Finite Group Databasebeta

← Group #317082

Character table — Group #317082

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size1111222222224444444448888888881616161616161616161616161616161632323232
order12222244444444488888888888888822444444888888884488
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
χ5111111111111111111111-1-1-1-11-1-1-1-1111-1111-1-1-1-1-111-1-111-1-1
χ6111111111111111111111-1-1-1-11-1-1-1-111-1111-11-1-1-1-1-1-111-1-111
χ7111111111111111111111-1-1-1-11-1-1-1-1-1-11-1-1-11-1111111-1-1-1-111
χ8111111111111111111111-1-1-1-11-1-1-1-1-1-1-11-1-1-111111-1-11111-1-1
χ9111111111111111-1-1-1-1-1-11111-1-1-1-1-11-11-11-11-111-1-1-1-1111-11-1
χ10111111111111111-1-1-1-1-1-11111-1-1-1-1-11-1-111-1-1111-1-111-1-1-11-11
χ11111111111111111-1-1-1-1-1-11111-1-1-1-1-1-111-1-111-1-1-111-1-111-11-11
χ12111111111111111-1-1-1-1-1-11111-1-1-1-1-1-11-11-11-11-1-11111-1-11-11-1
χ13111111111111111-1-1-1-1-1-1-1-1-1-1-111111-1111-111-1-111-1-1-1-11-1-11
χ14111111111111111-1-1-1-1-1-1-1-1-1-1-111111-1-1-11-1-1-1-1-1111111-111-1
χ15111111111111111-1-1-1-1-1-1-1-1-1-1-11111-1111-111111-1-1-1-1-1-1-111-1
χ16111111111111111-1-1-1-1-1-1-1-1-1-1-11111-11-1-1-11-1-111-1-111111-1-11
χ1722222222-2-222-2-2-22222-2-20000-200002200-2-200000000000000
χ1822222222-2-222-2-2-22222-2-20000-20000-2-2002200000000000000
χ1922222222-2-222-2-2-2-2-2-2-2220000200002-200-2200000000000000
χ2022222222-2-222-2-2-2-2-2-2-222000020000-22002-200000000000000
χ21222222-2-2-2-2-2-22-220000002i2i−2i−2i00000002000-200000002i−2i0000
χ22222222-2-2-2-2-2-22-220000002i2i−2i−2i0000000-200020000000−2i2i0000
χ23222222-2-2-2-2-2-22-22000000−2i−2i2i2i00000002000-20000000−2i2i0000
χ24222222-2-2-2-2-2-22-22000000−2i−2i2i2i0000000-2000200000002i−2i0000
χ252222-2-22-2-2-22-2-2220000002i−2i2i−2i000000002000-200002i−2i000000
χ262222-2-22-2-2-22-2-2220000002i−2i2i−2i00000000-200020000−2i2i000000
χ272222-2-22-2-2-22-2-222000000−2i2i−2i2i000000002000-20000−2i2i000000
χ282222-2-22-2-2-22-2-222000000−2i2i−2i2i00000000-2000200002i−2i000000
χ292222-2-2-2222-22-2-2222-2-2222-2-22-222-2-200000000000000000000
χ302222-2-2-2222-22-2-2222-2-222-222-2-2-2-22200000000000000000000
χ312222-2-2-2222-22-2-22-2-222-2-22-2-222-2-22200000000000000000000
χ322222-2-2-2222-22-2-22-2-222-2-2-222-2222-2-200000000000000000000
χ332222-2-2-22-2-2-2222-222-2-2-2-2000020000000000002i−2i2i−2i00000000
χ342222-2-2-22-2-2-2222-222-2-2-2-200002000000000000−2i2i−2i2i00000000
χ352222-2-2-22-2-2-2222-2-2-222220000-20000000000002i−2i−2i2i00000000
χ362222-2-2-22-2-2-2222-2-2-222220000-2000000000000−2i2i2i−2i00000000
χ37444444-4-444-4-4-44-400000000000000000000000000000000000
χ384444-4-44-4444-44-4-400000000000000000000000000000000000
χ3944-4-44-44-400-440000000000000022−2222−2200000000000000000000
χ4044-4-44-44-400-4400000000000000−2222−222200000000000000000000
χ4144-4-44-4-44004-40004-44-40000000000000000000000000000000
χ4244-4-44-4-44004-4000-44-440000000000000000000000000000000
χ4344-4-4-444400-4-40004-4-440000000000000000000000000000000
χ4444-4-4-444400-4-4000-444-40000000000000000000000000000000
χ4544-4-4-44-4-400440000000000000022−22−222200000000000000000000
χ4644-4-4-44-4-4004400000000000000−222222−2200000000000000000000
χ478-88-800008i−8i0000000000000000000000000000000000000000
χ488-88-80000−8i8i0000000000000000000000000000000000000000
χ498-8-8800000000000000042−4200000000000000000000000000000
χ508-8-88000000000000000−424200000000000000000000000000000

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