Finite Group Databasebeta

← Group #252209

Character table — Group #252209

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11111111222222224444448888888888888888888888161616161616161616161616161616161616
order12222222444444442244444444444444444488888888244444444488888888
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1
χ3111111111111111111111111-1-1-1-1-1-11-1-111111111111-111-1-1-1-1-1-1-11111-1-1-1-1
χ4111111111111111111111111-1-1-1-1-1-11-1-1111-1-1-1-1-1-1-1-1-111-1-1-11111-1-1-1-11111
χ51111111111111111111111-1-11111-1-11-1-11-1-111111111-1-1-111-11111-1-1-1-1-1-1-1-1
χ61111111111111111111111-1-11111-1-11-1-11-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-111111111
χ71111111111111111111111-1-1-1-1-1-1111111-1-1111111111-1-1-1-11-1-1-1-1-1-1-1-11111
χ81111111111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11-1-1-1-1111111111-1-1-1-1
χ91111111111111111-1-1-1-111111111-1-1-111-1-1-11111-1-1-1-111-1-1-1-111-1-111-1-111-1-1
χ101111111111111111-1-1-1-111111111-1-1-111-1-1-1-1-1-1-1111111-1-1-1-1-1-111-1-111-1-111
χ111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-11-1111-1-11111-1-1-1-111
χ121111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-11-111111-1-1-1-11111-1-1
χ131111111111111111-1-1-1-111-1-1111111-1-1-1-1111111-1-1-1-1-1-11-1-1111-1-1-1-111-1-111
χ141111111111111111-1-1-1-111-1-1111111-1-1-1-111-1-1-1-11111-1-11-1-11-1-11111-1-111-1-1
χ151111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-111-1111111-1-1-1-11-1111-1-1-111-1-11111-1-1
χ161111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-111-111-1-1-1-111111-1111-111-1-111-1-1-1-111
χ172222222222-2-222-2-22222-2-200000022-222-20000000000-20000-2000000000000
χ182222222222-2-222-2-22222-2-2000000-2-2-2-2-2-20000000000200002000000000000
χ192222222222-2-222-2-2-2-2-2-2-2-2000000222-2-22000000000020000-2000000000000
χ202222222222-2-222-2-2-2-2-2-2-2-2000000-2-222220000000000-200002000000000000
χ2122222222-2-222-2-22222-2-2-2-222000000200-2-2-2000000000-22000000000000000
χ2222222222-2-222-2-22222-2-2-2-2-2-2000000200-2220000000002-2000000000000000
χ2322222222-2-222-2-222-2-222-2-222000000-200222000000000-2-2000000000000000
χ2422222222-2-222-2-222-2-222-2-2-2-2000000-2002-2-200000000022000000000000000
χ2522222222-2-2-2-2-2-2-2-222-2-2220022-2-200-200200000000000002-20000000000000
χ2622222222-2-2-2-2-2-2-2-222-2-22200-2-22200-20020000000000000-220000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-222220022-2-200200-20000000000000-220000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2222200-2-22200200-200000000000002-20000000000000
χ2922-22-22-2-2-2-20022002-22-2000000002i−2i02i−2i000i2i2−i2−i2i2i2−i2−i2000000000000002−22−2
χ3022-22-22-2-2-2-20022002-22-2000000002i−2i02i−2i000−i2−i2i2i2−i2−i2i2i200000000000000−22−22
χ3122-22-22-2-2-2-20022002-22-200000000−2i2i0−2i2i000i2i2−i2−i2i2i2−i2−i200000000000000−22−22
χ3222-22-22-2-2-2-20022002-22-200000000−2i2i0−2i2i000−i2−i2i2i2−i2−i2i2i2000000000000002−22−2
χ3322-22-22-2-2-2-2002200-22-22000000002i−2i0−2i2i000i2i2−i2−i2−i2−i2i2i200000000000000−222−2
χ3422-22-22-2-2-2-2002200-22-22000000002i−2i0−2i2i000−i2−i2i2i2i2i2−i2−i2000000000000002−2−22
χ3522-22-22-2-2-2-2002200-22-2200000000−2i2i02i−2i000i2i2−i2−i2−i2−i2i2i2000000000000002−2−22
χ3622-22-22-2-2-2-2002200-22-2200000000−2i2i02i−2i000−i2−i2i2i2i2i2−i2−i200000000000000−222−2
χ3722-2-2-2-2222-22-22-22-200002-2002i−2i2i−2i0000000000002i−2i2i−2i000000002-200000000
χ3822-2-2-2-2222-22-22-22-200002-2002i−2i2i−2i000000000000−2i2i−2i2i00000000-2200000000
χ3922-2-2-2-2222-22-22-22-200002-200−2i2i−2i2i0000000000002i−2i2i−2i00000000-2200000000
χ4022-2-2-2-2222-22-22-22-200002-200−2i2i−2i2i000000000000−2i2i−2i2i000000002-200000000
χ4122-2-2-2-222-22-22-22-2200002-2002i−2i−2i2i000000002i−2i2i−2i00000000002-20000000000
χ4222-2-2-2-222-22-22-22-2200002-2002i−2i−2i2i00000000−2i2i−2i2i0000000000-220000000000
χ4322-2-2-2-222-22-22-22-2200002-200−2i2i2i−2i000000002i−2i2i−2i0000000000-220000000000
χ4422-2-2-2-222-22-22-22-2200002-200−2i2i2i−2i00000000−2i2i−2i2i00000000002-20000000000
χ45444-44-4-4-44-400-44000000000000000000000022−22−22220000000000000000000000
χ46444-44-4-4-44-400-440000000000000000000000−222222−220000000000000000000000
χ47444-44-4-4-4-44004-40000000000000000000000000022−22−2222000000000000000000
χ48444-44-4-4-4-44004-400000000000000000000000000−222222−22000000000000000000
χ4944-44-44-4-44400-4-4004-4-44000000000000000000000000000000000000000000
χ5044-44-44-4-44400-4-400-444-4000000000000000000000000000000000000000000
χ5144-4-4-4-4444-4-444-4-440000-440000000000000000000000000000000000000000
χ5244-4-4-4-444-444-4-444-40000-440000000000000000000000000000000000000000
χ534-444-4-44-4004400-4-40000004-400000000000000000000000000000000000000
χ544-444-4-44-4004400-4-4000000-4400000000000000000000000000000000000000
χ554-444-4-44-400-4-400440000000000000000004i−4i00000000000000000000000000
χ564-444-4-44-400-4-40044000000000000000000−4i4i00000000000000000000000000
χ574-4-4-4444-4004-400-4400000000000000000000000000000000000000002i2−2i20000
χ584-4-4-4444-4004-400-440000000000000000000000000000000000000000−2i22i20000
χ594-4-4-4444-400-44004-4000000000000000000000000000000000000002i2−2i2000000
χ604-4-4-4444-400-44004-400000000000000000000000000000000000000−2i22i2000000
χ618-88-8-88-88000000000000000000000000000000000000000000000000000000
χ628-8-888-8-88000000000000000000000000000000000000000000000000000000

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