Finite Group Databasebeta

← Group #72340952

Character table — Group #72340952

Order 3072.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61
size134444444444444444848484864646464646464646464646464646464646464646464646464646464646464649696969696969696
order1222222222222222224443366666666666666666666666666666644444444
χ11111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111−1+i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i3211111111
χ3111111111111111111111−1−i32−1+i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1−i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i32−1+i3211111111
χ411111-1-1-1-1-1-1-1-1111111-1-1111111111-1-1-1-1-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-1-1-1
χ511111-1-1-1-1-1-1-1-1111111-1-1−1+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−i321+i321+i321+i321+i321+i321+i321+i321+i321111-1-1-1-1
χ611111-1-1-1-1-1-1-1-1111111-1-1−1−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+i321−i321−i321−i321−i321−i321−i321−i321−i321111-1-1-1-1
χ7222222222-2-2-2-2-2-2-2-2-222-2-1-11111-1-1-11111-1-1-1-11111-1-1-11111-1-1-1-100000000
χ8222222222-2-2-2-2-2-2-2-2-222-21−i321+i32−1+i32−1+i32−1+i32−1+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+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i321+i321+i3200000000
χ9222222222-2-2-2-2-2-2-2-2-222-21+i321−i32−1−i32−1−i32−1−i32−1−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−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i321−i321−i3200000000
χ1022222-2-2-2-22222-2-2-2-2-22-22-1-11111-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1111100000000
χ1122222-2-2-2-22222-2-2-2-2-22-221−i321+i32−1+i32−1+i32−1+i32−1+i321−i321−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+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i3200000000
χ1222222-2-2-2-22222-2-2-2-2-22-221+i321−i32−1−i32−1−i32−1−i32−1−i321+i321+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−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i3200000000
χ1333333333333333333333300000000000000000000000000000000-1-1-1-1-1-1-1-1
χ1433333333333333333-1-1-1-1000000000000000000000000000000003-1-1-13-1-1-1
χ1533333333333333333-1-1-1-100000000000000000000000000000000-13-1-1-13-1-1
χ1633333333333333333-1-1-1-100000000000000000000000000000000-1-13-1-1-13-1
χ1733333333333333333-1-1-1-100000000000000000000000000000000-1-1-13-1-1-13
χ1833333-3-3-3-3-3-3-3-3333333-3-300000000000000000000000000000000-1-1-1-11111
χ1933333-3-3-3-3-3-3-3-33333-1-111000000000000000000000000000000003-1-1-1-3111
χ2033333-3-3-3-3-3-3-3-33333-1-11100000000000000000000000000000000-13-1-11-311
χ2133333-3-3-3-3-3-3-3-33333-1-11100000000000000000000000000000000-1-13-111-31
χ2233333-3-3-3-3-3-3-3-33333-1-11100000000000000000000000000000000-1-1-13111-3
χ23444-4-444-4-444-4-444-4-400001111-1-11-1-111-1-111-1-111-1-11-1-111-1-111-1-100000000
χ24444-4-444-4-444-4-444-4-40000−1+i32−1−i32−1+i32−1+i321−i321−i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1−i32−1−i321+i321+i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i3200000000
