Finite Group Databasebeta

← Group #257953

Character table — Group #257953

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size111111112222222244444444888888888888888888888888816161616161616161616161616161616
order12222222444444442244444444444444488888888888888884444444444448888
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
χ3111111111111111111111111111-1-111-1-1111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1
χ4111111111111111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111
χ51111111111111111111111111-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-11-1-1-1-111111-1-1-1-1
χ61111111111111111111111111-1-111-1-111-1-1-1-1-1-1-1-111111111-1-11-1-1-1-11-1-1-1-11111
χ71111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-11111
χ81111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-11111-11111-1-1-1-1
χ91111111111111111-1-1-1-1-1-111-11111-1-1111111-1-1-1-11111-1-1-1-1-11-111-1-1-111-1-111-1-1
χ101111111111111111-1-1-1-1-1-111-11111-1-111-1-1-1-11111-1-1-1-11111-11-111-1-1-1-1-111-1-111
χ111111111111111111-1-1-1-1-1-111-111-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-111-1-1111-1-111-1-111
χ121111111111111111-1-1-1-1-1-111-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-111-1-111111-1-111-1-1
χ131111111111111111-1-1-1-1-1-111-1-1-11111111111-1-1-1-1-1-1-1-111111-1-1-1-111-111-1-1-1-111
χ141111111111111111-1-1-1-1-1-111-1-1-1111111-1-1-1-111111111-1-1-1-11-1-1-1-111-1-1-11111-1-1
χ151111111111111111-1-1-1-1-1-111-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-111111-1111-1-11-1-11111-1-1
χ161111111111111111-1-1-1-1-1-111-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-11-1111-1-1111-1-1-1-111
χ172222222222-2-222-2-222-2-2-2-2-2-22002200-2-2000000000000000000-20000200000000
χ182222222222-2-222-2-222-2-2-2-2-2-2200-2-2002200000000000000000020000-200000000
χ192222222222-2-222-2-2-2-22222-2-2-2002200-2-200000000000000000020000-200000000
χ202222222222-2-222-2-2-2-22222-2-2-200-2-20022000000000000000000-20000200000000
χ2122222222-2-222-2-22222-2-222-2-2-2220022000000000000000000-2-200000000000000
χ2222222222-2-222-2-22222-2-222-2-2-2-2-200-2-20000000000000000002200000000000000
χ2322222222-2-222-2-222-2-222-2-2-2-222200-2-20000000000000000002-200000000000000
χ2422222222-2-222-2-222-2-222-2-2-2-22-2-20022000000000000000000-2200000000000000
χ2522222222-2-2-2-2-2-2-2-22222-2-222-20000000000000000000000000002-22-2000000000
χ2622222222-2-2-2-2-2-2-2-22222-2-222-2000000000000000000000000000-22-22000000000
χ2722222222-2-2-2-2-2-2-2-2-2-2-2-2222220000000000000000000000000002-2-22000000000
χ2822222222-2-2-2-2-2-2-2-2-2-2-2-222222000000000000000000000000000-222-2000000000
χ292-22-222-2-2-2-22-2222-20000002-20002i−2i002i−2i000022-2-20000000000000000002i−2i0000
χ302-22-222-2-2-2-22-2222-20000002-20002i−2i002i−2i0000-2-222000000000000000000−2i2i0000
χ312-22-222-2-2-2-22-2222-20000002-2000−2i2i00−2i2i000022-2-2000000000000000000−2i2i0000
χ322-22-222-2-2-2-22-2222-20000002-2000−2i2i00−2i2i0000-2-2220000000000000000002i−2i0000
χ332-22-222-2-2-2-2-2222-22000000-220002i−2i00−2i2i22-2-2000000000000000000002i−2i000000
χ342-22-222-2-2-2-2-2222-22000000-220002i−2i00−2i2i-2-22200000000000000000000−2i2i000000
χ352-22-222-2-2-2-2-2222-22000000-22000−2i2i002i−2i22-2-200000000000000000000−2i2i000000
χ362-22-222-2-2-2-2-2222-22000000-22000−2i2i002i−2i-2-222000000000000000000002i−2i000000
χ372-2-2-2-222200-2-200222-2002-20002-2002-2002−22−22−22−222−2−222−2−20000000000000000
χ382-2-2-2-222200-2-200222-2002-20002-2002-200−22−22−22−22−2−222−2−2220000000000000000
χ392-2-2-2-222200-2-200222-2002-2000-2200-22002−22−22−22−2−2−222−2−2220000000000000000
χ402-2-2-2-222200-2-200222-2002-2000-2200-2200−22−22−22−2222−2−222−2−20000000000000000
χ412-2-2-2-222200-2-20022-2200-220002-200-22002−22−2−22−2222−2−2−2−2220000000000000000
χ422-2-2-2-222200-2-20022-2200-220002-200-2200−22−222−22−2−2−22222−2−20000000000000000
χ432-2-2-2-222200-2-20022-2200-22000-22002-2002−22−2−22−22−2−22222−2−20000000000000000
χ442-2-2-2-222200-2-20022-2200-22000-22002-200−22−222−22−222−2−2−2−2220000000000000000
χ45444-4-4-44-44-4004-40000000000000000000000000000000000000000000000022−2200
χ46444-4-4-44-44-4004-400000000000000000000000000000000000000000000000−222200
χ47444-4-4-44-4-4400-44000000000000000000000000000000000000000000000000022−22
χ48444-4-4-44-4-4400-440000000000000000000000000000000000000000000000000−2222
χ4944-44-44-4-4004-400-440000000000000000022−22−22220000000000000000000000000000
χ5044-44-44-4-4004-400-4400000000000000000−222222−220000000000000000000000000000
χ5144-44-44-4-400-44004-400000000000000000000022−22−2222000000000000000000000000
χ5244-44-44-4-400-44004-4000000000000000000000−222222−22000000000000000000000000
χ5344-4-44-4-4400000000004-40000000000000000000002i−2i2i−2i2i−2i2i−2i0000000000000000
χ5444-4-44-4-4400000000004-4000000000000000000000−2i2i−2i2i−2i2i−2i2i0000000000000000
χ5544-4-44-4-440000000000-440000000000000000000002i−2i2i−2i−2i2i−2i2i0000000000000000
χ5644-4-44-4-440000000000-44000000000000000000000−2i2i−2i2i2i−2i2i−2i0000000000000000
χ574-444-4-4-444-400-4400000000000000000000000000000002i2−2i2−2i22i20000000000000000
χ584-444-4-4-444-400-440000000000000000000000000000000−2i22i22i2−2i20000000000000000
χ594-444-4-4-44-44004-40000000000000000000000000002i2−2i2−2i22i200000000000000000000
χ604-444-4-4-44-44004-4000000000000000000000000000−2i22i22i2−2i200000000000000000000
χ614-44-444-4-4444-4-4-44-4000000-4400000000000000000000000000000000000000000
χ624-44-444-4-444-44-4-4-440000004-400000000000000000000000000000000000000000
χ634-4-4-4-4444004400-4-44-400-440000000000000000000000000000000000000000000
χ644-4-4-4-4444004400-4-4-44004-40000000000000000000000000000000000000000000
χ658-8-888-88-8000000000000000000000000000000000000000000000000000000000

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