Finite Group Databasebeta

← Group #5871

Character table — Group #5871

Order 192.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66
size111122222244444444444411112222224444444444441111222222444444444444
order1222444444244444444444366612121212121261212121212121212121212366612121212121261212121212121212121212
χ1111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111-1-1-1-11-1-1-1-11111111111111-1-1-1-11-1-1-1-11111111111111-1-1-1-11-1-1-1-1
χ31111111111-1-1-111-1-1-111-1-11111111111-1-1-111-1-1-111-1-11111111111-1-1-111-1-1-111-1-1
χ41111111111-1-1-1-1-111-1-1-1111111111111-1-1-1-1-111-1-1-1111111111111-1-1-1-1-111-1-1-111
χ5111111-1-1-1-111-11-11-1-11-11-1111111-1-1-1-111-11-11-1-11-11-1111111-1-1-1-111-11-11-1-11-11-1
χ6111111-1-1-1-111-1-11-11-1-11-11111111-1-1-1-111-1-11-11-1-11-11111111-1-1-1-111-1-11-11-1-11-11
χ7111111-1-1-1-1-1-111-1-1111-1-11111111-1-1-1-1-1-111-1-1111-1-11111111-1-1-1-1-1-111-1-1111-1-11
χ8111111-1-1-1-1-1-11-111-11-111-1111111-1-1-1-1-1-11-111-11-111-1111111-1-1-1-1-1-11-111-11-111-1
χ91111-1-111-1-11-111-1-11-1-111-11111-1-111-1-11-111-1-11-1-111-11111-1-111-1-11-111-1-11-1-111-1
χ101111-1-111-1-11-11-111-1-11-1-111111-1-111-1-11-11-111-1-11-1-111111-1-111-1-11-11-111-1-11-1-11
χ111111-1-111-1-1-11-11-11-11-11-111111-1-111-1-1-11-11-11-11-11-111111-1-111-1-1-11-11-11-11-11-11
χ121111-1-111-1-1-11-1-11-1111-11-11111-1-111-1-1-11-1-11-1111-11-11111-1-111-1-1-11-1-11-1111-11-1
χ131111-1-1-1-1111-1-111-1-11-1-1111111-1-1-1-1111-1-111-1-11-1-1111111-1-1-1-1111-1-111-1-11-1-111
χ141111-1-1-1-1111-1-1-1-111111-1-11111-1-1-1-1111-1-1-1-111111-1-11111-1-1-1-1111-1-1-1-111111-1-1
χ151111-1-1-1-111-1111111-1-1-1-1-11111-1-1-1-111-1111111-1-1-1-1-11111-1-1-1-111-1111111-1-1-1-1-1
χ161111-1-1-1-111-111-1-1-1-1-111111111-1-1-1-111-111-1-1-1-1-111111111-1-1-1-111-111-1-1-1-1-11111
χ172-2-222i−2i2i−2i2-20000000000002-2-222i−2i2i−2i2-20000000000002-2-222i−2i2i−2i2-2000000000000
χ182-2-222i−2i−2i2i-220000000000002-2-222i−2i−2i2i-220000000000002-2-222i−2i−2i2i-22000000000000
χ192-2-22−2i2i2i−2i-220000000000002-2-22−2i2i2i−2i-220000000000002-2-22−2i2i2i−2i-22000000000000
χ202-2-22−2i2i−2i2i2-20000000000002-2-22−2i2i−2i2i2-20000000000002-2-22−2i2i−2i2i2-2000000000000
χ2144-4-400000000000000000044-4-400000000000000000044-4-4000000000000000000
χ224-44-40000000000000000004-44-40000000000000000004-44-4000000000000000000
χ231111111111111111111111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32
χ241111111111111-1-1-1-11-1-1-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+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+i321+i321+i32−1−i321+i321+i321+i321+i32
χ251111111111-1-1-111-1-1-111-1-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i32−1+i32−1+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−i321+i321+i321+i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i321+i321+i32
χ261111111111-1-1-1-1-111-1-1-111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−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+i321+i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i32
χ27111111-1-1-1-111-11-11-1-11-11-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−i32−1+i321−i32−1+i321−i321−i32−1+i321−i32−1+i321−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i32−1−i321+i32−1−i321+i321+i32−1−i321+i32−1−i321+i32
χ28111111-1-1-1-111-1-11-11-1-11-11−1+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−i321−i32−1+i321−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−i321+i32−1−i321+i321+i32−1−i321+i32−1−i32
