Finite Group Databasebeta

← Group #265684

Character table — Group #265684

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size111111112222222244444444888888888888888888888888816161616161616161616161616161616
order12222222222244444444444422444444444444444888888884444444444448888
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111-1-1-1-111111111-1-11-1-11-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ411111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-111111111
χ5111111111111111111111111-1-11-1-1111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1
χ6111111111111111111111111-1-11-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-111-1-1-1-11111
χ7111111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-111111111111111-1-1-1-1-1-1-1-1-1-11111
χ8111111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-111-1111111-1-1-1-1
χ9111111111111-1-1-1-11-1-1-1-111111-1111111-1-1-1-111-1-11111-1-1-1-11-1-11-1-11-111-1-111-1-1
χ10111111111111-1-1-1-11-1-1-1-111111-1111111-1-1-1-1-1-1111111-1-1-1-1-11-1-11-1-11-1-111-1-111
χ11111111111111-1-1-1-11-1-1-1-111111-111-1-1-1-1111111-1-1-1-1-1-111111-1-11-1-11-1-1-111-1-111
χ12111111111111-1-1-1-11-1-1-1-111111-111-1-1-1-11111-1-111-1-1-1-11111-11-1-11-1-1111-1-111-1-1
χ13111111111111-1-1-1-11-1-1-1-1111-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-111111-11-111-1111-1-1-1-111
χ14111111111111-1-1-1-11-1-1-1-1111-1-1-1-1-11111-1-1-1-1-1-111-1-1-1-11111-1111-111-1-1-11111-1-1
χ15111111111111-1-1-1-11-1-1-1-1111-1-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-11-11-111-11-1-11111-1-1
χ16111111111111-1-1-1-11-1-1-1-1111-1-1-1-1-1-1-1-1-11111-1-1111111-1-1-1-1-1111-111-111-1-1-1-111
χ172222222222222222-2-2-222-2-2-200-20000000000222200000000-2-200000000000000
χ182222222222222222-2-2-222-2-2-200-20000000000-2-2-2-2000000002200000000000000
χ19222222222222-2-2-2-2-222-2-2-2-2-2002000000000022-2-200000000-2200000000000000
χ20222222222222-2-2-2-2-222-2-2-2-2-20020000000000-2-222000000002-200000000000000
χ2122222222-2-2-2-222222-2-2-2-2-2-220020000000000000000000000000220-2-200000000
χ2222222222-2-2-2-222222-2-2-2-2-2-220020000000000000000000000000-2-202200000000
χ2322222222-2-2-2-22222-222-2-222-222-2-2-20000000000000000000000200-20000000000
χ2422222222-2-2-2-22222-222-2-222-2-2-2-2220000000000000000000000-20020000000000
χ2522222222-2-2-2-2-2-2-2-222222-2-2200-200000000000000000000000002-20-2200000000
χ2622222222-2-2-2-2-2-2-2-222222-2-2200-20000000000000000000000000-2202-200000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-22222-2222-2-20000000000000000000000-20020000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-22222-2-2-22220000000000000000000000200-20000000000
χ2922-222-2-2-222-2-20000200002-2-22-202-222-2-20000000022-2-200000000000000000000
χ3022-222-2-2-222-2-20000200002-2-22-202-2-2-22200000000-2-22200000000000000000000
χ3122-222-2-2-222-2-20000200002-2-2-220-2222-2-200000000-2-22200000000000000000000
χ3222-222-2-2-222-2-20000200002-2-2-220-22-2-2220000000022-2-200000000000000000000
χ3322-222-2-2-2-2-2220000-200002-222-20-2200002i2i−2i−2i000000002i2i−2i−2i0000000000000000
χ3422-222-2-2-2-2-2220000-200002-222-20-220000−2i−2i2i2i00000000−2i−2i2i2i0000000000000000
χ3522-222-2-2-2-2-2220000-200002-22-2202-200002i2i−2i−2i00000000−2i−2i2i2i0000000000000000
χ3622-222-2-2-2-2-2220000-200002-22-2202-20000−2i−2i2i2i000000002i2i−2i−2i0000000000000000
χ372-2-2-22-2222-2-2222-2-20002-200000000000000002-22-22−22−22−22−20000000000002−22−2
χ382-2-2-22-2222-2-2222-2-20002-200000000000000002-22-2−22−22−22−22000000000000−22−22
χ392-2-2-22-2222-2-2222-2-20002-20000000000000000-22-222−22−22−22−2000000000000−22−22
χ402-2-2-22-2222-2-2222-2-20002-20000000000000000-22-22−22−22−22−220000000000002−22−2
χ412-2-2-22-2222-2-22-2-222000-2200000000000000002-2-222−22−2−22−220000000000002−2−22
χ422-2-2-22-2222-2-22-2-222000-2200000000000000002-2-22−22−222−22−2000000000000−222−2
χ432-2-2-22-2222-2-22-2-222000-220000000000000000-222-22−22−2−22−22000000000000−222−2
χ442-2-2-22-2222-2-22-2-222000-220000000000000000-222-2−22−222−22−20000000000002−2−22
χ45444-4-4-44-400004-44-4000000000000000000000000000000000000000002-22-20000
χ46444-4-4-44-400004-44-400000000000000000000000000000000000000000-22-220000
χ47444-4-4-44-40000-44-44000000000000000000000000000000000000000002-2-220000
χ48444-4-4-44-40000-44-4400000000000000000000000000000000000000000-222-20000
χ4944-444-4-4-444-4-40000-40000-44400000000000000000000000000000000000000000
χ5044-444-4-4-4-4-444000040000-44-400000000000000000000000000000000000000000
χ514-444-4-4-440000000004i−4i00000000002i−2i2i−2i2-22-20000000000000000000000000000
χ524-444-4-4-440000000004i−4i0000000000−2i2i−2i2i-22-220000000000000000000000000000
χ534-444-4-4-44000000000−4i4i00000000002i−2i2i−2i-22-220000000000000000000000000000
χ544-444-4-4-44000000000−4i4i0000000000−2i2i−2i2i2-22-20000000000000000000000000000
χ554-44-444-4-44-44-40000000000000000000000000000022−22−222200000000000000000000
χ564-44-444-4-44-44-400000000000000000000000000000−222222−2200000000000000000000
χ574-44-444-4-4-44-440000000000000000000000000000000002i2−2i2−2i22i20000000000000000
χ584-44-444-4-4-44-44000000000000000000000000000000000−2i22i22i2−2i20000000000000000
χ594-4-44-444-400004-4-4400000000000002i−2i−2i2i2i−2i−2i2i0000000000000000000000000000
χ604-4-44-444-400004-4-440000000000000−2i2i2i−2i−2i2i2i−2i0000000000000000000000000000
χ614-4-44-444-40000-444-400000000000002i−2i−2i2i−2i2i2i−2i0000000000000000000000000000
χ624-4-44-444-40000-444-40000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000000000000000
χ634-4-4-44-444-444-444-4-4000-4400000000000000000000000000000000000000000000
χ644-4-4-44-444-444-4-4-4440004-400000000000000000000000000000000000000000000
χ6588-8-8-88-88000000000000000000000000000000000000000000000000000000000

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