Finite Group Databasebeta

← Group #317989

Character table — Group #317989

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size1111222222444444444444888888881616161616161616161616161616161632323232
order12224444442444888888888888888822224444888888888888
χ111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-111-1-11111-1-1-1-1-1-1-1-1
χ3111111111111111111111111111111-1-111-1-111-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ5111111111111111111-1-1-1-111-1-1-1-1-1-1111-1111-1-1-1-1-111-1-111-1-1
χ6111111111111111111-1-1-1-111-1-1-1-1-1-111-1111-11-1-1-1-1-1-111-1-111
χ7111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11-1-1-11-1111111-1-1-1-111
χ8111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-11-1-1-111111-1-11111-1-1
χ911111111111111-1-1-1-11111-1-111-1-1-1-11-1111-11111-1-1-1-1-1-11-11-1
χ1011111111111111-1-1-1-11111-1-111-1-1-1-11-1-1-11-1-1-111-1-11111-11-11
χ1111111111111111-1-1-1-11111-1-111-1-1-1-1-1111-1111-1-111-1-1-1-1-11-11
χ1211111111111111-1-1-1-11111-1-111-1-1-1-1-11-1-1-11-1-1-1-11111111-11-1
χ1311111111111111-1-1-1-1-1-1-1-1-1-1-1-111111-11-11-11-1-1-111-1-1111-1-11
χ1411111111111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-111-1-11-1-11111-1-1-111-1
χ1511111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-111-111-1-1-1-111-111-1
χ1611111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-11-11-11-1111-1-111-1-11-1-11
χ1722222222-2-2-2-2-2222-2-222-2-22-22-222-2-200000000000000000000
χ1822222222-2-2-2-2-2222-2-2-2-2222-2-22-2-22200000000000000000000
χ1922222222-2-2-2-2-22-2-22222-2-2-222-2-2-22200000000000000000000
χ2022222222-2-2-2-2-22-2-222-2-222-22-2222-2-200000000000000000000
χ21222222-2-222-22-2-20000222200-2-20000002200-2-2000000000000
χ22222222-2-222-22-2-20000222200-2-2000000-2-20022000000000000
χ23222222-2-222-22-2-20000-2-2-2-200220000002-200-22000000000000
χ24222222-2-222-22-2-20000-2-2-2-20022000000-22002-2000000000000
χ25222222-2-2-2-22-22-2000022-2-200-2200000000000000002i−2i2i−2i0000
χ26222222-2-2-2-22-22-2000022-2-200-220000000000000000−2i2i−2i2i0000
χ27222222-2-2-2-22-22-20000-2-222002-200000000000000002i−2i−2i2i0000
χ28222222-2-2-2-22-22-20000-2-222002-20000000000000000−2i2i2i−2i0000
χ292222-2-22222-2-22-222220000-2-20000002-200-2200000000000000
χ302222-2-22222-2-22-222220000-2-2000000-22002-200000000000000
χ312222-2-22222-2-22-2-2-2-2-20000220000002200-2-200000000000000
χ322222-2-22222-2-22-2-2-2-2-2000022000000-2-2002200000000000000
χ332222-2-222-2-222-2-222-2-20000-22000000000000002i−2i2i−2i00000000
χ342222-2-222-2-222-2-222-2-20000-2200000000000000−2i2i−2i2i00000000
χ352222-2-222-2-222-2-2-2-22200002-2000000000000002i−2i−2i2i00000000
χ362222-2-222-2-222-2-2-2-22200002-200000000000000−2i2i2i−2i00000000
χ374444-4-4-4-4444-4-44000000000000000000000000000000000000
χ384444-4-4-4-4-4-4-4444000000000000000000000000000000000000
χ3944-4-400004-400002i2−2i22i2−2i222−2222−2200002i−2i2i−2i00000000000000000000
χ4044-4-400004-400002i2−2i22i2−2i2−2222−22220000−2i2i−2i2i00000000000000000000
χ4144-4-400004-40000−2i22i2−2i22i222−2222−220000−2i2i−2i2i00000000000000000000
χ4244-4-400004-40000−2i22i2−2i22i2−2222−222200002i−2i2i−2i00000000000000000000
χ4344-4-40000-4400002i2−2i2−2i22i222−22−222200002i−2i−2i2i00000000000000000000
χ4444-4-40000-4400002i2−2i2−2i22i2−222222−220000−2i2i2i−2i00000000000000000000
χ4544-4-40000-440000−2i22i22i2−2i222−22−22220000−2i2i2i−2i00000000000000000000
χ4644-4-40000-440000−2i22i22i2−2i2−222222−2200002i−2i−2i2i00000000000000000000
χ478-88-8008-8000000000000000000000000000000000000000000
χ488-88-800-88000000000000000000000000000000000000000000
χ498-8-888-800000000000000000000000000000000000000000000
χ508-8-88-8800000000000000000000000000000000000000000000

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