χ29111111-1-1-1-1-1-111-1-1111-1-11−1+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+i321−i321−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−i321+i321+i32−1−i32
χ30111111-1-1-1-1-1-11-111-11-111-1−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1+i321−i32−1+i32−1+i321−i32−1+i321−i32−1+i32−1+i321−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i321+i32−1−i32−1−i321+i32−1−i321+i32−1−i32−1−i321+i32
χ311111-1-111-1-11-111-1-11-1-111-1−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+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+i32−1−i32−1−i321+i321+i32−1−i321+i32−1−i32−1−i321+i321+i32−1−i321+i321+i32−1−i32−1−i321+i32
χ321111-1-111-1-11-11-111-1-11-1-11−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i321−i32−1+i321−i32−1+i32−1+i321−i321−i32−1+i321−i321−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−i321+i321+i32−1−i321+i321+i32−1−i32
χ331111-1-111-1-1-11-11-11-11-11-11−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i321−i32−1+i321−i32−1+i321−i32−1+i321−i32−1+i321−i32−1+i321−i32−1+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i321+i32−1−i321+i32−1−i321+i32−1−i321+i32−1−i321+i32−1−i321+i32−1−i32
χ341111-1-111-1-1-11-1-11-1111-11-1−1+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+i321−i32−1+i321−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−i321+i32−1−i321+i32
χ351111-1-1-1-1111-1-111-1-11-1-111−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i321−i321−i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i321+i321+i32−1−i32−1−i32
χ361111-1-1-1-1111-1-1-1-111111-1-1−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i321−i321−i321−i321−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−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i32
χ371111-1-1-1-111-1111111-1-1-1-1-1−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−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−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i32
χ381111-1-1-1-111-111-1-1-1-1-11111−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−i32−1+i32−1+i321−i321−i321−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+i32−1−i32−1−i321+i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i32
χ392-2-222i−2i2i−2i2-2000000000000−1+i31−i31−i3−1+i32ζ7−2ζ72ζ7−2ζ7−1+i31−i3000000000000−1−i31+i31+i3−1−i32ζ11−2ζ112ζ11−2ζ11−1−i31+i3000000000000
χ402-2-222i−2i−2i2i-22000000000000−1+i31−i31−i3−1+i32ζ7−2ζ7−2ζ72ζ71−i3−1+i3000000000000−1−i31+i31+i3−1−i32ζ11−2ζ11−2ζ112ζ111+i3−1−i3000000000000
χ412-2-22−2i2i2i−2i-22000000000000−1+i31−i31−i3−1+i3−2ζ72ζ72ζ7−2ζ71−i3−1+i3000000000000−1−i31+i31+i3−1−i3−2ζ112ζ112ζ11−2ζ111+i3−1−i3000000000000
χ422-2-22−2i2i−2i2i2-2000000000000−1+i31−i31−i3−1+i3−2ζ72ζ7−2ζ72ζ7−1+i31−i3000000000000−1−i31+i31+i3−1−i3−2ζ112ζ11−2ζ112ζ11−1−i31+i3000000000000
χ4344-4-4000000000000000000−2+2i3−2+2i32−2i32−2i3000000000000000000−2−2i3−2−2i32+2i32+2i3000000000000000000
χ444-44-4000000000000000000−2+2i32−2i3−2+2i32−2i3000000000000000000−2−2i32+2i3−2−2i32+2i3000000000000000000
χ451111111111111111111111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32
χ461111111111111-1-1-1-11-1-1-1-1−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−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−i321−i321−i32−1+i321−i321−i321−i321−i32
χ471111111111-1-1-111-1-1-111-1-1−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i32−1−i32−1−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+i321−i321−i321−i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i321−i321−i32
χ481111111111-1-1-1-1-111-1-1-111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+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−i321−i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i32
