Finite Group Databasebeta

← Group #313709

Character table — Group #313709

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size111111112222222244444444448888888888888888888816161616161616161616161616163232
order12222222444444442222448888224444888888888888882244444488888824
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-11111-1-1-1-1-1-11111-111-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-111-1-111111111111111-1-1-1-11-1-1111-1-1-1-1-1-1
χ411111111111111111111111111-1-111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-111-111-1-11-1-111-1-11-1
χ61111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-11-1-1-1-111-1-111-11
χ71111111111111111111111-1-1-1-1-1-11111-1-111-1-1-1-111-1-1-1-1-1-11-11111-1-1-1-111-11
χ81111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-11-1-111-11111-1-11-1
χ91111111111111111-1-1-1-111111111-1-1111111-1-1-1-1111111-1-111-1-1-1-1-1-11111-1-1
χ101111111111111111-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111-1-1111-1-1-1-111
χ111111111111111111-1-1-1-1111111-1-1-1-1-1-11111-1-1-1-111111111-1-1-111-1-1-1-1-1-1-111
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111111111-1-1
χ131111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-1-1-11-111-11111-1-1-11
χ141111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-11111-1-11111-1-1-111111-1-1-1-1111-1
χ151111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-111111111-1-1-1-1111-1-1-1-1-111-1-1111-1
χ161111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-1-1-11111-1-11111111-11-1-11-1-111-1-1-11
χ17222222222-22-22-22-20000-2-22222220022-2-200000000000000-2-2000000000000
χ18222222222-22-22-22-20000-2-22222-2-200-2-2-2-20000000000000022000000000000
χ19222222222-22-22-22-20000-2-2-2-2-2-22200-2-222000000000000002-2000000000000
χ20222222222-22-22-22-20000-2-2-2-2-2-2-2-200222200000000000000-22000000000000
χ2122222222-22-22-22-222222-2-2000000-2-20000220000-2-200000000-200200000000
χ2222222222-22-22-22-222222-2-2000000-2-20000-2-200002200000000200-200000000
χ2322222222-22-22-22-22-2-2-2-2-2-2000000220000220000-2-200000000200-200000000
χ2422222222-22-22-22-22-2-2-2-2-2-2000000220000-2-200002200000000-200200000000
χ252-22-222-2-222-2-222-2-222-2-2-222i2i−2i−2i002-2002i−2i002i2i−2i−2i0000000000000000000000
χ262-22-222-2-222-2-222-2-222-2-2-22−2i−2i2i2i002-200−2i2i00−2i−2i2i2i0000000000000000000000
χ272-22-222-2-222-2-222-2-2-2-222-222i2i−2i−2i00-22002i−2i00−2i−2i2i2i0000000000000000000000
χ282-22-222-2-222-2-222-2-2-2-222-22−2i−2i2i2i00-2200−2i2i002i2i−2i−2i0000000000000000000000
χ292-22-222-2-22-2-222-2-2200002-22i2i−2i−2i000000−2i2i0000000000002-20002i−2i000000000
χ302-22-222-2-22-2-222-2-2200002-22i2i−2i−2i000000−2i2i000000000000-22000−2i2i000000000
χ312-22-222-2-22-2-222-2-2200002-2−2i−2i2i2i0000002i−2i0000000000002-2000−2i2i000000000
χ322-22-222-2-22-2-222-2-2200002-2−2i−2i2i2i0000002i−2i000000000000-220002i−2i000000000
χ332-22-222-2-2-222-2-222-222-2-22-2000000-220000000000002i2i−2i−2i000000002i−2i000000
χ342-22-222-2-2-222-2-222-222-2-22-2000000-22000000000000−2i−2i2i2i00000000−2i2i000000
χ352-22-222-2-2-222-2-222-2-2-2222-20000002-20000000000002i2i−2i−2i00000000−2i2i000000
χ362-22-222-2-2-222-2-222-2-2-2222-20000002-2000000000000−2i−2i2i2i000000002i−2i000000
χ372-2-2-22-222-20-2020200000002-22-22-2002-2002−200002−22−22−200000000002−22−200
χ382-2-2-22-222-20-2020200000002-22-22-2002-200−220000−22−22−220000000000−22−2200
χ392-2-2-22-222-20-2020200000002-22-2-2200-22002−200002−22−22−20000000000−22−2200
χ402-2-2-22-222-20-2020200000002-22-2-2200-2200−220000−22−22−2200000000002−22−200
χ412-2-2-22-222-20-202020000000-22-222-200-22002−200002−2−22−2200000000002−2−2200
χ422-2-2-22-222-20-202020000000-22-222-200-2200−220000−222−22−20000000000−222−200
χ432-2-2-22-222-20-202020000000-22-22-22002-2002−200002−2−22−220000000000−222−200
χ442-2-2-22-222-20-202020000000-22-22-22002-200−220000−222−22−200000000002−2−2200
χ4544444444-4-4-4-4-4-4-4-40000440000000000000000000000000000000000000000
χ4644-444-4-4-440-40-4040000000000000000000000000002i2−2i2−2i22i20000000000000000
χ4744-444-4-4-440-40-404000000000000000000000000000−2i22i22i2−2i20000000000000000
χ4844-444-4-4-4-404040-400000004i−4i−4i4i000000000000000000000000000000000000
χ4944-444-4-4-4-404040-40000000−4i4i4i−4i000000000000000000000000000000000000
χ5044-4-4-444-404040-40-4000000000000000000002i2−2i22i2−2i20000000000000000000000
χ5144-4-4-444-404040-40-400000000000000000000−2i22i2−2i22i20000000000000000000000
χ5244-4-4-444-40-40-404044-44-4000000000000000000000000000000000000000000
χ5344-4-4-444-40-40-40404-44-44000000000000000000000000000000000000000000
χ544-44-444-4-4-4-444-4-4440000-440000000000000000000000000000000000000000
χ554-4-44-44-44040-40-4040000000000000000000022−22−22220000000000000000000000
χ564-4-44-44-44040-40-40400000000000000000000−222222−220000000000000000000000
χ574-4-44-44-440-404040-44-4-44000000000000000000000000000000000000000000
χ584-4-44-44-440-404040-4-444-4000000000000000000000000000000000000000000
χ594-4-4-44-4444040-40-4000000000000000000022−220000−222200000000000000000000
χ604-4-4-44-4444040-40-40000000000000000000−2222000022−2200000000000000000000
χ61888-8-8-8-88000000000000000000000000000000000000000000000000000000
χ628-888-8-88-8000000000000000000000000000000000000000000000000000000

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