Finite Group Databasebeta

← Group #252210

Character table — Group #252210

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
χ3111111111111111111111111111-1-1-1-1-1-11-1-111111111-11-1-1-11-1-1-1-11111-1-1-1-1
χ4111111111111111111111111111-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-1-11-1-1-111111-1-1-1-11111
χ51111111111111111111111-1-11-1-11111-1-11-1-111111111-1-111-1-11111-1-1-1-1-1-1-1-1
χ61111111111111111111111-1-11-1-11111-1-11-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111
χ71111111111111111111111-1-11-1-1-1-1-1-111111111111111-1-1-11-1-1-1-1-1-1-1-1-11111
χ81111111111111111111111-1-11-1-1-1-1-1-111111-1-1-1-1-1-1-1-11-1-1-11-111111111-1-1-1-1
χ91111111111111111-1-1-1-11111-1-1-11111-1-1-1111111-1-1-1-111-1-1-1-111-1-111-1-111-1-1
χ101111111111111111-1-1-1-11111-1-1-11111-1-1-111-1-1-1-1111111-1-1-1-1-1-111-1-111-1-111
χ111111111111111111-1-1-1-11111-1-1-1-1-1-1-111-1-1-11111-1-1-1-1-11111-1-1-11111-1-1-1-111
χ121111111111111111-1-1-1-11111-1-1-1-1-1-1-111-1-1-1-1-1-1-11111-11111-111-1-1-1-11111-1-1
χ131111111111111111-1-1-1-111-1-1-111111111-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-111-1-111
χ141111111111111111-1-1-1-111-1-1-111111111-1-1-1-1-1-1-11111-1-1-1-111-1-11111-1-111-1-1
χ151111111111111111-1-1-1-111-1-1-111-1-1-1-1-1-1-1111111-1-1-1-11-111-11-1-111-1-11111-1-1
χ161111111111111111-1-1-1-111-1-1-111-1-1-1-1-1-1-111-1-1-1-111111-111-1111-1-111-1-1-1-111
χ172222222222-2-222-2-22222-2-200-200000022-22200000000-2000-20000000000000
χ182222222222-2-222-2-22222-2-200-2000000-2-2-2-2-200000000200020000000000000
χ192222222222-2-222-2-2-2-2-2-2-2-2002000000222-2-2000000002000-20000000000000
χ202222222222-2-222-2-2-2-2-2-2-2-2002000000-2-222200000000-200020000000000000
χ2122222222-2-222-2-22222-2-2-2-222-2-2-2000000200000000000-20002000000000000
χ2222222222-2-222-2-22222-2-2-2-2-2-2-2220000002000000000002000-2000000000000
χ2322222222-2-222-2-222-2-222-2-222222000000-200000000000-2000-2000000000000
χ2422222222-2-222-2-222-2-222-2-2-2-22-2-2000000-20000000000020002000000000000
χ2522222222-2-2-2-2-2-2-2-222-2-2220020022-2-200-20000000000002-200000000000000
χ2622222222-2-2-2-2-2-2-2-222-2-22200200-2-22200-2000000000000-2200000000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2222200-20022-2-2002000000000000-2200000000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2222200-200-2-2220020000000000002-200000000000000
χ2922-22-2-22-2-2-20022002-22-2000000000002i−2i02i−2ii2i2−i2−i2i2i2−i2−i2000000000000002−22−2
χ3022-22-2-22-2-2-20022002-22-2000000000002i−2i02i−2i−i2−i2i2i2−i2−i2i2i200000000000000−22−22
χ3122-22-2-22-2-2-20022002-22-200000000000−2i2i0−2i2ii2i2−i2−i2i2i2−i2−i200000000000000−22−22
χ3222-22-2-22-2-2-20022002-22-200000000000−2i2i0−2i2i−i2−i2i2i2−i2−i2i2i2000000000000002−22−2
χ3322-22-2-22-2-2-2002200-22-22000000000002i−2i0−2i2ii2i2−i2−i2−i2−i2i2i200000000000000−222−2
χ3422-22-2-22-2-2-2002200-22-22000000000002i−2i0−2i2i−i2−i2i2i2i2i2−i2−i2000000000000002−2−22
χ3522-22-2-22-2-2-2002200-22-2200000000000−2i2i02i−2ii2i2−i2−i2−i2−i2i2i2000000000000002−2−22
χ3622-22-2-22-2-2-2002200-22-2200000000000−2i2i02i−2i−i2−i2i2i2i2i2−i2−i200000000000000−222−2
χ3722-2-22-2-222-22-22-22-200002-2000002i−2i2i−2i0000000002i−2i2i−2i000000002-200000000
χ3822-2-22-2-222-22-22-22-200002-2000002i−2i2i−2i000000000−2i2i−2i2i00000000-2200000000
χ3922-2-22-2-222-22-22-22-200002-200000−2i2i−2i2i0000000002i−2i2i−2i00000000-2200000000
χ4022-2-22-2-222-22-22-22-200002-200000−2i2i−2i2i000000000−2i2i−2i2i000000002-200000000
χ4122-2-22-2-22-22-22-22-2200002-2000002i−2i−2i2i000002i−2i2i−2i00000000002-20000000000
χ4222-2-22-2-22-22-22-22-2200002-2000002i−2i−2i2i00000−2i2i−2i2i0000000000-220000000000
χ4322-2-22-2-22-22-22-22-2200002-200000−2i2i2i−2i000002i−2i2i−2i0000000000-220000000000
χ4422-2-22-2-22-22-22-22-2200002-200000−2i2i2i−2i00000−2i2i−2i2i00000000002-20000000000
χ45444-4-44-4-44-400-44000000000000000000000022−22−22220000000000000000000000
χ46444-4-44-4-44-400-440000000000000000000000−222222−220000000000000000000000
χ47444-4-44-4-4-44004-40000000000000000000000000022−22−2222000000000000000000
χ48444-4-44-4-4-44004-400000000000000000000000000−222222−22000000000000000000
χ4944-44-4-44-44400-4-4004-4-44000000000000000000000000000000000000000000
χ5044-44-4-44-44400-4-400-444-4000000000000000000000000000000000000000000
χ5144-4-44-4-444-4-444-4-440000-440000000000000000000000000000000000000000
χ5244-4-44-4-44-444-4-444-40000-440000000000000000000000000000000000000000
χ534-444-4-4-44004400-4-40000000004i−4i00000000000000000000000000000000000
χ544-444-4-4-44004400-4-4000000000−4i4i00000000000000000000000000000000000
χ554-444-4-4-4400-4-400440000004-400000000000000000000000000000000000000
χ564-444-4-4-4400-4-40044000000-4400000000000000000000000000000000000000
χ574-4-4-4-4444004-400-440000000000000000000000000000000000000022−22000000
χ584-4-4-4-4444004-400-4400000000000000000000000000000000000000−2222000000
χ594-4-4-4-444400-44004-4000000000000000000000000000000000000000022−220000
χ604-4-4-4-444400-44004-40000000000000000000000000000000000000000−22220000
χ618-88-88-88-8000000000000000000000000000000000000000000000000000000
χ628-8-8888-8-8000000000000000000000000000000000000000000000000000000

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