Finite Group Databasebeta

← Group #249713

Character table — Group #249713

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444444888888888888888888888888161616161616161616161616161632
order12222222444444444444448888222244444488888888888888224444448888884
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-111-1-11111-1-1-1-1-1-111-1111-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-11111111111111111-1-11-1-1-1-1-111-1-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111-1-111111
χ51111111111111111111111-1-1-1-1111111-1-111-1-111-1-1-1-111-1-1-1-1-1-1111-111-1-1-1-111-1
χ61111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-111-1-1-11111-1-11
χ71111111111111111111111-1-1-1-111-1-1-1-11111-1-111-1-1-1-111-1-1-1-1111-1-11-1-1-1-111-1-11
χ81111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-111111-1-111-1
χ91111111111111111-1-1-1-1111111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-111111-1-1-1-11
χ101111111111111111-1-1-1-1111111-1-1111111-1-11111-1-1-1-1111111-1-1-1-1-11-1-1-1-11111-1
χ111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1111111-1
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-111-111-1-1-1-1-1-11
χ131111111111111111-1-1-1-111-1-1-1-1-1-11111-1-111-1-1-1-11111-1-11111111-1-1-111-1-111-1-1-1
χ141111111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-111111111-1-1-1-111-1-1-1-1-1-111-1-1111
χ151111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-1-11111-1-11111-1-1-1-1-1-1111
χ161111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1-1111111111-1-1-1
χ17222222222-22-22-22-20000-2-222220022-2-2-2-200-2-2000000000000000002000000000
χ18222222222-22-22-22-20000-2-2222200-2-2222200-2-200000000000000000-2000000000
χ19222222222-22-22-22-20000-2-2-2-2-2-20022-2-222002200000000000000000-2000000000
χ20222222222-22-22-22-20000-2-2-2-2-2-200-2-222-2-20022000000000000000002000000000
χ2122222222-22-22-22-222222-2-20000-2-20000002200-2-2000022000000-2000000000000
χ2222222222-22-22-22-222222-2-20000-2-2000000-2-200220000-2-20000002000000000000
χ2322222222-22-22-22-22-2-2-2-2-2-20000220000002200220000-2-2000000-2000000000000
χ2422222222-22-22-22-22-2-2-2-2-2-2000022000000-2-200-2-20000220000002000000000000
χ2522-2-222-2-2020-20-2022i2i−2i−2i00i2i2−i2−i2000000002i−2ii2−i20022−2−22-2i2i2−i2−i2000000002−200000
χ2622-2-222-2-2020-20-2022i2i−2i−2i00i2i2−i2−i200000000−2i2ii2−i20022−2−2-22−i2−i2i2i200000000−2200000
χ2722-2-222-2-2020-20-2022i2i−2i−2i00−i2−i2i2i2000000002i−2i−i2i200−2−2222-2−i2−i2i2i200000000−2200000
χ2822-2-222-2-2020-20-2022i2i−2i−2i00−i2−i2i2i200000000−2i2i−i2i200−2−222-22i2i2−i2−i2000000002−200000
χ2922-2-222-2-2020-20-202−2i−2i2i2i00i2i2−i2−i2000000002i−2ii2−i200−2−222-22−i2−i2i2i2000000002−200000
χ3022-2-222-2-2020-20-202−2i−2i2i2i00i2i2−i2−i200000000−2i2ii2−i200−2−2222-2i2i2−i2−i200000000−2200000
χ3122-2-222-2-2020-20-202−2i−2i2i2i00−i2−i2i2i2000000002i−2i−i2i20022−2−2-22i2i2−i2−i200000000−2200000
χ3222-2-222-2-2020-20-202−2i−2i2i2i00−i2−i2i2i200000000−2i2i−i2i20022−2−22-2−i2−i2i2i2000000002−200000
χ332-2-2-2-22222-2-222-2-222-22-2-2200002-200000000000000000000000000002-200002-20
χ342-2-2-2-22222-2-222-2-222-22-2-2200002-20000000000000000000000000000-220000-220
χ352-2-2-2-22222-2-222-2-22-22-22-220000-2200000000000000000000000000002-20000-220
χ362-2-2-2-22222-2-222-2-22-22-22-220000-220000000000000000000000000000-2200002-20
χ372-2-2-2-2222-222-2-222-20000-220000002-22-2000000002-22-20000002-20000000000000
χ382-2-2-2-2222-222-2-222-20000-220000002-22-200000000-22-22000000-220000000000000
χ392-2-2-2-2222-222-2-222-20000-22000000-22-22000000002-22-2000000-220000000000000
χ402-2-2-2-2222-222-2-222-20000-22000000-22-2200000000-22-220000002-20000000000000
χ412-2-2-2-2222-2-222-2-2222-22-22-20000-222-2-220000000000000000000002-20000000000
χ422-2-2-2-2222-2-222-2-2222-22-22-20000-22-222-2000000000000000000000-220000000000
χ432-2-2-2-2222-2-222-2-222-22-222-200002-22-2-22000000000000000000000-220000000000
χ442-2-2-2-2222-2-222-2-222-22-222-200002-2-222-20000000000000000000002-20000000000
χ4544444444-4-4-4-4-4-4-4-40000440000000000000000000000000000000000000000000
χ46444-4-4-44-44040-40-4000000000000000004-40000000000000000000000000000000
χ47444-4-4-44-44040-40-400000000000000000-440000000000000000000000000000000
χ48444-4-4-44-4-40-404040000000000000000000000000000000000000000000002i2−2i2000
χ49444-4-4-44-4-40-40404000000000000000000000000000000000000000000000−2i22i2000
χ5044-4-444-4-40-404040-40000002i22i2−2i2−2i20000000000−2i22i2000000000000000000000000000
χ5144-4-444-4-40-404040-4000000−2i2−2i22i22i200000000002i2−2i2000000000000000000000000000
χ524-444-44-4-404040-40-400000000000000000000000022−22−2222000000000000000000000
χ534-444-44-4-404040-40-4000000000000000000000000−222222−22000000000000000000000
χ544-444-44-4-40-40-404044i−4i−4i4i000000000000000000000000000000000000000000000
χ554-444-44-4-40-40-40404−4i4i4i−4i000000000000000000000000000000000000000000000
χ564-44-44-4-440000000000000022−2222−2200000000000022−220000002-22-2000000000000000
χ574-44-44-4-440000000000000022−2222−22000000000000−2222000000-22-22000000000000000
χ584-44-44-4-4400000000000000−2222−222200000000000022−22000000-22-22000000000000000
χ594-44-44-4-4400000000000000−2222−2222000000000000−22220000002-22-2000000000000000
χ604-4-444-44-440-40-40400000000000000000000000000000002i2−2i2−2i22i2000000000000000
χ614-4-444-44-440-40-4040000000000000000000000000000000−2i22i22i2−2i2000000000000000
χ624-4-444-44-4-404040-400000004i−4i−4i4i000000000000000000000000000000000000000
χ634-4-444-44-4-404040-40000000−4i4i4i−4i000000000000000000000000000000000000000
χ644-4-4-4-444444-4-444-4-400004-40000000000000000000000000000000000000000000
χ6588-88-8-8-88000000000000000000000000000000000000000000000000000000000

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