Finite Group Databasebeta

← Group #72340920

Character table — Group #72340920

Order 6144.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60
size1344444442424242424242424242424242424484848484848489696969696969696969696969696256256256256256256256256256256256256256256256256
order122222222222222222222442444444444444444444443366666666666666
χ1111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111−1+i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32
χ311111111111111111111111111111111111111111111−1−i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32
χ4333333333333333-1-1-1-1-1-1-1-1-1333-1-1-133-1-1-1-1-1-1-1-1-1-1-1-10000000000000000
χ533333333333-1-1-1-13333-1-1-1-1-13-1-133-1-1-133-1-1-1-1-1-1-1-1-1-10000000000000000
χ633333333333-1-1-1-1-1-1-1-1333333-1-1-1-13-1-1-1-133-1-1-1-1-1-1-1-10000000000000000
χ733333333333-1-1-1-1-1-1-1-1-1-1-1-1-13-1-1-1-1-1-1-1-1-1-1-13333-1-1-1-10000000000000000
χ833333333333-1-1-1-1-1-1-1-1-1-1-1-1-13-1-1-1-1-1-1-1-1-1-1-1-1-1-1-133330000000000000000
χ9333333333-1-133-1-133-1-133-1-1-1-13-13-13-1-1-1-1-1-13-1-1-13-1-1-10000000000000000
χ10333333333-1-133-1-1-1-133-1-1333-13-1-13-1-1-1-1-1-1-1-13-1-1-13-1-10000000000000000
χ11333333333-1-133-1-1-1-1-1-1-1-1-1-1-1-13-1-1-1-1-1-13-13-1-1-13-1-1-13-10000000000000000
χ12333333333-1-133-1-1-1-1-1-1-1-1-1-1-1-13-1-1-1-1-1-1-13-13-1-1-13-1-1-130000000000000000
χ13333333333-1-1-1-13333-1-1-1-1333-1-133-1-1-1-1-1-1-1-1-1-13-1-1-1-130000000000000000
χ14333333333-1-1-1-133-1-13333-1-1-1-1-13-133-1-1-1-1-1-1-1-1-13-1-13-10000000000000000
χ15333333333-1-1-1-133-1-1-1-1-1-1-1-1-1-1-13-1-1-1-1-13-1-133-1-1-1-13-1-10000000000000000
χ16333333333-1-1-1-133-1-1-1-1-1-1-1-1-1-1-13-1-1-1-1-1-133-1-13-1-13-1-1-10000000000000000
χ17333333333-1-1-1-1-1-133-1-1-1-1-1-1-1-1-1-13-1-13-1-1-13-1-1-1-13-13-1-10000000000000000
χ18333333333-1-1-1-1-1-133-1-1-1-1-1-1-1-1-1-13-1-1-13-1-1-13-13-1-1-1-13-10000000000000000
χ19333333333-1-1-1-1-1-1-1-133-1-1-1-1-1-1-1-1-13-13-1-1-1-13-1-13-13-1-1-10000000000000000
χ20333333333-1-1-1-1-1-1-1-133-1-1-1-1-1-1-1-1-13-1-13-1-13-13-1-1-1-1-1-130000000000000000
χ21333333333-1-1-1-1-1-1-1-1-1-133-1-1-1-1-1-1-1-133-13-1-1-1-13-1-1-1-1-130000000000000000
χ22333333333-1-1-1-1-1-1-1-1-1-133-1-1-1-1-1-1-1-13-13-13-1-1-1-13-1-13-1-10000000000000000
χ23333333333-1-1-1-1-1-1-1-1-1-1-1-1333-1-1-1-1-1-13-1-13-1-13-1-1-1-1-13-10000000000000000
χ24333333333-1-1-1-1-1-1-1-1-1-1-1-1333-1-1-1-1-1-1-133-1-1-1-1-1-133-1-1-10000000000000000
χ2544444-4-4-4-400000000000044-40000000000000000000011111-1-1-1-1111-1-1-1-1
χ2644444-4-4-4-400000000000044-400000000000000000000−1+i32−1−i32−1+i32−1+i32−1+i321−i321−i321−i321−i32−1−i32−1−i32−1−i321+i321+i321+i321+i32
χ2744444-4-4-4-400000000000044-400000000000000000000−1−i32−1+i32−1−i32−1−i32−1−i321+i321+i321+i321+i32−1+i32−1+i32−1+i321−i321−i321−i321−i32
χ28444-4-444-4-400000000004400000000-400000000000000111-1-111-1-11-1-111-1-1
χ29444-4-444-4-400000000004400000000-400000000000000−1+i32−1−i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32