χ25444-4-444-4-444-4-444-4-40000−1−i32−1+i32−1−i32−1−i321+i321+i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1+i32−1+i321−i321−i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i3200000000
χ26444-4-444-4-4-4-444-4-444000011-1-1111-1-1-1-11111-1-1-1-1111-1-1-1-11111-1-100000000
χ27444-4-444-4-4-4-444-4-4440000−1+i32−1−i321−i321−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−i321+i321+i321+i321+i32−1−i32−1−i32−1−i32−1−i321+i321+i3200000000
χ28444-4-444-4-4-4-444-4-4440000−1−i32−1+i321+i321+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+i321−i321−i321−i321−i32−1+i32−1+i32−1+i32−1+i321−i321−i3200000000
χ29444-4-4-4-44444-4-4-4-444000011-1-1111-1-111-1-1-1-111-1-1111-1-111-1-1-1-11100000000
χ30444-4-4-4-44444-4-4-4-4440000−1+i32−1−i321−i321−i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i321+i321+i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i3200000000
χ31444-4-4-4-44444-4-4-4-4440000−1−i32−1+i321+i321+i32−1−i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i321+i321+i32−1−i32−1−i321−i321−i32−1+i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i321−i321−i32−1+i32−1+i3200000000
χ32444-4-4-4-444-4-44444-4-400001111-1-11-1-1-1-111-1-11111-1-11-1-1-1-111-1-11100000000
χ33444-4-4-4-444-4-44444-4-40000−1+i32−1−i32−1+i32−1+i321−i321−i32−1+i321−i321−i321−i321−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−i321+i321+i32−1−i32−1−i3200000000
χ34444-4-4-4-444-4-44444-4-40000−1−i32−1+i32−1−i32−1−i321+i321+i32−1−i321+i321+i321+i321+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+i321−i321−i32−1+i32−1+i3200000000
χ3544-44-44-44-44-44-44-44-40000111-11-1-11-11-11-11-11-11-11-1-11-11-11-11-11-100000000
χ3644-44-44-44-44-44-44-44-40000−1+i32−1−i32−1+i321−i32−1+i321−i321−i32−1+i321−i32−1+i321−i32−1+i321−i32−1+i321−i32−1+i321−i32−1−i321+i32−1−i321+i321+i32−1−i321+i32−1−i321+i32−1−i321+i32−1−i321+i32−1−i321+i3200000000
χ3744-44-44-44-44-44-44-44-40000−1−i32−1+i32−1−i321+i32−1−i321+i321+i32−1−i321+i32−1−i321+i32−1−i321+i32−1−i321+i32−1−i321+i32−1+i321−i32−1+i321−i321−i32−1+i321−i32−1+i321−i32−1+i321−i32−1+i321−i32−1+i321−i3200000000
χ3844-44-44-44-4-44-44-44-44000011-11-11-11-1-11-111-11-1-11-11-11-1-11-111-11-100000000
χ3944-44-44-44-4-44-44-44-440000−1+i32−1−i321−i32−1+i321−i32−1+i321−i32−1+i321−i321−i32−1+i321−i32−1+i32−1+i321−i32−1+i321−i321+i32−1−i321+i32−1−i321+i32−1−i321+i321+i32−1−i321+i32−1−i32−1−i321+i32−1−i321+i3200000000
χ4044-44-44-44-4-44-44-44-440000−1−i32−1+i321+i32−1−i321+i32−1−i321+i32−1−i321+i321+i32−1−i321+i32−1−i32−1−i321+i32−1−i321+i321−i32−1+i321−i32−1+i321−i32−1+i321−i321−i32−1+i321−i32−1+i32−1+i321−i32−1+i321−i3200000000
χ4144-44-4-44-444-44-4-44-44000011-11-11-11-11-11-1-11-11-11-11-11-11-11-1-11-1100000000
χ4244-44-4-44-444-44-4-44-440000−1+i32−1−i321−i32−1+i321−i32−1+i321−i32−1+i321−i32−1+i321−i32−1+i321−i321−i32−1+i321−i32−1+i321+i32−1−i321+i32−1−i321+i32−1−i321+i32−1−i321+i32−1−i321+i321+i32−1−i321+i32−1−i3200000000
