Finite Group Databasebeta

← Group #264178

Character table — Group #264178

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size111111112222222244444444448888888888888888888816161616161616161616161616163232
order12222222444444444444448888444444888888888888882444444488888844
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-1111111-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1111111111111111-1-1-1-1-1-11-1-1-1-111-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-111
χ51111111111111111111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1111-1-1-1-11-1
χ61111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1111-1-1-1-1-1-11111-11
χ71111111111111111111111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-11-1-1-11111-1-111-1-1-11
χ81111111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111-111-1-1111-1
χ91111111111111111-1-1-1-1111111-1-11111111111-1-1-1-11111-11-1-11-1-1-11111-1-1-1-1
χ101111111111111111-1-1-1-1111111-1-11111-1-1-1-111-1-1-1-1-1-1-1-111-1-11-1-11-1-1-1-11111
χ111111111111111111-1-1-1-1111111-1-1-1-1-1-1111111-1-1-1-11111-1-111-111-1-1-1-1-1-1-111
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11-111-1111111111-1-1
χ131111111111111111-1-1-1-111-1-1-1-1-1-111-1-11111-1-11111-1-1-1-1-11-1-1-111-111-1-111-11
χ141111111111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-1-1-11111111111-1-1-1111-1-111-1-11-1
χ151111111111111111-1-1-1-111-1-1-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-1111-1-1-1-1-111111-1
χ161111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111111-1111-1-1111-1-1-1-1-11
χ172222222222-2-2-2-2220000-2-222220022220000-2-2000000000-200-200000000000
χ182222222222-2-2-2-2220000-2-2222200-2-2-2-20000-2-2000000000200200000000000
χ192222222222-2-2-2-2220000-2-2-2-2-2-20022-2-2000022000000000-200200000000000
χ202222222222-2-2-2-2220000-2-2-2-2-2-200-2-222000022000000000200-200000000000
χ2122222222-2-22222-2-22222-2-20000-2-2000022-2-200000000002000000-200000000
χ2222222222-2-22222-2-22222-2-20000-2-20000-2-2220000000000-2000000200000000
χ2322222222-2-22222-2-2-2-2-2-2-2-2000022000022-2-20000000000-2000000200000000
χ2422222222-2-22222-2-2-2-2-2-2-2-20000220000-2-22200000000002000000-200000000
χ2522-2-22-22-22-200002-20000002i2i−2i−2i002-22i−2ii2−i2i2−i200000022−2−200000000i2−i22−20000
χ2622-2-22-22-22-200002-20000002i2i−2i−2i002-22i−2i−i2i2−i2i2000000−2−22200000000−i2i2−220000
χ2722-2-22-22-22-200002-20000002i2i−2i−2i00-22−2i2ii2−i2i2−i200000022−2−200000000−i2i2−220000
χ2822-2-22-22-22-200002-20000002i2i−2i−2i00-22−2i2i−i2i2−i2i2000000−2−22200000000i2−i22−20000
χ2922-2-22-22-22-200002-2000000−2i−2i2i2i002-2−2i2ii2−i2i2−i2000000−2−22200000000i2−i2−220000
χ3022-2-22-22-22-200002-2000000−2i−2i2i2i002-2−2i2i−i2i2−i2i200000022−2−200000000−i2i22−20000
χ3122-2-22-22-22-200002-2000000−2i−2i2i2i00-222i−2ii2−i2i2−i2000000−2−22200000000−i2i22−20000
χ3222-2-22-22-22-200002-2000000−2i−2i2i2i00-222i−2i−i2i2−i2i200000022−2−200000000i2−i2−220000
χ332-2-22-2-2222222-2-2-2-222-2-22-200002-2000000000000002i−2i2i−2i0000000000002i−2i00
χ342-2-22-2-2222222-2-2-2-222-2-22-200002-200000000000000−2i2i−2i2i000000000000−2i2i00
χ352-2-22-2-2222222-2-2-2-2-2-2222-20000-22000000000000002i−2i2i−2i000000000000−2i2i00
χ362-2-22-2-2222222-2-2-2-2-2-2222-20000-2200000000000000−2i2i−2i2i0000000000002i−2i00
χ372-2-22-2-222-2-222-2-22222-2-2-222-22-2-22000000002-222-2-200000000000000000000
χ382-2-22-2-222-2-222-2-22222-2-2-22-22-22-2200000000-22-2-22200000000000000000000
χ392-2-22-2-222-2-222-2-222-2-222-222-22-22-2000000002-2-2-22200000000000000000000
χ402-2-22-2-222-2-222-2-222-2-222-22-22-222-200000000-2222-2-200000000000000000000
χ412-2-22-2-222-2-2-2-2222200002-22-22-20000000000-2200000000002-202-2000000000
χ422-2-22-2-222-2-2-2-2222200002-22-22-20000000000-220000000000-220-22000000000
χ432-2-22-2-222-2-2-2-2222200002-2-22-2200000000002-200000000002-20-22000000000
χ442-2-22-2-222-2-2-2-2222200002-2-22-2200000000002-20000000000-2202-2000000000
χ4544444444-4-4-4-4-4-4-4-40000440000000000000000000000000000000000000000
χ4644-44-44-4-4004-44-400000000000000000000000022−2222−2200000000000000000000
χ4744-44-44-4-4004-44-4000000000000000000000000−2222−222200000000000000000000
χ4844-44-44-4-400-44-44004-44-4000000000000000000000000000000000000000000
χ4944-44-44-4-400-44-4400-44-44000000000000000000000000000000000000000000
χ5044-4-44-44-4-440000-4400000000000000002i2−2i2−2i22i200000000000000000000000000
χ5144-4-44-44-4-440000-440000000000000000−2i22i22i2−2i200000000000000000000000000
χ524-4444-4-4-4004-4-4400000000000000000000000022−22−222200000000000000000000
χ534-4444-4-4-4004-4-44000000000000000000000000−222222−2200000000000000000000
χ544-4444-4-4-400-444-4004-4-44000000000000000000000000000000000000000000
χ554-4444-4-4-400-444-400-444-4000000000000000000000000000000000000000000
χ564-44-4-444-44-40000-44000000000000000000000000002i2−2i2−2i22i20000000000000000
χ574-44-4-444-44-40000-4400000000000000000000000000−2i22i22i2−2i20000000000000000
χ584-44-4-444-4-4400004-40000004i−4i−4i4i000000000000000000000000000000000000
χ594-44-4-444-4-4400004-4000000−4i4i4i−4i000000000000000000000000000000000000
χ604-4-44-4-44444-4-444-4-40000-440000000000000000000000000000000000000000
χ61888-8-8-8-88000000000000000000000000000000000000000000000000000000
χ628-8-8-888-88000000000000000000000000000000000000000000000000000000

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