χ30444-4-444-4-400000000004400000000-400000000000000−1−i32−1+i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32
χ31444-4-4-4-444440000000000000-40000000000000000000111-1-1-1-1111-1-1-1-111
χ32444-4-4-4-444440000000000000-40000000000000000000−1+i32−1−i32−1+i321−i321−i321−i321−i32−1+i32−1+i32−1−i321+i321+i321+i321+i32−1−i32−1−i32
χ33444-4-4-4-444440000000000000-40000000000000000000−1−i32−1+i32−1−i321+i321+i321+i321+i32−1−i32−1−i32−1+i321−i321−i321−i321−i32−1+i32−1+i32
χ3444-44-44-44-40000000044000000000-400000000000000011-11-11-11-1-11-11-11-1
χ3544-44-44-44-40000000044000000000-4000000000000000−1+i32−1−i321−i32−1+i321−i32−1+i321−i32−1+i321−i321+i32−1−i321+i32−1−i321+i32−1−i321+i32
χ3644-44-44-44-40000000044000000000-4000000000000000−1−i32−1+i321+i32−1−i321+i32−1−i321+i32−1−i321+i321−i32−1+i321−i32−1+i321−i32−1+i321−i32
χ3744-44-4-44-440044000000000000-400000000000000000011-11-1-11-11-11-1-11-11
χ3844-44-4-44-440044000000000000-4000000000000000000−1+i32−1−i321−i32−1+i321−i321−i32−1+i321−i32−1+i321+i32−1−i321+i321+i32−1−i321+i32−1−i32
χ3944-44-4-44-440044000000000000-4000000000000000000−1−i32−1+i321+i32−1−i321+i321+i32−1−i321+i32−1−i321−i32−1+i321−i321−i32−1+i321−i32−1+i32
χ4044-4-444-4-4400004400000000000-40000000000000000011-1-111-1-11-1-111-1-11
χ4144-4-444-4-4400004400000000000-400000000000000000−1+i32−1−i321−i321−i32−1+i32−1+i321−i321−i32−1+i321+i321+i32−1−i32−1−i321+i321+i32−1−i32
χ4244-4-444-4-4400004400000000000-400000000000000000−1−i32−1+i321+i321+i32−1−i32−1−i321+i321+i32−1−i321−i321−i32−1+i32−1+i321−i321−i32−1+i32
χ4344-4-44-444-4000000440000000000-4000000000000000011-1-11-111-1-1-11-111-1
χ4444-4-44-444-4000000440000000000-40000000000000000−1+i32−1−i321−i321−i32−1+i321−i32−1+i32−1+i321−i321+i321+i32−1−i321+i32−1−i32−1−i321+i32
χ4544-4-44-444-4000000440000000000-40000000000000000−1−i32−1+i321+i321+i32−1−i321+i32−1−i32−1−i321+i321−i321−i32−1+i321−i32−1+i32−1+i321−i32
χ461212121212-12-12-12-12000000000000-4-44000000000000000000000000000000000000
χ47121212-12-121212-12-120000000000-4-4000000004000000000000000000000000000000
χ48121212-12-12-12-121212-4-40000000000000400000000000000000000000000000000000
χ491212-1212-1212-1212-1200000000-4-400000000040000000000000000000000000000000
χ501212-1212-12-1212-121200-4-400000000000040000000000000000000000000000000000
χ511212-12-121212-12-12120000-4-4000000000004000000000000000000000000000000000
χ521212-12-1212-121212-12000000-4-40000000000400000000000000000000000000000000
χ5324-800000004-44-44-44-44-44-44-40000000000000000000000000000000000000
χ5424-800000004-44-44-4-44-44-44-440000000000000000000000000000000000000
χ5524-800000004-4-44-444-44-4-44-440000000000000000000000000000000000000
χ5624-800000004-4-44-44-44-444-44-40000000000000000000000000000000000000
χ5724-80000000-444-4-444-4-444-4-440000000000000000000000000000000000000
χ5824-80000000-444-4-44-444-4-444-40000000000000000000000000000000000000
χ5924-80000000-44-444-44-4-44-444-40000000000000000000000000000000000000
χ6024-80000000-44-444-4-444-44-4-440000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).