χ4344-44-4-44-444-44-4-44-440000−1−i32−1+i321+i32−1−i321+i32−1−i321+i32−1−i321+i32−1−i321+i32−1−i321+i321+i32−1−i321+i32−1−i321−i32−1+i321−i32−1+i321−i32−1+i321−i32−1+i321−i32−1+i321−i321−i32−1+i321−i32−1+i3200000000
χ4444-44-4-44-44-44-444-44-40000111-11-1-11-1-11-11-11-111-11-1-11-1-11-11-11-1100000000
χ4544-44-4-44-44-44-444-44-40000−1+i32−1−i32−1+i321−i32−1+i321−i321−i32−1+i321−i321−i32−1+i321−i32−1+i321−i32−1+i321−i32−1+i32−1−i321+i32−1−i321+i321+i32−1−i321+i321+i32−1−i321+i32−1−i321+i32−1−i321+i32−1−i3200000000
χ4644-44-4-44-44-44-444-44-40000−1−i32−1+i32−1−i321+i32−1−i321+i321+i32−1−i321+i321+i32−1−i321+i32−1−i321+i32−1−i321+i32−1−i32−1+i321−i32−1+i321−i321−i32−1+i321−i321−i32−1+i321−i32−1+i321−i32−1+i321−i32−1+i3200000000
χ4744-4-444-4-444-4-444-4-440000111-1-11-1-111-1-111-1-111-1-11-1-111-1-111-1-1100000000
χ4844-4-444-4-444-4-444-4-440000−1+i32−1−i32−1+i321−i321−i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1−i321+i321+i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i3200000000
χ4944-4-444-4-444-4-444-4-440000−1−i32−1+i32−1−i321+i321+i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i321+i32−1−i32−1+i321−i321−i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i321−i32−1+i3200000000
χ5044-4-444-4-44-444-4-444-4000011-111-1-1-11-111-11-1-11-111-1-1-11-111-11-1-1100000000
χ5144-4-444-4-44-444-4-444-40000−1+i32−1−i321−i32−1+i32−1+i321−i321−i321−i32−1+i321−i32−1+i32−1+i321−i32−1+i321−i321−i32−1+i321+i32−1−i32−1−i321+i321+i321+i32−1−i321+i32−1−i32−1−i321+i32−1−i321+i321+i32−1−i3200000000
χ5244-4-444-4-44-444-4-444-40000−1−i32−1+i321+i32−1−i32−1−i321+i321+i321+i32−1−i321+i32−1−i32−1−i321+i32−1−i321+i321+i32−1−i321−i32−1+i32−1+i321−i321−i321−i32−1+i321−i32−1+i32−1+i321−i32−1+i321−i321−i32−1+i3200000000
χ5344-4-44-444-44-4-44-444-4000011-111-1-1-111-1-11-111-1-111-1-1-111-1-11-111-100000000
χ5444-4-44-444-44-4-44-444-40000−1+i32−1−i321−i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i321−i321−i32−1+i321−i32−1+i32−1+i321−i321+i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i321+i32−1−i32−1−i321+i3200000000
χ5544-4-44-444-44-4-44-444-40000−1−i32−1+i321+i32−1−i32−1−i321+i321+i321+i32−1−i32−1−i321+i321+i32−1−i321+i32−1−i32−1−i321+i321−i32−1+i32−1+i321−i321−i321−i32−1+i32−1+i321−i321−i32−1+i321−i32−1+i32−1+i321−i3200000000
χ5644-4-44-444-4-444-44-4-440000111-1-11-1-11-111-1-111-11-1-11-1-11-111-1-111-100000000
χ5744-4-44-444-4-444-44-4-440000−1+i32−1−i32−1+i321−i321−i32−1+i321−i321−i32−1+i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i32−1−i321+i321+i32−1−i321+i321+i32−1−i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i3200000000
χ5844-4-44-444-4-444-44-4-440000−1−i32−1+i32−1−i321+i321+i32−1−i321+i321+i32−1−i321+i32−1−i32−1−i321+i321+i32−1−i32−1−i321+i32−1+i321−i321−i32−1+i321−i321−i32−1+i321−i32−1+i32−1+i321−i321−i32−1+i32−1+i321−i3200000000
χ59666666666-6-6-6-6-6-6-6-62-2-220000000000000000000000000000000000000000
χ6066666-6-6-6-66666-6-6-6-62-22-20000000000000000000000000000000000000000
χ6148-1600000000000000000000000000000000000000000000000000000000000

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