Finite Group Databasebeta

← Group #72222712

Character table — Group #72222712

Order 2304.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65C66C67C68C69C70C71C72
size1133441212121216161616161616163399121236363636484848484848484844121216164848484864646464646464644412121616484848486464646464646464
order12222244443366666622222244446666666636666612121212336666663666661212121233666666
χ1111111111111111111111111111111111111111111111111111111111111111111111111
χ21111111111−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321111111111−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321111111111−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321111111111−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32
χ31111111111−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321111111111−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321111111111−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321111111111−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32
χ41111-1-111-1-1111-1-11-1-11111-1-111-1-1111-1-11-1-11111-1-111-1-1111-1-11-1-11111-1-111-1-1111-1-11-1-1
χ51111-1-111-1-1−1−i32−1+i32−1−i321+i321+i32−1+i321−i321−i321111-1-111-1-1−1−i32−1+i32−1−i321+i321+i32−1+i321−i321−i321111-1-111-1-1−1−i32−1+i32−1−i321+i321+i32−1+i321−i321−i321111-1-111-1-1−1−i32−1+i32−1−i321+i321+i32−1+i321−i321−i32
χ61111-1-111-1-1−1+i32−1−i32−1+i321−i321−i32−1−i321+i321+i321111-1-111-1-1−1+i32−1−i32−1+i321−i321−i32−1−i321+i321+i321111-1-111-1-1−1+i32−1−i32−1+i321−i321−i32−1−i321+i321+i321111-1-111-1-1−1+i32−1−i32−1+i321−i321−i32−1−i321+i321+i32
χ72-22-22-20000-1-111-111-12-22-22-20000-1-111-111-12-22-22-20000-1-111-111-12-22-22-20000-1-111-111-1
χ82-22-22-200001+i321−i32−1−i32−1−i321+i32−1+i32−1+i321−i322-22-22-200001+i321−i32−1−i32−1−i321+i32−1+i32−1+i321−i322-22-22-200001+i321−i32−1−i32−1−i321+i32−1+i32−1+i321−i322-22-22-200001+i321−i32−1−i32−1−i321+i32−1+i32−1+i321−i32
χ92-22-22-200001−i321+i32−1+i32−1+i321−i32−1−i32−1−i321+i322-22-22-200001−i321+i32−1+i32−1+i321−i32−1−i32−1−i321+i322-22-22-200001−i321+i32−1+i32−1+i321−i32−1−i32−1−i321+i322-22-22-200001−i321+i32−1+i32−1+i321−i32−1−i32−1−i321+i32
χ102-22-2-220000-1-11-111-112-22-2-220000-1-11-111-112-22-2-220000-1-11-111-112-22-2-220000-1-11-111-11
χ112-22-2-2200001+i321−i32−1−i321+i32−1−i32−1+i321−i32−1+i322-22-2-2200001+i321−i32−1−i321+i32−1−i32−1+i321−i32−1+i322-22-2-2200001+i321−i32−1−i321+i32−1−i32−1+i321−i32−1+i322-22-2-2200001+i321−i32−1−i321+i32−1−i32−1+i321−i32−1+i32
χ122-22-2-2200001−i321+i32−1+i321−i32−1+i32−1−i321+i32−1−i322-22-2-2200001−i321+i32−1+i321−i32−1+i32−1−i321+i32−1−i322-22-2-2200001−i321+i32−1+i321−i32−1+i32−1−i321+i32−1−i322-22-2-2200001−i321+i32−1+i321−i32−1+i32−1−i321+i32−1−i32
χ13333333-1-1-1-100000000333333-1-1-1-100000000333333-1-1-1-100000000333333-1-1-1-100000000
χ143333-3-3-1-111000000003333-3-3-1-111000000003333-3-3-1-111000000003333-3-3-1-11100000000
χ1566-2-2002i−2i000000000066-2-2002i−2i000000000066-2-2002i−2i000000000066-2-2002i−2i0000000000
χ1666-2-200−2i2i000000000066-2-200−2i2i000000000066-2-200−2i2i000000000066-2-200−2i2i0000000000
χ176-6-2200002-2000000006-6-2200002-2000000006-6-2200002-2000000006-6-2200002-200000000
