Finite Group Databasebeta

← Group #312704

Character table — Group #312704

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size111111112222222244444444448888888888888888888816161616161616161616161616163232
order12222222444444444444448888224444888888888888884444444488888844
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1111111-1-1-1-1-1-111-11111-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-111-1-111111111111111-1-11-1-1-1-11-1-111-1-1-1-1
χ411111111111111111111111111-1-111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111
χ51111111111111111111111-1-1-1-11111-1-111-1-1-1-1-1-111-1-1-1-1-11111-1-1111-1-1-1-1-11
χ61111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-11-111-1-1-1-1-111111-1
χ71111111111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1-1-11-11-1-1111-1-1-1-1111-1
χ81111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-111111-1-1-1-111-11111-1-1-11
χ91111111111111111-1-1-1-111111111-1-11111-1-1-1-11111111111-1-1-1-1-1-111-1-111-1-1
χ101111111111111111-1-1-1-111111111-1-111-1-1-1-1-1-111-1-1-1-1-1-1111-1-1-1-11-1-111-1-111
χ111111111111111111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-111111111-1-1-11111-1-1-1-1-1-1-111
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111111111-1-1
χ131111111111111111-1-1-1-111-1-1-1-111-1-1-1-1111111-1-111-1-1-1-1-11-1-1-111-11111-1-11-1
χ141111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-11111-111-1-1111-1-1-1-111-11
χ151111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-11-1-111-1-1-1-1-11111-11
χ161111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111111-1111-1-1111-1-1-1-11-1
χ17222222222-22-22-22-20000-2-22222220022000000-2-2000000-2-200000000000000
χ18222222222-22-22-22-20000-2-22222-2-200-2-2000000-2-20000002200000000000000
χ19222222222-22-22-22-20000-2-2-2-2-2-22200-2-2000000220000002-200000000000000
χ20222222222-22-22-22-20000-2-2-2-2-2-2-2-2002200000022000000-2200000000000000
χ2122222222-22-22-22-222222-2-2000000-2-20022000000-2-200000020000-200000000
χ2222222222-22-22-22-222222-2-2000000-2-200-2-200000022000000-20000200000000
χ2322222222-22-22-22-22-2-2-2-2-2-2000000220022000000-2-2000000-20000200000000
χ2422222222-22-22-22-22-2-2-2-2-2-20000002200-2-20000002200000020000-200000000
χ252-222-22-2-220-20-20200000002i2i−2i−2i2-2002i−2ii2−i2000000i2−i222−2−200000000i2−i2002−200
χ262-222-22-2-220-20-20200000002i2i−2i−2i2-2002i−2i−i2i2000000−i2i2−2−22200000000−i2i200−2200
χ272-222-22-2-220-20-20200000002i2i−2i−2i-2200−2i2ii2−i2000000i2−i222−2−200000000−i2i200−2200
χ282-222-22-2-220-20-20200000002i2i−2i−2i-2200−2i2i−i2i2000000−i2i2−2−22200000000i2−i2002−200
χ292-222-22-2-220-20-2020000000−2i−2i2i2i2-200−2i2ii2−i2000000i2−i2−2−22200000000i2−i200−2200
χ302-222-22-2-220-20-2020000000−2i−2i2i2i2-200−2i2i−i2i2000000−i2i222−2−200000000−i2i2002−200
χ312-222-22-2-220-20-2020000000−2i−2i2i2i-22002i−2ii2−i2000000i2−i2−2−22200000000−i2i2002−200
χ322-222-22-2-220-20-2020000000−2i−2i2i2i-22002i−2i−i2i2000000−i2i222−2−200000000i2−i200−2200
χ332-2-222-2-2222-2-222-2-22i2i−2i−2i-222i−2i2i−2i002i−2i000022-2-22i−2i0000000000000000000000
χ342-2-222-2-2222-2-222-2-22i2i−2i−2i-22−2i2i−2i2i002i−2i0000-2-222−2i2i0000000000000000000000
χ352-2-222-2-2222-2-222-2-2−2i−2i2i2i-222i−2i2i−2i00−2i2i0000-2-2222i−2i0000000000000000000000
χ362-2-222-2-2222-2-222-2-2−2i−2i2i2i-22−2i2i−2i2i00−2i2i000022-2-2−2i2i0000000000000000000000
χ372-2-222-2-222-2-222-2-2200002-22i−2i2i−2i000000000000−2i2i0000000002i−2i2-2000000000
χ382-2-222-2-222-2-222-2-2200002-22i−2i2i−2i000000000000−2i2i000000000−2i2i-22000000000
χ392-2-222-2-222-2-222-2-2200002-2−2i2i−2i2i0000000000002i−2i0000000002i−2i-22000000000
χ402-2-222-2-222-2-222-2-2200002-2−2i2i−2i2i0000000000002i−2i000000000−2i2i2-2000000000
χ412-2-222-2-22-222-2-222-22i2i−2i−2i2-2000000−2i2i0000000000002i−2i2i−2i00000000002-20000
χ422-2-222-2-22-222-2-222-22i2i−2i−2i2-2000000−2i2i000000000000−2i2i−2i2i0000000000-220000
χ432-2-222-2-22-222-2-222-2−2i−2i2i2i2-20000002i−2i0000000000002i−2i2i−2i0000000000-220000
χ442-2-222-2-22-222-2-222-2−2i−2i2i2i2-20000002i−2i000000000000−2i2i−2i2i00000000002-20000
χ4544444444-4-4-4-4-4-4-4-40000440000000000000000000000000000000000000000
χ4644-44-4-44-44040-40-400000004-4-44000000000000000000000000000000000000
χ4744-44-4-44-44040-40-40000000-444-4000000000000000000000000000000000000
χ4844-44-4-44-4-40-404040000000000000000000000000002i2−2i2−2i22i20000000000000000
χ4944-44-4-44-4-40-40404000000000000000000000000000−2i22i22i2−2i20000000000000000
χ5044-4-444-4-404040-40-44-44-4000000000000000000000000000000000000000000
χ5144-4-444-4-404040-40-4-44-44000000000000000000000000000000000000000000
χ5244-4-444-4-40-40-404040000000000000000002i2−2i22i2−2i2000000000000000000000000
χ5344-4-444-4-40-40-40404000000000000000000−2i22i2−2i22i2000000000000000000000000
χ544-444-44-4-4-404040-4000000000000000002i2−2i2000000−2i22i200000000000000000000
χ554-444-44-4-4-404040-400000000000000000−2i22i20000002i2−2i200000000000000000000
χ564-44-44-44-4040-40-4044i−4i−4i4i000000000000000000000000000000000000000000
χ574-44-44-44-4040-40-404−4i4i4i−4i000000000000000000000000000000000000000000
χ584-44-44-44-40-404040-40000000000000000002i2−2i2−2i22i2000000000000000000000000
χ594-44-44-44-40-404040-4000000000000000000−2i22i22i2−2i2000000000000000000000000
χ604-4-444-4-44-4-444-4-4440000-440000000000000000000000000000000000000000
χ61888-8-8-8-88000000000000000000000000000000000000000000000000000000
χ628-8-8-8-8888000000000000000000000000000000000000000000000000000000

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