Finite Group Databasebeta

← Group #152323

Character table — Group #152323

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41
size1122244444488888888888888881616161616163232323232323232
order12222224444222244444444444424888844448888
χ111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ311111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1
χ411111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ51111111111111-1-11111111111-1-1-1-1-1-1-1-1ii−i−iii−i−i
χ61111111111111-1-11111111111-1-1-1-1-1-1-1-1−i−iii−i−iii
χ71111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111ii−i−i−i−iii
χ81111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111−i−iiiii−i−i
χ911111-1-11-1-111111-1-11111-1-1-1-111-1-111-1-11-11-11-11-1
χ1011111-1-11-1-111111-1-11111-1-1-1-111-1-111-1-1-11-11-11-11
χ1111111-1-11-1-111111-1-1-1-1-1-1111111-1-1-1-1111-11-1-11-11
χ1211111-1-11-1-111111-1-1-1-1-1-1111111-1-1-1-111-11-111-11-1
χ1311111-1-11-1-1111-1-1-1-11111-1-1-1-1-1-111-1-111i−i−iii−i−ii
χ1411111-1-11-1-1111-1-1-1-11111-1-1-1-1-1-111-1-111−iii−i−iii−i
χ1511111-1-11-1-1111-1-1-1-1-1-1-1-11111-1-11111-1-1i−i−ii−iii−i
χ1611111-1-11-1-1111-1-1-1-1-1-1-1-11111-1-11111-1-1−iii−ii−i−ii
χ1722222222222-2-222-2-200000000-2-22-2000000000000
χ1822222222222-2-2-2-2-2-20000000022-22000000000000
χ1922222-2-22-2-22-2-2222200000000-2-2-22000000000000
χ2022222-2-22-2-22-2-2-2-22200000000222-2000000000000
χ2122-22-200200-22-22-20000002i2i−2i−2i2-200002i−2i00000000
χ2222-22-200200-22-22-2000000−2i−2i2i2i2-20000−2i2i00000000
χ2322-22-200200-22-2-220000002i2i−2i−2i-220000−2i2i00000000
χ2422-22-200200-22-2-22000000−2i−2i2i2i-2200002i−2i00000000
χ2522-22-200200-2-222-2002i2i−2i−2i0000-22002i−2i0000000000
χ2622-22-200200-2-222-200−2i−2i2i2i0000-2200−2i2i0000000000
χ2722-22-200200-2-22-22002i2i−2i−2i00002-200−2i2i0000000000
χ2822-22-200200-2-22-2200−2i−2i2i2i00002-2002i−2i0000000000
χ294444444-4-4-4-4000000000000000000000000000000
χ3044444-4-4-444-4000000000000000000000000000000
χ31444-4-44-400000000002i−2i2i−2i2i−2i2i−2i0000000000000000
χ32444-4-44-40000000000−2i2i−2i2i−2i2i−2i2i0000000000000000
χ33444-4-4-4400000000002i−2i2i−2i−2i2i−2i2i0000000000000000
χ34444-4-4-440000000000−2i2i−2i2i2i−2i2i−2i0000000000000000
χ3544-44-400-400400004-4000000000000000000000000
χ3644-44-400-40040000-44000000000000000000000000
χ3744-4-440004-400000002-2-222-2-220000000000000000
χ3844-4-440004-40000000-222-2-222-20000000000000000
χ3944-4-44000-4400000002-2-22-222-20000000000000000
χ4044-4-44000-440000000-222-22-2-220000000000000000
χ4116-16000000000000000000000000000000000000000

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