Finite Group Databasebeta

← Group #253213

Character table — Group #253213

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size111111112222222244444444888888888888888888888888816161616161616161616161616161616
order12222222444444442244444444444444488888888888888882444444444448888
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-11-1-111111111-1-1-1-1-1-1-1-1-111-1-1-1-1-11111-1-1-1-1
χ41111111111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-111111111-111-1-1-1-1-1-1-1-1-11111
χ5111111111111111111111111-1-1-1-11111111111111111111111-1-11-1-1-1-1-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-11-1-1-1-111111111
χ7111111111111111111111111-1-1-1-1-1-11-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111
χ8111111111111111111111111-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-111111111-1-1-1-111111111-1-1-1-1
χ91111111111111111-1-1-1-1-1-111111111-1-1-11111-1-1-1-11111-1-1-1-1-1-1-1111-1-111-1-111-1-1
χ101111111111111111-1-1-1-1-1-111111111-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1111-1-1-1-111-1-111
χ111111111111111111-1-1-1-1-1-1111111-1-1-1111111-1-1-1-1-1-1-1-111111-1-1-1-1-11111-1-1-1-111
χ121111111111111111-1-1-1-1-1-1111111-1-1-111-1-1-1-111111111-1-1-1-11-1-1-1-1-111-1-11111-1-1
χ131111111111111111-1-1-1-1-1-111-1-1-1-111-1-1-11111-1-1-1-11111-1-1-1-1-1111-1-111-1-111-1-111
χ141111111111111111-1-1-1-1-1-111-1-1-1-111-1-1-1-1-1-1-11111-1-1-1-11111-1111-1-11111-1-111-1-1
χ151111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111111-111-1-1-1-11111-1-1
χ161111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1111-111-1-111-1-1-1-111
χ172222222222-2-222-2-222-2-222-2-2000022-2220000000000000000-200-2000000000000
χ182222222222-2-222-2-222-2-222-2-20000-2-2-2-2-200000000000000002002000000000000
χ192222222222-2-222-2-2-2-222-2-2-2-20000222-2-20000000000000000200-2000000000000
χ202222222222-2-222-2-2-2-222-2-2-2-20000-2-22220000000000000000-2002000000000000
χ2122222222-2-222-2-22222-2-2-2-2-2-222-2-20020000000000000000000-220000000000000
χ2222222222-2-222-2-22222-2-2-2-2-2-2-2-22200200000000000000000002-20000000000000
χ2322222222-2-222-2-222-2-22222-2-222-2-200-200000000000000000002-20000000000000
χ2422222222-2-222-2-222-2-22222-2-2-2-22200-20000000000000000000-220000000000000
χ2522222222-2-2-2-2-2-2-2-22222-2-222000000-200000000000000000000002-22-200000000
χ2622222222-2-2-2-2-2-2-2-22222-2-222000000-20000000000000000000000-22-2200000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-22222000000200000000000000000000002-2-2200000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-2222200000020000000000000000000000-222-200000000
χ2922-2-222-2-2-2-20022002-2002-20000002i−2i02i−2i22−2−222−2−2i2i2−i2−i2i2i2−i2−i20000000000000000
χ3022-2-222-2-2-2-20022002-2002-20000002i−2i02i−2i−2−222−2−222−i2−i2i2i2−i2−i2i2i20000000000000000
χ3122-2-222-2-2-2-20022002-2002-2000000−2i2i0−2i2i22−2−222−2−2−i2−i2i2i2−i2−i2i2i20000000000000000
χ3222-2-222-2-2-2-20022002-2002-2000000−2i2i0−2i2i−2−222−2−222i2i2−i2−i2i2i2−i2−i20000000000000000
χ3322-2-222-2-2-2-2002200-2200-220000002i−2i0−2i2i22−2−2−2−222i2i2−i2−i2−i2−i2i2i20000000000000000
χ3422-2-222-2-2-2-2002200-2200-220000002i−2i0−2i2i−2−22222−2−2−i2−i2i2i2i2i2−i2−i20000000000000000
χ3522-2-222-2-2-2-2002200-2200-22000000−2i2i02i−2i22−2−2−2−222−i2−i2i2i2i2i2−i2−i20000000000000000
χ3622-2-222-2-2-2-2002200-2200-22000000−2i2i02i−2i−2−22222−2−2i2i2−i2−i2−i2−i2i2i20000000000000000
χ372-22-22-2-222-2222-2-2-20000002-22i−2i2i−2i0000000002i−2i2i−2i0000000000000000002-20000
χ382-22-22-2-222-2222-2-2-20000002-22i−2i2i−2i000000000−2i2i−2i2i000000000000000000-220000
χ392-22-22-2-222-2222-2-2-20000002-2−2i2i−2i2i0000000002i−2i2i−2i000000000000000000-220000
χ402-22-22-2-222-2222-2-2-20000002-2−2i2i−2i2i000000000−2i2i−2i2i0000000000000000002-20000
χ412-22-22-2-22-2222-22-2-2000000-222i−2i−2i2i000002i−2i2i−2i000000000000000000002-2000000
χ422-22-22-2-22-2222-22-2-2000000-222i−2i−2i2i00000−2i2i−2i2i00000000000000000000-22000000
χ432-22-22-2-22-2222-22-2-2000000-22−2i2i2i−2i000002i−2i2i−2i00000000000000000000-22000000
χ442-22-22-2-22-2222-22-2-2000000-22−2i2i2i−2i00000−2i2i−2i2i000000000000000000002-2000000
χ45444-4-4-44-400000000004-40000000000000000000002-22-22-22-20000000000000000
χ46444-4-4-44-400000000004-4000000000000000000000-22-22-22-220000000000000000
χ47444-4-4-44-40000000000-440000000000000000000002-22-2-22-220000000000000000
χ48444-4-4-44-40000000000-44000000000000000000000-22-222-22-20000000000000000
χ4944-44-4-4-44004-4004-400000000000000000000000002i2−2i2−2i22i200000000000000000000
χ5044-44-4-4-44004-4004-40000000000000000000000000−2i22i22i2−2i200000000000000000000
χ5144-44-4-4-4400-4400-44000000000000000000000000000002i2−2i2−2i22i20000000000000000
χ5244-44-4-4-4400-4400-4400000000000000000000000000000−2i22i22i2−2i20000000000000000
χ5344-4-444-4-44400-4-4004-400-440000000000000000000000000000000000000000000
χ5444-4-444-4-44400-4-400-44004-40000000000000000000000000000000000000000000
χ554-44-44-4-444-4-4-44-444000000-4400000000000000000000000000000000000000000
χ564-44-44-4-44-44-4-4-44440000004-400000000000000000000000000000000000000000
χ574-4-444-44-44-400-4400000000000000000002i2−2i2−2i22i20000000000000000000000000000
χ584-4-444-44-44-400-440000000000000000000−2i22i22i2−2i20000000000000000000000000000
χ594-4-444-44-4-44004-4000000000000000000000002i2−2i2−2i22i2000000000000000000000000
χ604-4-444-44-4-44004-400000000000000000000000−2i22i22i2−2i2000000000000000000000000
χ614-4-4-4-4444004-400-4400000000000000000000000000000000000000000000022−2200
χ624-4-4-4-4444004-400-44000000000000000000000000000000000000000000000−222200
χ634-4-4-4-444400-44004-40000000000000000000000000000000000000000000000022−22
χ644-4-4-4-444400-44004-400000000000000000000000000000000000000000000000−2222
χ658-888-88-8-8000000000000000000000000000000000000000000000000000000000

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