χ49111111-1-1-1-111-11-11-1-11-11-1−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i32−1−i321+i32−1−i321+i321+i32−1−i321+i32−1−i321+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321−i32−1+i321−i32−1+i321−i321−i32−1+i321−i32−1+i321−i32
χ50111111-1-1-1-111-1-11-11-1-11-11−1−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+i321+i32−1−i321+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+i321−i32−1+i321−i321−i32−1+i321−i32−1+i32
χ51111111-1-1-1-1-1-111-1-1111-1-11−1−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−i321+i321+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+i321−i321−i32−1+i32
χ52111111-1-1-1-1-1-11-111-11-111-1−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i321+i321+i32−1−i321+i32−1−i32−1−i321+i32−1−i321+i32−1−i32−1−i321+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i321−i32−1+i321−i32−1+i32−1+i321−i32−1+i321−i32−1+i32−1+i321−i32
χ531111-1-111-1-11-111-1-11-1-111-1−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−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−i32−1+i32−1+i321−i321−i32−1+i321−i32−1+i32−1+i321−i321−i32−1+i321−i321−i32−1+i32−1+i321−i32
χ541111-1-111-1-11-11-111-1-11-1-11−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i321+i32−1−i321+i32−1−i32−1−i321+i321+i32−1−i321+i321+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+i321−i321−i32−1+i321−i321−i32−1+i32
χ551111-1-111-1-1-11-11-11-11-11-11−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i321+i32−1−i321+i32−1−i321+i32−1−i321+i32−1−i321+i32−1−i321+i32−1−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i321−i32−1+i321−i32−1+i321−i32−1+i321−i32−1+i321−i32−1+i321−i32−1+i32
χ561111-1-111-1-1-11-1-11-1111-11-1−1−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−i321+i32−1−i321+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+i321−i32−1+i321−i32
χ571111-1-1-1-1111-1-111-1-11-1-111−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i321+i321+i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i321−i321−i32−1+i32−1+i32
χ581111-1-1-1-1111-1-1-1-111111-1-1−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1−i321+i321+i321+i321+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+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32−1+i321−i321−i32
χ591111-1-1-1-111-1111111-1-1-1-1-1−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321+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+i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i321−i32
χ601111-1-1-1-111-111-1-1-1-1-11111−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321+i32−1−i32−1−i321+i321+i321+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−i32−1+i32−1+i321−i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i32
χ612-2-222i−2i2i−2i2-2000000000000−1−i31+i31+i3−1−i32ζ11−2ζ112ζ11−2ζ11−1−i31+i3000000000000−1+i31−i31−i3−1+i32ζ7−2ζ72ζ7−2ζ7−1+i31−i3000000000000
χ622-2-222i−2i−2i2i-22000000000000−1−i31+i31+i3−1−i32ζ11−2ζ11−2ζ112ζ111+i3−1−i3000000000000−1+i31−i31−i3−1+i32ζ7−2ζ7−2ζ72ζ71−i3−1+i3000000000000
χ632-2-22−2i2i2i−2i-22000000000000−1−i31+i31+i3−1−i3−2ζ112ζ112ζ11−2ζ111+i3−1−i3000000000000−1+i31−i31−i3−1+i3−2ζ72ζ72ζ7−2ζ71−i3−1+i3000000000000
χ642-2-22−2i2i−2i2i2-2000000000000−1−i31+i31+i3−1−i3−2ζ112ζ11−2ζ112ζ11−1−i31+i3000000000000−1+i31−i31−i3−1+i3−2ζ72ζ7−2ζ72ζ7−1+i31−i3000000000000
χ6544-4-4000000000000000000−2−2i3−2−2i32+2i32+2i3000000000000000000−2+2i3−2+2i32−2i32−2i3000000000000000000
χ664-44-4000000000000000000−2−2i32+2i3−2−2i32+2i3000000000000000000−2+2i32−2i3−2+2i32−2i3000000000000000000

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