χ186-6-220000-22000000006-6-220000-22000000006-6-220000-22000000006-6-220000-2200000000
χ19111111111111111111111111111111111111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32
χ201111111111−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321111111111−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−1−i32111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i321−1+i32−1+i32−1+i32111
χ211111111111−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321111111111−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i321−1−i32−1−i32−1−i32111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321−1+i32111−1+i32−1+i32−1+i32
χ221111-1-111-1-1111-1-11-1-11111-1-111-1-1111-1-11-1-1−1+i32−1+i32−1+i32−1+i321−i321−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−i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i32−1−i321+i321+i32−1−i321+i321+i32
χ231111-1-111-1-1−1−i32−1+i32−1−i321+i321+i32−1+i321−i321−i321111-1-111-1-1−1−i32−1+i32−1−i321+i321+i32−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i321−1−i321-1-1−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1+i321−1+i321−i321−i321-1-1
χ241111-1-111-1-1−1+i32−1−i32−1+i321−i321−i32−1−i321+i321+i321111-1-111-1-1−1+i32−1−i32−1+i321−i321−i32−1−i321+i321+i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1−i321−1−i321+i321+i321-1-1−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i321−1+i321-1-1−1+i321−i321−i32
χ252-22-22-20000-1-111-111-12-22-22-20000-1-111-111-1−1+i31−i3−1+i31−i3−1+i31−i300001−i321−i32−1+i32−1+i321−i32−1+i32−1+i321−i32−1−i31+i3−1−i31+i3−1−i31+i300001+i321+i32−1−i32−1−i321+i32−1−i32−1−i321+i32
χ262-22-22-200001+i321−i32−1−i32−1−i321+i32−1+i32−1+i321−i322-22-22-200001+i321−i32−1−i32−1−i321+i32−1+i32−1+i321−i32−1+i31−i3−1+i31−i3−1+i31−i30000-11+i3211-1−1−i32−1−i321+i32−1−i31+i3−1−i31+i3−1−i31+i300001−i32-1−1+i32−1+i321−i3211-1
χ272-22-22-200001−i321+i32−1+i32−1+i321−i32−1−i32−1−i321+i322-22-22-200001−i321+i32−1+i32−1+i321−i32−1−i32−1−i321+i32−1+i31−i3−1+i31−i3−1+i31−i300001+i32-1−1−i32−1−i321+i3211-1−1−i31+i3−1−i31+i3−1−i31+i30000-11−i3211-1−1+i32−1+i321−i32
χ282-22-2-220000-1-11-111-112-22-2-220000-1-11-111-11−1+i31−i3−1+i31−i31−i3−1+i300001−i321−i32−1+i321−i32−1+i32−1+i321−i32−1+i32−1−i31+i3−1−i31+i31+i3−1−i300001+i321+i32−1−i321+i32−1−i32−1−i321+i32−1−i32
χ292-22-2-2200001+i321−i32−1−i321+i32−1−i32−1+i321−i32−1+i322-22-2-2200001+i321−i32−1−i321+i32−1−i32−1+i321−i32−1+i32−1+i31−i3−1+i31−i31−i3−1+i30000-11+i321-11−1−i321+i32−1−i32−1−i31+i3−1−i31+i31+i3−1−i300001−i32-1−1+i321−i32−1+i321-11
χ302-22-2-2200001−i321+i32−1+i321−i32−1+i32−1−i321+i32−1−i322-22-2-2200001−i321+i32−1+i321−i32−1+i32−1−i321+i32−1−i32−1+i31−i3−1+i31−i31−i3−1+i300001+i32-1−1−i321+i32−1−i321-11−1−i31+i3−1−i31+i31+i3−1−i30000-11−i321-11−1+i321−i32−1+i32
χ31333333-1-1-1-100000000333333-1-1-1-100000000−3+3i32−3+3i32−3+3i32−3+3i32−3+3i32−3+3i321−i321−i321−i321−i3200000000−3−3i32−3−3i32−3−3i32−3−3i32−3−3i32−3−3i321+i321+i321+i321+i3200000000
χ323333-3-3-1-111000000003333-3-3-1-11100000000−3+3i32−3+3i32−3+3i32−3+3i323−3i323−3i321−i321−i32−1+i32−1+i3200000000−3−3i32−3−3i32−3−3i32−3−3i323+3i323+3i321+i321+i32−1−i32−1−i3200000000
