Finite Group Databasebeta

← Group #250021

Character table — Group #250021

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11112222224444444444448888888888888888161616161616161616161616161616163232
order12224444442224444488884444448888888888222244444488888888
χ111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-1-1-1111111111-11-111-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1-111-1-1111111-1-1-11-1-1-1-11-11-111-1-11-1
χ4111111111111111111111111-1-1-1-1-1-111111111-1-1-1-1-11-1-1-11-11-1-111-11
χ5111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-11-11111111-1-1-1-1-1-1
χ6111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111
χ7111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111111-1-1-11-11-1-1-111-11
χ8111111111111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1111-111-1-1-11-1111-1-11-1
χ911111111111-1-1-1-11111111-1-11111111111-1-1-1-11-1-1-11-1-1-1-1-1111111-1-1
χ1011111111111-1-1-1-11111111-1-11111-1-1-1-111-1-1-1-11-1-1111-1-111-1-1-1-1-1-111
χ1111111111111-1-1-1-11111111-1-1-1-1-1-111-1-111-1-1-1-1-111-1-1111-111-111-1-1-11
χ1211111111111-1-1-1-11111111-1-1-1-1-1-1-1-11111-1-1-1-1-1111-1-1111-1-11-1-1111-1
χ1311111111111-1-1-1-1111-1-1-1-1-1-111111111-1-11111-111-1-1-1-1-1-1-111-1-1-1-111
χ1411111111111-1-1-1-1111-1-1-1-1-1-11111-1-1-1-1-1-11111-1111-11-1-111-1-11111-1-1
χ1511111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111-1-1-11111-111-1-1-1111-1
χ1611111111111-1-1-1-1111-1-1-1-1-1-1-1-1-1-1-1-111-1-111111-1-111-1111-1-1111-1-1-11
χ17222222-2-222-20000-2-2222220022-2-20000-2-200002000-20000000000000
χ18222222-2-222-20000-2-22222200-2-2220000-2-20000-200020000000000000
χ19222222-2-222-20000-2-22-2-2-2-20022-2-20000220000-200020000000000000
χ20222222-2-222-20000-2-22-2-2-2-200-2-22200002200002000-20000000000000
χ2122222-2222-2-222-2-22-2-200002-200000022000000000002000-20-2000000
χ2222222-2222-2-222-2-22-2-200002-2000000-2-200000000000-2000202000000
χ2322222-2222-2-2-2-2222-2-20000-220000002200000000000-200020-2000000
χ2422222-2222-2-2-2-2222-2-20000-22000000-2-2000000000002000-202000000
χ252222-2222-22-222-2-2-22-20000-2200002200000000000-2000020-20000000
χ262222-2222-22-222-2-2-22-20000-220000-2-20000000000020000-2020000000
χ272222-2222-22-2-2-222-22-200002-20000220000000000020000-20-20000000
χ282222-2222-22-2-2-222-22-200002-20000-2-200000000000-200002020000000
χ292222-2-222-2-222222-2-220000-2-22-22-200000000000000002-20000000000
χ302222-2-222-2-222222-2-220000-2-2-22-220000000000000000-220000000000
χ312222-2-222-2-22-2-2-2-2-2-220000222-22-20000000000000000-220000000000
χ322222-2-222-2-22-2-2-2-2-2-22000022-22-2200000000000000002-20000000000
χ332222-2-2-2-2-2-2-200002220000002-2-2200000022-2-202-2000000000000000
χ342222-2-2-2-2-2-2-200002220000002-2-22000000-2-2220-22000000000000000
χ352222-2-2-2-2-2-2-20000222000000-222-200000022-2-20-22000000000000000
χ362222-2-2-2-2-2-2-20000222000000-222-2000000-2-22202-2000000000000000
χ3744444-4-4-44-440000-44-400000000000000000000000000000000000000
χ384444-44-4-4-44400004-4-400000000000000000000000000000000000000
χ3944-4-4004-4000004-40002i2i−2i−2i00000000002i−2i2i−2i2i−2i000000000000000000
χ4044-4-4004-4000004-4000−2i−2i2i2i0000000000−2i2i−2i2i−2i2i000000000000000000
χ4144-4-4004-400000-440002i2i−2i−2i00000000002i−2i−2i2i−2i2i000000000000000000
χ4244-4-4004-400000-44000−2i−2i2i2i0000000000−2i2i2i−2i2i−2i000000000000000000
χ4344-4-400-440004-4000002i2i−2i−2i0000000000−2i2i2i−2i−2i2i000000000000000000
χ4444-4-400-440004-400000−2i−2i2i2i00000000002i−2i−2i2i2i−2i000000000000000000
χ4544-4-400-44000-44000002i2i−2i−2i0000000000−2i2i−2i2i2i−2i000000000000000000
χ4644-4-400-44000-4400000−2i−2i2i2i00000000002i−2i2i−2i−2i2i000000000000000000
χ474-44-404000-40000000022−2222−220000002i2−2i2000000000000000000002i−2i0000
χ484-44-404000-40000000022−2222−22000000−2i22i200000000000000000000−2i2i0000
χ494-44-404000-400000000−2222−22220000002i2−2i200000000000000000000−2i2i0000
χ504-44-404000-400000000−2222−2222000000−2i22i2000000000000000000002i−2i0000
χ514-4-444000-40000000002i2−2i2−2i22i2000000002i2−2i2000000000000000000002-200
χ524-4-444000-40000000002i2−2i2−2i22i200000000−2i22i200000000000000000000-2200
χ534-4-444000-4000000000−2i22i22i2−2i2000000002i2−2i200000000000000000000-2200
χ544-4-444000-4000000000−2i22i22i2−2i200000000−2i22i2000000000000000000002-200
χ558-88-80-800080000000000000000000000000000000000000000000000
χ568-8-88-8000800000000000000000000000000000000000000000000000

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