Finite Group Databasebeta

← Group #312488

Character table — Group #312488

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size11111111222222224444444444888888888888888888888888161616161616161616161616161632
order12222222444444444444448888444444444488888888888888444444448888884
χ111111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1-1-111111111111111111-1-1-1-1-1-1-1-1-111-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-111-1-1-1-1-111-1-1111
χ51111111111111111111111-1-1-1-1111111-1-11111-1-1-1-1-1-111-1-1-1-1111-111-1-111-1-1-1-1-1
χ61111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111111
χ71111111111111111111111-1-1-1-111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-11-1-11-1-111-1-1-1-1111
χ81111111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1111-1-1111111-1-1-1
χ91111111111111111-1-1-1-1111111-1-111111111-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-1-1-111-1-11
χ101111111111111111-1-1-1-1111111-1-1111111-1-111-1-1-1-111111111-1-1-11-1-1-1-111-1-111-1
χ111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-11-1-1-11111111111-1
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-111-11111-1-1-1-1-1-11
χ131111111111111111-1-1-1-111-1-1-1-1-1-11111-1-111-1-11111-1-1-1-11111111-1-1-111-1-1-1-111-1
χ141111111111111111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1-1-1111111-1-11
χ151111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1-1-111111-1-1111-1-111-1-1-1-11
χ161111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-111-1-1-1-1-111111-1-1-1-11111-1
χ17222222222-22-22-22-20000-2-222220022-2-2-2-200000000-2-2000000000200000000000
χ18222222222-22-22-22-20000-2-2222200-2-2222200000000-2-2000000000-200000000000
χ19222222222-22-22-22-20000-2-2-2-2-2-20022-2-2220000000022000000000-200000000000
χ20222222222-22-22-22-20000-2-2-2-2-2-200-2-222-2-20000000022000000000200000000000
χ2122222222-22-22-22-222222-2-20000-2-200000022-2-2000000220000-200000000000000
χ2222222222-22-22-22-222222-2-20000-2-2000000-2-222000000-2-20000200000000000000
χ2322222222-22-22-22-22-2-2-2-2-2-20000220000002222000000-2-20000-200000000000000
χ2422222222-22-22-22-22-2-2-2-2-2-2000022000000-2-2-2-2000000220000200000000000000
χ2522-2-22-22-22-2-222-2-222i2i−2i−2i-2200002i−2i000000000000000000000002-2000002i−2i00000
χ2622-2-22-22-22-2-222-2-222i2i−2i−2i-2200002i−2i00000000000000000000000-2200000−2i2i00000
χ2722-2-22-22-22-2-222-2-22−2i−2i2i2i-220000−2i2i000000000000000000000002-200000−2i2i00000
χ2822-2-22-22-22-2-222-2-22−2i−2i2i2i-220000−2i2i00000000000000000000000-22000002i−2i00000
χ2922-2-22-22-2-222-2-222-20000-220000002i−2i2i−2i0000002i2i−2i−2i000000000000002-20000000
χ3022-2-22-22-2-222-2-222-20000-220000002i−2i2i−2i000000−2i−2i2i2i00000000000000-220000000
χ3122-2-22-22-2-222-2-222-20000-22000000−2i2i−2i2i0000002i2i−2i−2i00000000000000-220000000
χ3222-2-22-22-2-222-2-222-20000-22000000−2i2i−2i2i000000−2i−2i2i2i000000000000002-20000000
χ3322-2-22-22-2-2-222-2-2222i2i−2i−2i2-20000−2i2i2i−2i−2i2i00000000000000000000002-2000000000
χ3422-2-22-22-2-2-222-2-2222i2i−2i−2i2-20000−2i2i−2i2i2i−2i0000000000000000000000-22000000000
χ3522-2-22-22-2-2-222-2-222−2i−2i2i2i2-200002i−2i2i−2i−2i2i0000000000000000000000-22000000000
χ3622-2-22-22-2-2-222-2-222−2i−2i2i2i2-200002i−2i−2i2i2i−2i00000000000000000000002-2000000000
χ372-2-2-222-2202020-20-22i−2i2i−2i0022−2−2000000002-200i2−i2i2−i22−22i−2ii2i2−i2−i200000000002−2000
χ382-2-2-222-2202020-20-22i−2i2i−2i0022−2−200000000-2200i2−i2i2−i22−2−2i2i−i2−i2i2i20000000000−22000
χ392-2-2-222-2202020-20-22i−2i2i−2i00−2−222000000002-200−i2i2−i2i2−222i−2i−i2−i2i2i20000000000−22000
χ402-2-2-222-2202020-20-22i−2i2i−2i00−2−22200000000-2200−i2i2−i2i2−22−2i2ii2i2−i2−i200000000002−2000
χ412-2-2-222-2202020-20-2−2i2i−2i2i0022−2−2000000002-200−i2i2−i2i22−2−2i2i−i2−i2i2i200000000002−2000
χ422-2-2-222-2202020-20-2−2i2i−2i2i0022−2−200000000-2200−i2i2−i2i22−22i−2ii2i2−i2−i20000000000−22000
χ432-2-2-222-2202020-20-2−2i2i−2i2i00−2−222000000002-200i2−i2i2−i2−22−2i2ii2i2−i2−i20000000000−22000
χ442-2-2-222-2202020-20-2−2i2i−2i2i00−2−22200000000-2200i2−i2i2−i2−222i−2i−i2−i2i2i200000000002−2000
χ4544444444-4-4-4-4-4-4-4-40000440000000000000000000000000000000000000000000
χ46444-4-44-4-440-40-404000000000000000000000000000000022−2222−22000000000000000
χ47444-4-44-4-440-40-4040000000000000000000000000000000−2222−2222000000000000000
χ48444-4-44-4-4-404040-400000004-44-4000000000000000000000000000000000000000
χ49444-4-44-4-4-404040-40000000-44-44000000000000000000000000000000000000000
χ5044-44-4-4-444040-40-4000000000000000004-40000000000000000000000000000000
χ5144-44-4-4-444040-40-400000000000000000-440000000000000000000000000000000
χ5244-44-4-4-44-40-40404000000000000000000000000000000000000000000000002i2−2i20
χ5344-44-4-4-44-40-4040400000000000000000000000000000000000000000000000−2i22i20
χ5444-4-44-44-444-4-444-4-400004-40000000000000000000000000000000000000000000
χ554-4444-4-4-4040-40-404000000000000000000000022−22−222200000000000000000000000
χ564-4444-4-4-4040-40-4040000000000000000000000−222222−2200000000000000000000000
χ574-4444-4-4-40-404040-44-4-44000000000000000000000000000000000000000000000
χ584-4444-4-4-40-404040-4-444-4000000000000000000000000000000000000000000000
χ594-4-44-444-40000000000000022−22−222200000000002i2−2i2000000002i−2i−2i2i000000000000000
χ604-4-44-444-40000000000000022−22−22220000000000−2i22i200000000−2i2i2i−2i000000000000000
χ614-4-44-444-400000000000000−222222−2200000000002i2−2i200000000−2i2i2i−2i000000000000000
χ624-4-44-444-400000000000000−222222−220000000000−2i22i2000000002i−2i−2i2i000000000000000
χ634-4-4-444-440-40-404040000002222−22−220000000000000000−2222000000000000000000000
χ644-4-4-444-440-40-40404000000−22−222222000000000000000022−22000000000000000000000
χ658-88-8-8-888000000000000000000000000000000000000000000000000000000000

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