Finite Group Databasebeta

← Group #240908

Character table — Group #240908

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111222222222222224444444488888888888888881616161616161616161616161616161616161616
order12222222444444444424444444444444448888888844444444888888888888
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-1
χ41111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111
χ511111111111111111111111111-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1-1-1-1-1-1-11111
χ611111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-111111111-1-1-1-1
χ711111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111-1-1-1-111-1-1-1-1
χ811111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-11111
χ911111-1-1111-1-1-1-1-1-111-111-1-1-1111111-1-1-1-11111-1-1-1-11-11-11-11-11-111-1-11-111-1-1
χ1011111-1-1111-1-1-1-1-1-111-111-1-1-1111111-1-1-1-11111-1-1-1-11-1-111-1-11-11-1-111-11-1-111
χ1111111-1-1111-1-1-1-1-1-111-111-1-1-1111111-1-1-1-1-1-1-1-11111-111-1-111-1-1111-1-1-11-1-111
χ1211111-1-1111-1-1-1-1-1-111-111-1-1-1111111-1-1-1-1-1-1-1-11111-11-11-11-111-1-1-1111-111-1-1
χ1311111-1-1111-1-1-1-1-1-111-111-1-1-111-1-1-1-111111111-1-1-1-1-111-1-111-1-11-1-111-1111-1-1
χ1411111-1-1111-1-1-1-1-1-111-111-1-1-111-1-1-1-111111111-1-1-1-1-11-11-11-111-111-1-11-1-1-111
χ1511111-1-1111-1-1-1-1-1-111-111-1-1-111-1-1-1-11111-1-1-1-111111-11-11-11-11-1-1-1111-1-1-111
χ1611111-1-1111-1-1-1-1-1-111-111-1-1-111-1-1-1-11111-1-1-1-111111-1-111-1-11-1111-1-1-1111-1-1
χ1722222222222222-2-2-2-222-2-2-2-2-2-2000000000000000000000000000000002i−2i2i−2i
χ1822222222222222-2-2-2-222-2-2-2-2-2-200000000000000000000000000000000−2i2i−2i2i
χ1922222222-2-2-2-2-2-222222-222-2-2-2-20000000000000000002-200-22000000000000
χ2022222222-2-2-2-2-2-222222-222-2-2-2-2000000000000000000-22002-2000000000000
χ2122222222-2-2-2-2-2-2-2-2-2-22-2-2-222220000000022-2-222-2-200000000000000000000
χ2222222222-2-2-2-2-2-2-2-2-2-22-2-2-2222200000000-2-222-2-22200000000000000000000
χ2322222-2-2222-2-2-2-222-2-2-22-2222-2-2000000000000000000000000000000002i−2i−2i2i
χ2422222-2-2222-2-2-2-222-2-2-22-2222-2-200000000000000000000000000000000−2i2i2i−2i
χ2522222-2-22-2-2222222-2-2-2-2-22-2-2220000000022-2-2-2-22200000000000000000000
χ2622222-2-22-2-2222222-2-2-2-2-22-2-22200000000-2-22222-2-200000000000000000000
χ2722222-2-22-2-22222-2-222-2-22-222-2-20000000000000000002200-2-2000000000000
χ2822222-2-22-2-22222-2-222-2-22-222-2-2000000000000000000-2-20022000000000000
χ292222-222-22222-2-22222-2-2-2-22-22-2000000000000000000000000220000-2-20000
χ302222-222-22222-2-22222-2-2-2-22-22-2000000000000000000000000-2-20000220000
χ312222-222-22222-2-2-2-2-2-2-2-222-22-222i2i−2i−2i2i2i−2i−2i0000000000000000000000000000
χ322222-222-22222-2-2-2-2-2-2-2-222-22-22−2i−2i2i2i−2i−2i2i2i0000000000000000000000000000
χ332222-222-2-2-2-2-2222222-22-2-2-22-2200000000000000002200-2-200000000000000
χ342222-222-2-2-2-2-2222222-22-2-2-22-220000000000000000-2-2002200000000000000
χ352222-222-2-2-2-2-222-2-2-2-2-22222-22-2000000000000000000000000002i−2i2i−2i000000
χ362222-222-2-2-2-2-222-2-2-2-2-22222-22-200000000000000000000000000−2i2i−2i2i000000
χ372222-2-2-2-222-2-22222-2-22-22-22-2-222i2i−2i−2i−2i−2i2i2i0000000000000000000000000000
χ382222-2-2-2-222-2-22222-2-22-22-22-2-22−2i−2i2i2i2i2i−2i−2i0000000000000000000000000000
χ392222-2-2-2-222-2-222-2-2222-2-22-222-20000000000000000000000002-20000-220000
χ402222-2-2-2-222-2-222-2-2222-2-22-222-2000000000000000000000000-2200002-20000
χ412222-2-2-2-2-2-222-2-222-2-2222-2-222-2000000000000000000000000002i−2i−2i2i000000
χ422222-2-2-2-2-2-222-2-222-2-2222-2-222-200000000000000000000000000−2i2i2i−2i000000
χ432222-2-2-2-2-2-222-2-2-2-22222-222-2-2200000000000000002-200-2200000000000000
χ442222-2-2-2-2-2-222-2-2-2-22222-222-2-220000000000000000-22002-200000000000000
χ4544-4-404-400000004-44-4000000002-22-22-22-20000000000000000000000000000
χ4644-4-404-400000004-44-400000000-22-22-22-220000000000000000000000000000
χ4744-4-404-40000000-44-44000000002i−2i−2i2i2i−2i−2i2i0000000000000000000000000000
χ4844-4-404-40000000-44-4400000000−2i2i2i−2i−2i2i2i−2i0000000000000000000000000000
χ4944-4-40-4400000004-4-44000000002i−2i−2i2i−2i2i2i−2i0000000000000000000000000000
χ5044-4-40-4400000004-4-4400000000−2i2i2i−2i2i−2i−2i2i0000000000000000000000000000
χ5144-4-40-440000000-444-4000000002-22-2-22-220000000000000000000000000000
χ5244-4-40-440000000-444-400000000-22-222-22-20000000000000000000000000000
χ534-44-4400-4004-44-4000000000000000000000022−2222−220000000000000000000000
χ544-44-4400-4004-44-40000000000000000000000−2222−22220000000000000000000000
χ554-44-4400-400-44-44000000000000000000000022−22−22220000000000000000000000
χ564-44-4400-400-44-440000000000000000000000−222222−220000000000000000000000
χ574-44-4-4004004-4-44000000000000000000002i2−2i200002i2−2i200000000000000000000
χ584-44-4-4004004-4-4400000000000000000000−2i22i20000−2i22i200000000000000000000
χ594-44-4-400400-444-4000000000000000000002i2−2i20000−2i22i200000000000000000000
χ604-44-4-400400-444-400000000000000000000−2i22i200002i2−2i200000000000000000000
χ618-8-8800008i−8i0000000000000000000000000000000000000000000000000000
χ628-8-880000−8i8i0000000000000000000000000000000000000000000000000000

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