χ3366-2-2002i−2i000000000066-2-2002i−2i0000000000−3+3i3−3+3i31−i31−i3002ζ7−2ζ70000000000−3−3i3−3−3i31+i31+i3002ζ11−2ζ110000000000
χ3466-2-200−2i2i000000000066-2-200−2i2i0000000000−3+3i3−3+3i31−i31−i300−2ζ72ζ70000000000−3−3i3−3−3i31+i31+i300−2ζ112ζ110000000000
χ356-6-2200002-2000000006-6-2200002-200000000−3+3i33−3i31−i3−1+i30000−1+i31−i300000000−3−3i33+3i31+i3−1−i30000−1−i31+i300000000
χ366-6-220000-22000000006-6-220000-2200000000−3+3i33−3i31−i3−1+i300001−i3−1+i300000000−3−3i33+3i31+i3−1−i300001+i3−1−i300000000
χ37111111111111111111111111111111111111−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32
χ381111111111−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i321111111111−1−i32−1+i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i321−1+i32−1+i32−1+i32111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i321−1−i32111−1−i32−1−i32−1−i32
χ391111111111−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i321111111111−1+i32−1−i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i321−1+i32111−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i321−1−i32−1−i32−1−i32111
χ401111-1-111-1-1111-1-11-1-11111-1-111-1-1111-1-11-1-1−1−i32−1−i32−1−i32−1−i321+i321+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+i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i32−1+i321−i321−i32−1+i321−i321−i32
χ411111-1-111-1-1−1−i32−1+i32−1−i321+i321+i32−1+i321−i321−i321111-1-111-1-1−1−i32−1+i32−1−i321+i321+i32−1+i321−i321−i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1+i321−1+i321−i321−i321-1-1−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i321−1−i321-1-1−1−i321+i321+i32
χ421111-1-111-1-1−1+i32−1−i32−1+i321−i321−i32−1−i321+i321+i321111-1-111-1-1−1+i32−1−i32−1+i321−i321−i32−1−i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i321−1+i321-1-1−1+i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1−i321−1−i321+i321+i321-1-1
χ432-22-22-20000-1-111-111-12-22-22-20000-1-111-111-1−1−i31+i3−1−i31+i3−1−i31+i300001+i321+i32−1−i32−1−i321+i32−1−i32−1−i321+i32−1+i31−i3−1+i31−i3−1+i31−i300001−i321−i32−1+i32−1+i321−i32−1+i32−1+i321−i32
χ442-22-22-200001+i321−i32−1−i32−1−i321+i32−1+i32−1+i321−i322-22-22-200001+i321−i32−1−i32−1−i321+i32−1+i32−1+i321−i32−1−i31+i3−1−i31+i3−1−i31+i300001−i32-1−1+i32−1+i321−i3211-1−1+i31−i3−1+i31−i3−1+i31−i30000-11+i3211-1−1−i32−1−i321+i32
χ452-22-22-200001−i321+i32−1+i32−1+i321−i32−1−i32−1−i321+i322-22-22-200001−i321+i32−1+i32−1+i321−i32−1−i32−1−i321+i32−1−i31+i3−1−i31+i3−1−i31+i30000-11−i3211-1−1+i32−1+i321−i32−1+i31−i3−1+i31−i3−1+i31−i300001+i32-1−1−i32−1−i321+i3211-1
χ462-22-2-220000-1-11-111-112-22-2-220000-1-11-111-11−1−i31+i3−1−i31+i31+i3−1−i300001+i321+i32−1−i321+i32−1−i32−1−i321+i32−1−i32−1+i31−i3−1+i31−i31−i3−1+i300001−i321−i32−1+i321−i32−1+i32−1+i321−i32−1+i32
χ472-22-2-2200001+i321−i32−1−i321+i32−1−i32−1+i321−i32−1+i322-22-2-2200001+i321−i32−1−i321+i32−1−i32−1+i321−i32−1+i32−1−i31+i3−1−i31+i31+i3−1−i300001−i32-1−1+i321−i32−1+i321-11−1+i31−i3−1+i31−i31−i3−1+i30000-11+i321-11−1−i321+i32−1−i32
χ482-22-2-2200001−i321+i32−1+i321−i32−1+i32−1−i321+i32−1−i322-22-2-2200001−i321+i32−1+i321−i32−1+i32−1−i321+i32−1−i32−1−i31+i3−1−i31+i31+i3−1−i30000-11−i321-11−1+i321−i32−1+i32−1+i31−i3−1+i31−i31−i3−1+i300001+i32-1−1−i321+i32−1−i321-11
