Finite Group Databasebeta

← Group #287341

Character table — Group #287341

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size1111111122222222222244444488888888888888888888888881616161616161616161616163232
order12222222444444444444444444488888888888888888888888822224444888844
χ111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111-1-1-1-111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111111-1-1-1-111111111-1-1-1-11111-1-111-1-111-1-1-1-1-1-1
χ41111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111111111-1-1-1-111111111-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1
χ6111111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-111-1-111-1-1-1-111
χ7111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-111-1-1-1-1-1-111
χ8111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1
χ911111111111-1-1-1-11111111-1-1-1-1-1111111-1-11111-1-1-1-111-1-1-1-1-1-11-1-1-11-11111-1-11-1
χ1011111111111-1-1-1-11111111-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-111111-1111-1-1-1-1-111-11
χ1111111111111-1-1-1-11111111-1-1-1-1-11111-1-1111111-1-1-1-1-1-111-1-1-1-1-11-1-1-1111-1-111-11
χ1211111111111-1-1-1-11111111-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1111111-1111-11-1-111-1-11-1
χ1311111111111-1-1-1-11111111-1-1-1-1-1-1-1-1-111-1-11111111111-1-1-1-1-1-1-1111-11-1-111-1-1-11
χ1411111111111-1-1-1-11111111-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-11111-11-1-1-1111-1-1111-1
χ1511111111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-11111111111-1-111-1-1-1-11-1111-1-1-1-1-1111-1
χ1611111111111-1-1-1-11111111-1-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-11111111-1-1-11-11111-1-1-11
χ172222222222-222222-2-2-22-2-222-2-2-20000000000000000000000002200-2-200000000
χ182222222222-222222-2-2-22-2-222-2-2-2000000000000000000000000-2-2002200000000
χ192222222222-2-2-2-2-22-2-2-22-2-2-2-22220000000000000000000000002-200-2200000000
χ202222222222-2-2-2-2-22-2-2-22-2-2-2-2222000000000000000000000000-22002-200000000
χ2122222222-2-222222-2222-2-2-2-2-222-20000222200000000-2-2-2-2000000000000000000
χ2222222222-2-222222-2222-2-2-2-2-222-20000-2-2-2-2000000002222000000000000000000
χ2322222222-2-22-2-2-2-2-2222-2-2-222-2-22000022-2-200000000-2-222000000000000000000
χ2422222222-2-22-2-2-2-2-2222-2-2-222-2-220000-2-2220000000022-2-2000000000000000000
χ2522222222-2-2-22222-2-2-2-2-222-2-2-2-222i2i−2i−2i000000002i2i−2i−2i0000000000000000000000
χ2622222222-2-2-22222-2-2-2-2-222-2-2-2-22−2i−2i2i2i00000000−2i−2i2i2i0000000000000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2222222-22i2i−2i−2i00000000−2i−2i2i2i0000000000000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-2222222-2−2i−2i2i2i000000002i2i−2i−2i0000000000000000000000
χ29222-2-22-2-22-220000-22-2-222-200000000000002i2i−2i−2i2i−2i2i−2i00000000002-20000000000
χ30222-2-22-2-22-220000-22-2-222-200000000000002i2i−2i−2i−2i2i−2i2i0000000000-220000000000
χ31222-2-22-2-22-220000-22-2-222-20000000000000−2i−2i2i2i2i−2i2i−2i0000000000-220000000000
χ32222-2-22-2-22-220000-22-2-222-20000000000000−2i−2i2i2i−2i2i−2i2i00000000002-20000000000
χ33222-2-22-2-2-22-200002-222-22-2000000000000000002-2-2200002i2i−2i−2i0000002i−2i000000
χ34222-2-22-2-2-22-200002-222-22-2000000000000000002-2-220000−2i−2i2i2i000000−2i2i000000
χ35222-2-22-2-2-22-200002-222-22-200000000000000000-222-200002i2i−2i−2i000000−2i2i000000
χ36222-2-22-2-2-22-200002-222-22-200000000000000000-222-20000−2i−2i2i2i0000002i−2i000000
χ372-2-2-2-222200-222-2-202-22000002-20000000002−22−200002-22-22−22−2000000002−22−200
χ382-2-2-2-222200-222-2-202-22000002-20000000002−22−20000-22-222−22−200000000−22−2200
χ392-2-2-2-222200-222-2-202-22000002-2000000000−22−2200002-22-2−22−2200000000−22−2200
χ402-2-2-2-222200-222-2-202-22000002-2000000000−22−220000-22-22−22−22000000002−22−200
χ412-2-2-2-222200-2-2-22202-2200000-220000000002−22−200002-2-22−22−22000000002−2−2200
χ422-2-2-2-222200-2-2-22202-2200000-220000000002−22−20000-222-2−22−2200000000−222−200
χ432-2-2-2-222200-2-2-22202-2200000-22000000000−22−2200002-2-222−22−200000000−222−200
χ442-2-2-2-222200-2-2-22202-2200000-22000000000−22−220000-222-22−22−2000000002−2−2200
χ45444-4-44-4-44-4-40000-4-4444-440000000000000000000000000000000000000000000
χ46444-4-44-4-4-444000044-4-4-4-440000000000000000000000000000000000000000000
χ4744-44-4-44-40004-44-400000000000000002i2−2i22i2−2i2000000000000000000000000000000
χ4844-44-4-44-40004-44-40000000000000000−2i22i2−2i22i2000000000000000000000000000000
χ4944-44-4-44-4000-44-4400000000000000002i2−2i2−2i22i2000000000000000000000000000000
χ5044-44-4-44-4000-44-440000000000000000−2i22i22i2−2i2000000000000000000000000000000
χ514-444-4-4-444-4000004000-400000002i2−2i22i2−2i20000000000000000000000000000000000
χ524-444-4-4-444-4000004000-40000000−2i22i2−2i22i20000000000000000000000000000000000
χ534-444-4-4-44-4400000-40004000000022−22−22220000000000000000000000000000000000
χ544-444-4-4-44-4400000-400040000000−222222−220000000000000000000000000000000000
χ554-44-44-44-44404-4-44-4000-4004-400000000000000000000000000000000000000000
χ564-44-44-44-4440-444-4-4000-400-4400000000000000000000000000000000000000000
χ574-44-44-44-4-4-404-4-444000400-4400000000000000000000000000000000000000000
χ584-44-44-44-4-4-40-444-440004004-400000000000000000000000000000000000000000
χ594-4-4444-4-400400000-4-4400000000000000000000000000002i2−2i2−2i22i200000000000000
χ604-4-4444-4-400400000-4-440000000000000000000000000000−2i22i22i2−2i200000000000000
χ614-4-4444-4-400-40000044-400000000000000002i2−2i2−2i22i200000000000000000000000000
χ624-4-4444-4-400-40000044-40000000000000000−2i22i22i2−2i200000000000000000000000000
χ634-4-4-4-444400444-4-40-44-400000-44000000000000000000000000000000000000000
χ644-4-4-4-4444004-4-4440-44-4000004-4000000000000000000000000000000000000000
χ6588-8-88-8-88000000000000000000000000000000000000000000000000000000000

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