Finite Group Databasebeta

← Group #149784

Character table — Group #149784

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44
size1111222222444488888888888888881616161616163232323232323232
order12222244442244444444448888888844444488888888
χ111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-1
χ41111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111
χ5111111111111111111-1-1-1-111111111-1-1-1-1-1-1ii−i−iii−i−i
χ6111111111111111111-1-1-1-111111111-1-1-1-1-1-1−i−iii−i−iii
χ7111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111ii−i−i−i−iii
χ8111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111−i−iiiii−i−i
χ9111111-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-111-1-11-11-11-11-1
χ10111111-1-1-1-1-1-11111-1-111111111-1-1-1-1-1-111-1-1-11-11-11-11
χ11111111-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-1111-11-1-11-11
χ12111111-1-1-1-1-1-11111-1-11111-1-1-1-11111-1-1-1-111-11-111-11-1
χ13111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111-1-111i−i−iii−i−ii
χ14111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-1-1-111-1-111−iii−i−iii−i
χ15111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1i−i−ii−iii−i
χ16111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111111-1-1−iii−ii−i−ii
χ1722222222222222-2-2-2-222-2-2000000002-2000000000000
χ1822222222222222-2-2-2-2-2-22200000000-22000000000000
χ19222222-2-2-2-2-2-222-2-22222-2-200000000-22000000000000
χ20222222-2-2-2-2-2-222-2-222-2-222000000002-2000000000000
χ2122-2-2-220000002-22-2002i−2i2i−2i00002i2i−2i−2i00002-200000000
χ2222-2-2-220000002-22-2002i−2i2i−2i0000−2i−2i2i2i0000-2200000000
χ2322-2-2-220000002-22-200−2i2i−2i2i00002i2i−2i−2i0000-2200000000
χ2422-2-2-220000002-22-200−2i2i−2i2i0000−2i−2i2i2i00002-200000000
χ2522-2-2-220000002-2-22002i−2i−2i2i2i2i−2i−2i0000002-20000000000
χ2622-2-2-220000002-2-22002i−2i−2i2i−2i−2i2i2i000000-220000000000
χ2722-2-2-220000002-2-2200−2i2i2i−2i2i2i−2i−2i000000-220000000000
χ2822-2-2-220000002-2-2200−2i2i2i−2i−2i−2i2i2i0000002-20000000000
χ294444444444-4-4-4-4000000000000000000000000000000
χ30444444-4-4-4-444-4-4000000000000000000000000000000
χ314444-4-444-4-40000000000002i−2i2i−2i2i−2i2i−2i00000000000000
χ324444-4-444-4-4000000000000−2i2i−2i2i−2i2i−2i2i00000000000000
χ334444-4-4-4-4440000000000002i−2i2i−2i−2i2i−2i2i00000000000000
χ344444-4-4-4-444000000000000−2i2i−2i2i2i−2i2i−2i00000000000000
χ3544-4-44-400004-400000000002-2-222-2-2200000000000000
χ3644-4-44-400004-40000000000-222-2-222-200000000000000
χ3744-4-44-40000-4400000000002-2-22-222-200000000000000
χ3844-4-44-40000-440000000000-222-22-2-2200000000000000
χ3944-4-4-44000000-44004-400000000000000000000000000
χ4044-4-4-44000000-4400-4400000000000000000000000000
χ418-88-800008i−8i0000000000000000000000000000000000
χ428-88-80000−8i8i0000000000000000000000000000000000
χ438-8-88008i−8i000000000000000000000000000000000000
χ448-8-8800−8i8i000000000000000000000000000000000000

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