Finite Group Databasebeta

← Group #268009

Character table — Group #268009

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50
size1111222244444444488888888881616161616161616161616161616161616161616161632
order12222244224444444222444888822244444888888888888884
χ111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1111111-1
χ311111111111111111111111-1-1-1-11111-1-1-1-1-1-111-1-111-1-1-1-1-1-11
χ411111111111111111111111-1-1-1-11-1-11111111-1-111-1-1-1-1-1-1-1-1-1
χ5111111111111-1-11111-1-111-11111-111-11111-1-1-1-1-1-1-1-111-1-1-1-11
χ6111111111111-1-11111-1-111-11111-1-1-1-1-1-1-1-11111111111-1-1-1-1-1
χ7111111111111-1-11111-1-111-1-1-1-1-1-111-1-1-1-1-111-1-111-1-1-1-111111
χ8111111111111-1-11111-1-111-1-1-1-1-1-1-1-1-11111-1-111-1-111-1-11111-1
χ91111111111-1-111111-111-1-1111-1-1-111-11-11-11-1111-1-1-11-111-1-1-1
χ101111111111-1-111111-111-1-1111-1-1-1-1-1-1-11-11-11-1-1-11111-111-1-11
χ111111111111-1-111111-111-1-11-1-111-111-1-11-11-1111-11-1-1-11-1-111-1
χ121111111111-1-111111-111-1-11-1-111-1-1-1-11-11-11-1-1-11-111-11-1-1111
χ131111111111-1-1-1-1111-1-1-1-1-1-111-1-111111-11-1-11-1-1-11111-1-1-111-1
χ141111111111-1-1-1-1111-1-1-1-1-1-111-1-11-1-11-11-111-1111-1-1-11-1-1-1111
χ151111111111-1-1-1-1111-1-1-1-1-1-1-1-1111111-11-111-1-1-11-111-1111-1-1-1
χ161111111111-1-1-1-1111-1-1-1-1-1-1-1-1111-1-111-11-1-1111-11-1-1-1111-1-11
χ1722222222-2-222222-2-2-2-2-22-220000-20020000000000000000000
χ1822222222-2-222-2-22-2-2-2222-2-20000200-20000000000000000000
χ1922222222-2-2-2-2222-2-22-2-2-2220000200-20000000000000000000
χ2022222222-2-2-2-2-2-22-2-2222-22-20000-20020000000000000000000
χ21222222-2-2222200-2-2-2200-2-2000000000000000000000002i−2i2i−2i0
χ22222222-2-2222200-2-2-2200-2-200000000000000000000000−2i2i−2i2i0
χ23222222-2-222-2-200-2-2-2-20022000000000000000000000002i−2i−2i2i0
χ24222222-2-222-2-200-2-2-2-2002200000000000000000000000−2i2i2i−2i0
χ25222222-2-2-2-22200-222-200-22022220000000000000000-2-200000
χ26222222-2-2-2-22200-222-200-220-2-2-2-200000000000000002200000
χ27222222-2-2-2-2-2-200-2222002-2022-2-20000000000000000-2200000
χ28222222-2-2-2-2-2-200-2222002-20-2-22200000000000000002-200000
χ292222-2-2222-20022-22-202-200-20000000020-202000-20000000000
χ302222-2-2222-20022-22-202-200-200000000-2020-200020000000000
χ312222-2-2222-200-2-2-22-20-220020000000020-20-200020000000000
χ322222-2-2222-200-2-2-22-20-2200200000000-20202000-20000000000
χ332222-2-222-220022-2-220-2200-200000000020-202000-2000000000
χ342222-2-222-220022-2-220-2200-2000000000-2020-20002000000000
χ352222-2-222-2200-2-2-2-2202-200200000000020-20-20002000000000
χ362222-2-222-2200-2-2-2-2202-2002000000000-20202000-2000000000
χ374444-4-4-4-44-400004-44000000000000000000000000000000000
χ384444-4-4-4-4-44000044-4000000000000000000000000000000000
χ3944-4-4-4400004-4000000000002i2−2i22i2−2i200000000000000000000000
χ4044-4-4-4400004-400000000000−2i22i2−2i22i200000000000000000000000
χ4144-4-4-440000-44000000000002i2−2i2−2i22i200000000000000000000000
χ4244-4-4-440000-4400000000000−2i22i22i2−2i200000000000000000000000
χ434-4-4400-4400004-4000000000000002-200000002-200000000000
χ444-4-4400-4400004-400000000000000-220000000-2200000000000
χ454-4-4400-440000-44000000000000002-20000000-2200000000000
χ464-4-4400-440000-4400000000000000-2200000002-200000000000
χ4788-8-88-800000000000000000000000000000000000000000000
χ488-88-8000000000000000000000000000000000000022−220000000
χ498-88-80000000000000000000000000000000000000−22220000000
χ508-8-88008-8000000000000000000000000000000000000000000

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