Finite Group Databasebeta

← Group #263389

Character table — Group #263389

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size11112222224444444488888888888888161616161616161616161616161632323232
order12222244444444888822444444888888222444444488888888
χ111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1
χ31111111111111111111111-1-1-1-111111111-1-1-111-1-1-1-1-1-1-111-1-1
χ41111111111111111111111-1-1-1-1111111-1-1111-1-11-1-1-1-1-1-1-1-111
χ5111111111111111111-1-1-1-1111111-1-1-1-111111111-1-1-1-111-1-1-1-1
χ6111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ7111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-1-111-11111-1-1-1-111
χ8111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1111-1-111111-1-111-1-1
χ911111111111111-1-1-1-111111111-1-1-1-1-1-11-11-1-11-1111-1-1-1-11-11-1
χ1011111111111111-1-1-1-111111111-1-1-1-1-1-1-11-111-11-111-1-1-1-1-11-11
χ1111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-11-1-1111-1-1-1-111111-1-11
χ1211111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-111-1-1-111-1-11111-111-1
χ1311111111111111-1-1-1-1-1-1-1-11111-1-111111-11-1-11-11-1-111-1-1-11-11
χ1411111111111111-1-1-1-1-1-1-1-11111-1-11111-11-111-11-1-1-111-1-11-11-1
χ1511111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111-1-1111-1-111-1-111-111-1
χ1611111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-111-1-1-11111-1-1111-1-11
χ172222222222-2-2-2-2222200002-22-2-2-200000000000000002-20000
χ182222222222-2-2-2-222220000-22-22-2-20000000000000000-220000
χ192222222222-2-2-2-2-2-2-2-200002-22-2220000000000000000-220000
χ202222222222-2-2-2-2-2-2-2-20000-22-222200000000000000002-20000
χ21222222-2-2-2-222-2-20000000022-2-2002i2i−2i−2i00000000002i−2i000000
χ22222222-2-2-2-222-2-20000000022-2-200−2i−2i2i2i0000000000−2i2i000000
χ23222222-2-2-2-222-2-200000000-2-222002i2i−2i−2i0000000000−2i2i000000
χ24222222-2-2-2-222-2-200000000-2-22200−2i−2i2i2i00000000002i−2i000000
χ25222222-2-2-2-2-2-222000022-2-22-2-22000000000000002-200000000
χ26222222-2-2-2-2-2-222000022-2-2-222-200000000000000-2200000000
χ27222222-2-2-2-2-2-2220000-2-2222-2-2200000000000000-2200000000
χ28222222-2-2-2-2-2-2220000-2-222-222-2000000000000002-200000000
χ292222-2-22-2-222-22-222-2-2000000002-200000022-200-20000000000
χ302222-2-22-2-222-22-222-2-2000000002-2000000-2-220020000000000
χ312222-2-22-2-222-22-2-2-22200000000-220000002-2200-20000000000
χ322222-2-22-2-222-22-2-2-22200000000-22000000-22-20020000000000
χ332222-2-22-2-22-22-2222-2-200000000-22000022000-2-200000000000
χ342222-2-22-2-22-22-2222-2-200000000-220000-2-20002200000000000
χ352222-2-22-2-22-22-22-2-222000000002-200002-2000-2200000000000
χ362222-2-22-2-22-22-22-2-222000000002-20000-220002-200000000000
χ374444-4-4-444-44-4-44000000000000000000000000000000000000
χ384444-4-4-444-4-444-4000000000000000000000000000000000000
χ3944-4-40004i−4i0000022−222i2−2i22-22i−2i0000002ζ−2ζ2ζ3−2ζ3000000000000000000
χ4044-4-40004i−4i0000022−222i2−2i2-22−2i2i000000−2ζ2ζ−2ζ32ζ3000000000000000000
χ4144-4-40004i−4i00000−2222−2i22i22-22i−2i000000−2ζ2ζ−2ζ32ζ3000000000000000000
χ4244-4-40004i−4i00000−2222−2i22i2-22−2i2i0000002ζ−2ζ2ζ3−2ζ3000000000000000000
χ4344-4-4000−4i4i0000022−22−2i22i22-2−2i2i000000−2ζ32ζ3−2ζ2ζ000000000000000000
χ4444-4-4000−4i4i0000022−22−2i22i2-222i−2i0000002ζ3−2ζ32ζ−2ζ000000000000000000
χ4544-4-4000−4i4i00000−22222i2−2i22-2−2i2i0000002ζ3−2ζ32ζ−2ζ000000000000000000
χ4644-4-4000−4i4i00000−22222i2−2i2-222i−2i000000−2ζ32ζ3−2ζ2ζ000000000000000000
χ478-88-800800-80000000000000000000000000000000000000000
χ488-88-800-80080000000000000000000000000000000000000000
χ498-8-888-800000000000000000000000000000000000000000000
χ508-8-88-8800000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.