χ49333333-1-1-1-100000000333333-1-1-1-100000000−3−3i32−3−3i32−3−3i32−3−3i32−3−3i32−3−3i321+i321+i321+i321+i3200000000−3+3i32−3+3i32−3+3i32−3+3i32−3+3i32−3+3i321−i321−i321−i321−i3200000000
χ503333-3-3-1-111000000003333-3-3-1-11100000000−3−3i32−3−3i32−3−3i32−3−3i323+3i323+3i321+i321+i32−1−i32−1−i3200000000−3+3i32−3+3i32−3+3i32−3+3i323−3i323−3i321−i321−i32−1+i32−1+i3200000000
χ5166-2-2002i−2i000000000066-2-2002i−2i0000000000−3−3i3−3−3i31+i31+i3002ζ11−2ζ110000000000−3+3i3−3+3i31−i31−i3002ζ7−2ζ70000000000
χ5266-2-200−2i2i000000000066-2-200−2i2i0000000000−3−3i3−3−3i31+i31+i300−2ζ112ζ110000000000−3+3i3−3+3i31−i31−i300−2ζ72ζ70000000000
χ536-6-2200002-2000000006-6-2200002-200000000−3−3i33+3i31+i3−1−i30000−1−i31+i300000000−3+3i33−3i31−i3−1+i30000−1+i31−i300000000
χ546-6-220000-22000000006-6-220000-2200000000−3−3i33+3i31+i3−1−i300001+i3−1−i300000000−3+3i33−3i31−i3−1+i300001−i3−1+i300000000
χ55333333333333333333-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1000000000000000000000000000000000000
χ563333333333−3−3i32−3+3i32−3−3i32−3−3i32−3−3i32−3+3i32−3+3i32−3+3i32-1-1-1-1-1-1-1-1-1-11+i321−i321+i321+i321+i321−i321−i321−i32000000000000000000000000000000000000
χ573333333333−3+3i32−3−3i32−3+3i32−3+3i32−3+3i32−3−3i32−3−3i32−3−3i32-1-1-1-1-1-1-1-1-1-11−i321+i321−i321−i321−i321+i321+i321+i32000000000000000000000000000000000000
χ583333-3-333-3-3333-3-33-3-3-1-1-1-111-1-111-1-1-111-111000000000000000000000000000000000000
χ593333-3-333-3-3−3−3i32−3+3i32−3−3i323+3i323+3i32−3+3i323−3i323−3i32-1-1-1-111-1-1111+i321−i321+i32−1−i32−1−i321−i32−1+i32−1+i32000000000000000000000000000000000000
χ603333-3-333-3-3−3+3i32−3−3i32−3+3i323−3i323−3i32−3−3i323+3i323+3i32-1-1-1-111-1-1111−i321+i321−i32−1+i32−1+i321+i32−1−i32−1−i32000000000000000000000000000000000000
χ616-66-66-60000-3-333-333-3-22-22-22000011-1-11-1-11000000000000000000000000000000000000
χ626-66-66-600003+3i323−3i32−3−3i32−3−3i323+3i32−3+3i32−3+3i323−3i32-22-22-220000−1−i32−1+i321+i321+i32−1−i321−i321−i32−1+i32000000000000000000000000000000000000
χ636-66-66-600003−3i323+3i32−3+3i32−3+3i323−3i32−3−3i32−3−3i323+3i32-22-22-220000−1+i32−1−i321−i321−i32−1+i321+i321+i32−1−i32000000000000000000000000000000000000
χ646-66-6-660000-3-33-333-33-22-222-2000011-11-1-11-1000000000000000000000000000000000000
χ656-66-6-6600003+3i323−3i32−3−3i323+3i32−3−3i32−3+3i323−3i32−3+3i32-22-222-20000−1−i32−1+i321+i32−1−i321+i321−i32−1+i321−i32000000000000000000000000000000000000
χ666-66-6-6600003−3i323+3i32−3+3i323−3i32−3+3i32−3−3i323+3i32−3−3i32-22-222-20000−1+i32−1−i321−i32−1+i321−i321+i32−1−i321+i32000000000000000000000000000000000000
χ67999999-3-3-3-300000000-3-3-3-3-3-3111100000000000000000000000000000000000000000000
χ689999-9-9-3-33300000000-3-3-3-33311-1-100000000000000000000000000000000000000000000
χ691818-6-6006i−6i0000000000-6-62200−2i2i0000000000000000000000000000000000000000000000
χ701818-6-600−6i6i0000000000-6-622002i−2i0000000000000000000000000000000000000000000000
χ7118-18-6600006-600000000-662-20000-2200000000000000000000000000000000000000000000
χ7218-18-660000-6600000000-662-200002-200000000000000000000000000000000000000000000

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