Finite Group Databasebeta

← Group #313802

Character table — Group #313802

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size111111112222222244444444448888888888888888888816161616161616161616161616163232
order12222222444444444444448888224444888888888888884444444488888844
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-11111-1-1-1-1-1-1-11-111111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-1111111111111111-11-1-1-1-1-111-1-1-1-1-1-1
χ41111111111111111111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-1111-1-1-111-1-1-1-111-11
χ61111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-11-1-1-1-1111111-1-11-1
χ71111111111111111111111-1-1-1-111-1-111-1-111-1-1-1-111-1-1-1-11-11111-1-1-1-111-1-11-1
χ81111111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11111-1-1-1111-1-111-1-111-11
χ91111111111111111-1-1-1-1111111-1-111111111-1-1-1-1111111-11-11-1-1-1-1-1-11111-1-1
χ101111111111111111-1-1-1-1111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-111
χ111111111111111111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-111
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-11-11-11111111111-1-1
χ131111111111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-11-1-111-1-111-1-1111-1
χ141111111111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-1-1-11111-1-11111111-111-1-1-1-111-1-1-11
χ151111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1-1-1-11-1-1111111-1-1-11
χ161111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-11111-1-111111-111-1-111-1-1-1-1111-1
χ17222222222-22-22-22-20000-2-22222002222-2-20000000000000-20-2000000000000
χ18222222222-22-22-22-20000-2-2222200-2-2-2-2-2-20000000000000202000000000000
χ19222222222-22-22-22-20000-2-2-2-2-2-20022-2-2220000000000000-202000000000000
χ20222222222-22-22-22-20000-2-2-2-2-2-200-2-22222000000000000020-2000000000000
χ2122222222-22-22-22-222222-2-20000-2-2000000220000-2-20000-2020000000000000
χ2222222222-22-22-22-222222-2-20000-2-2000000-2-2000022000020-20000000000000
χ2322222222-22-22-22-22-2-2-2-2-2-2000022000000220000-2-2000020-20000000000000
χ2422222222-22-22-22-22-2-2-2-2-2-2000022000000-2-20000220000-2020000000000000
χ2522-222-2-2-2-20-20202000000022-2-2002i−2i2i−2i002−200002−222−2−20000000000i2−i2i2−i200
χ2622-222-2-2-2-20-20202000000022-2-2002i−2i2i−2i00−220000−22−2−2220000000000−i2i2−i2i200
χ2722-222-2-2-2-20-20202000000022-2-200−2i2i−2i2i002−200002−222−2−20000000000−i2i2−i2i200
χ2822-222-2-2-2-20-20202000000022-2-200−2i2i−2i2i00−220000−22−2−2220000000000i2−i2i2−i200
χ2922-222-2-2-2-20-202020000000-2-222002i−2i−2i2i002−200002−2−2−2220000000000−i2i2i2−i200
χ3022-222-2-2-2-20-202020000000-2-222002i−2i−2i2i00−220000−2222−2−20000000000i2−i2−i2i200
χ3122-222-2-2-2-20-202020000000-2-22200−2i2i2i−2i002−200002−2−2−2220000000000i2−i2−i2i200
χ3222-222-2-2-2-20-202020000000-2-22200−2i2i2i−2i00−220000−2222−2−20000000000−i2i2i2−i200
χ332-2-2-2222-222-2-222-2-222-2-2-222i−2i2i−2i2-200002i−2i002i2i−2i−2i0000000000000000000000
χ342-2-2-2222-222-2-222-2-222-2-2-22−2i2i−2i2i2-20000−2i2i00−2i−2i2i2i0000000000000000000000
χ352-2-2-2222-222-2-222-2-2-2-222-222i−2i2i−2i-2200002i−2i00−2i−2i2i2i0000000000000000000000
χ362-2-2-2222-222-2-222-2-2-2-222-22−2i2i−2i2i-220000−2i2i002i2i−2i−2i0000000000000000000000
χ372-2-2-2222-22-2-222-2-2200002-22i−2i2i−2i000000−2i2i00000000000000002-22i−2i00000000
χ382-2-2-2222-22-2-222-2-2200002-22i−2i2i−2i000000−2i2i0000000000000000-22−2i2i00000000
χ392-2-2-2222-22-2-222-2-2200002-2−2i2i−2i2i0000002i−2i00000000000000002-2−2i2i00000000
χ402-2-2-2222-22-2-222-2-2200002-2−2i2i−2i2i0000002i−2i0000000000000000-222i−2i00000000
χ412-2-2-2222-2-222-2-222-222-2-22-20000-22000000000000002i−2i2i−2i000000002i−2i000000
χ422-2-2-2222-2-222-2-222-222-2-22-20000-2200000000000000−2i2i−2i2i00000000−2i2i000000
χ432-2-2-2222-2-222-2-222-2-2-2222-200002-2000000000000002i−2i2i−2i00000000−2i2i000000
χ442-2-2-2222-2-222-2-222-2-2-2222-200002-200000000000000−2i2i−2i2i000000002i−2i000000
χ4544444444-4-4-4-4-4-4-4-40000440000000000000000000000000000000000000000
χ4644-444-4-4-44040-40-4000000000000000000022−220000−222200000000000000000000
χ4744-444-4-4-44040-40-40000000000000000000−2222000022−2200000000000000000000
χ4844-4-4-44-44040-40-404000000000000000000002i2−2i22i2−2i20000000000000000000000
χ4944-4-4-44-44040-40-40400000000000000000000−2i22i2−2i22i20000000000000000000000
χ5044-4-4-44-440-404040-44i−4i4i−4i000000000000000000000000000000000000000000
χ5144-4-4-44-440-404040-4−4i4i−4i4i000000000000000000000000000000000000000000
χ524-444-44-4-404040-40-40000000000000000000022−22−22220000000000000000000000
χ534-444-44-4-404040-40-400000000000000000000−222222−220000000000000000000000
χ544-444-44-4-40-40-404044i−4i−4i4i000000000000000000000000000000000000000000
χ554-444-44-4-40-40-40404−4i4i4i−4i000000000000000000000000000000000000000000
χ564-44-44-4-4440-40-4040000000000000000000000000002i2−2i2−2i22i20000000000000000
χ574-44-44-4-4440-40-404000000000000000000000000000−2i22i22i2−2i20000000000000000
χ584-44-44-4-44-404040-400000004i−4i−4i4i000000000000000000000000000000000000
χ594-44-44-4-44-404040-40000000−4i4i4i−4i000000000000000000000000000000000000
χ604-4-4-4444-4-4-444-4-4440000-440000000000000000000000000000000000000000
χ61888-8-8-88-8000000000000000000000000000000000000000000000000000000
χ628-8-88-8-888000000000000000000000000000000000000000000000000000000

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