111111-1-11−1+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+i321−i321−i321−i321−i321−i321−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−i32−1−i321+i321+i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32
χ4411111111-1-111-1-1-1-1-1-1-1-11111-1-11-1111-1−1+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+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+i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i32−1−i32−1−i32−1−i321+i32
χ4511111111-1-1-1-1111111-1-11111-1-11-1-1-1-11−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+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−i321+i321+i321+i321+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−i321+i321+i321+i321+i32−1−i32
χ4611111111-1-1-1-11111-1-1-1-1-1-1-1-11111-111-1−1+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−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−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i32−1−i32−1−i321+i32
χ4711111111-1-1-1-111-1-1111111-1-111-1-11-11-1−1+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+i32−1+i32−1+i32−1+i32−1+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+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+i32−1−i321+i32−1−i321+i32
χ4811111111-1-1-1-111-1-1-1-111-1-111-1-1-1111-11−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−i321−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+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−i321+i32−1−i32
χ492222-2-2-2-22-22-22-2000000000000000000−1+i3−1+i3−1+i3−1+i31−i31−i31−i31−i3−1+i31−i3−1+i31−i3−1+i31−i3000000000000000000−1−i3−1−i3−1−i3−1−i31+i31+i31+i31+i3−1−i31+i3−1−i31+i3−1−i31+i3000000000000000000
χ502222-2-2-2-22-2-22-22000000000000000000−1+i3−1+i3−1+i3−1+i31−i31−i31−i31−i3−1+i31−i31−i3−1+i31−i3−1+i3000000000000000000−1−i3−1−i3−1−i3−1−i31+i31+i31+i31+i3−1−i31+i31+i3−1−i31+i3−1−i3000000000000000000
χ512222-2-2-2-2-222-2-22000000000000000000−1+i3−1+i3−1+i3−1+i31−i31−i31−i31−i31−i3−1+i3−1+i31−i31−i3−1+i3000000000000000000−1−i3−1−i3−1−i3−1−i31+i31+i31+i31+i31+i3−1−i3−1−i31+i31+i3−1−i3000000000000000000
χ522222-2-2-2-2-22-222-2000000000000000000−1+i3−1+i3−1+i3−1+i31−i31−i31−i31−i31−i3−1+i31−i3−1+i3−1+i31−i3000000000000000000−1−i3−1−i3−1−i3−1−i31+i31+i31+i31+i31+i3−1−i31+i3−1−i3−1−i31+i3000000000000000000
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χ912-2-222-2-220000000000-222i−2i00−2i2i000000−1−i31+i31+i3−1−i3−1−i31+i31+i3−1−i300000000001+i3−1−i32ζ11−2ζ1100−2ζ112ζ11000000−1+i31−i31−i3−1+i3−1+i31−i31−i3−1+i300000000001−i3−1+i32ζ7−2ζ700−2ζ72ζ7000000
χ922-2-222-2-220000000000-22−2i2i002i−2i000000−1−i31+i31+i3−1−i3−1−i31+i31+i3−1−i300000000001+i3−1−i3−2ζ112ζ11002ζ11−2ζ11000000−1+i31−i31−i3−1+i3−1+i31−i31−i3−1+i300000000001−i3−1+i3−2ζ72ζ7002ζ7−2ζ7000000
χ9344-4-444-4-4000000000000000000000000−2−2i3−2−2i32+2i32+2i3−2−2i3−2−2i32+2i32+2i3000000000000000000000000−2+2i3−2+2i32−2i32−2i3−2+2i3−2+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
χ964-4-44-444-4000000000000000000000000−2−2i32+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.