Finite Group Databasebeta

← Group #312798

Character table — Group #312798

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size111111112222222244444444448888888888888888888816161616161616161616161616163232
order12222222444444444444448888444444888888888888882244444488888824
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1111111-1-1-1-1-1-1111-111-11-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-111111111111111-1-1-11-1-11-1-1-111-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111
χ51111111111111111111111-1-1-1-11111-1-111-1-1-1-1-1-111-1-1-1-111-11-1-111-1-1-1-1111-1
χ61111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-111111-1-1-11
χ71111111111111111111111-1-1-1-111-1-11111-1-1-1-1-1-111-1-1-1-1-1-111111-111-1-1-1-1-11
χ81111111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11111-1-11-111-1-1-1-111111-1
χ91111111111111111-1-1-1-1111111-1-1111111-1-1-1-111111111-1-11-1-1-1-1111-1-111-1-1
χ101111111111111111-1-1-1-1111111-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-111-1-111-1-111-1-111
χ111111111111111111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-11111111111-1-111-1-1-1-1-1-1-1-111
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111-11111-1111111-1-1
χ131111111111111111-1-1-1-111-1-1-1-1-1-111-1-1111111-1-111-1-1-1-1-1-1-1-111-11-1-11111-11
χ141111111111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-11111111-1-1-1-11-1
χ151111111111111111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-111-1-1-1-1111-1-1-1-1-11111-1-11-1
χ161111111111111111-1-1-1-111-1-1-1-1-1-1-1-111-1-11111-1-1-1-111111111-1-11-1-1-1-1-111-11
χ17222222222-22-22-22-20000-2-22222002222000000-2-200000000-20000-200000000
χ18222222222-22-22-22-20000-2-2222200-2-2-2-2000000-2-20000000020000200000000
χ19222222222-22-22-22-20000-2-2-2-2-2-20022-2-2000000220000000020000-200000000
χ20222222222-22-22-22-20000-2-2-2-2-2-200-2-2220000002200000000-20000200000000
χ2122222222-22-22-22-222222-2-20000-2-2000022000000-2-20000000-2002000000000
χ2222222222-22-22-22-222222-2-20000-2-20000-2-2000000220000000200-2000000000
χ2322222222-22-22-22-22-2-2-2-2-2-2000022000022000000-2-20000000200-2000000000
χ2422222222-22-22-22-22-2-2-2-2-2-20000220000-2-2000000220000000-2002000000000
χ252-222-2-22-222-2-222-2-22i2i−2i−2i-222i2i−2i−2i2i−2i00000022-2-22i−2i0000000000000000000000
χ262-222-2-22-222-2-222-2-22i2i−2i−2i-22−2i−2i2i2i2i−2i000000-2-222−2i2i0000000000000000000000
χ272-222-2-22-222-2-222-2-2−2i−2i2i2i-222i2i−2i−2i−2i2i000000-2-2222i−2i0000000000000000000000
χ282-222-2-22-222-2-222-2-2−2i−2i2i2i-22−2i−2i2i2i−2i2i00000022-2-2−2i2i0000000000000000000000
χ292-222-2-22-22-2-222-2-2200002-22i2i−2i−2i000000000000−2i2i0000002-2002i−2i0000000000
χ302-222-2-22-22-2-222-2-2200002-22i2i−2i−2i000000000000−2i2i000000-2200−2i2i0000000000
χ312-222-2-22-22-2-222-2-2200002-2−2i−2i2i2i0000000000002i−2i0000002-200−2i2i0000000000
χ322-222-2-22-22-2-222-2-2200002-2−2i−2i2i2i0000000000002i−2i000000-22002i−2i0000000000
χ332-222-2-22-2-222-2-222-22i2i−2i−2i2-20000−2i2i000000000000002i2i−2i−2i00000000002-20000
χ342-222-2-22-2-222-2-222-22i2i−2i−2i2-20000−2i2i00000000000000−2i−2i2i2i0000000000-220000
χ352-222-2-22-2-222-2-222-2−2i−2i2i2i2-200002i−2i000000000000002i2i−2i−2i0000000000-220000
χ362-222-2-22-2-222-2-222-2−2i−2i2i2i2-200002i−2i00000000000000−2i−2i2i2i00000000002-20000
χ372-22-22-2-222020-20-200000002-22-2002i−2i2i−2i2−20000002−22−22−200000000i2−i200i2−i200
χ382-22-22-2-222020-20-200000002-22-2002i−2i2i−2i−22000000−22−22−2200000000−i2i200−i2i200
χ392-22-22-2-222020-20-200000002-22-200−2i2i−2i2i2−20000002−22−22−200000000−i2i200−i2i200
χ402-22-22-2-222020-20-200000002-22-200−2i2i−2i2i−22000000−22−22−2200000000i2−i200i2−i200
χ412-22-22-2-222020-20-20000000-22-22002i−2i−2i2i2−20000002−2−22−2200000000−i2i200i2−i200
χ422-22-22-2-222020-20-20000000-22-22002i−2i−2i2i−22000000−222−22−200000000i2−i200−i2i200
χ432-22-22-2-222020-20-20000000-22-2200−2i2i2i−2i2−20000002−2−22−2200000000i2−i200−i2i200
χ442-22-22-2-222020-20-20000000-22-2200−2i2i2i−2i−22000000−222−22−200000000−i2i200i2−i200
χ4544444444-4-4-4-4-4-4-4-40000440000000000000000000000000000000000000000
χ46444-4-44-4-440-40-40400000004i−4i−4i4i000000000000000000000000000000000000
χ47444-4-44-4-440-40-4040000000−4i4i4i−4i000000000000000000000000000000000000
χ48444-4-44-4-4-404040-40000000000000000000000000002i2−2i2−2i22i20000000000000000
χ49444-4-44-4-4-404040-4000000000000000000000000000−2i22i22i2−2i20000000000000000
χ5044-444-4-4-4040-40-4040000000000000000002i2−2i22i2−2i2000000000000000000000000
χ5144-444-4-4-4040-40-404000000000000000000−2i22i2−2i22i2000000000000000000000000
χ5244-444-4-4-40-404040-44i−4i4i−4i000000000000000000000000000000000000000000
χ5344-444-4-4-40-404040-4−4i4i−4i4i000000000000000000000000000000000000000000
χ544-444-4-44-4-4-444-4-4440000-440000000000000000000000000000000000000000
χ554-44-44-4-44-40-404040000000000000000022−22000000−222200000000000000000000
χ564-44-44-4-44-40-4040400000000000000000−222200000022−2200000000000000000000
χ574-4-44-44-4404040-40-40000000000000000002i2−2i2−2i22i2000000000000000000000000
χ584-4-44-44-4404040-40-4000000000000000000−2i22i22i2−2i2000000000000000000000000
χ594-4-44-44-440-40-404044-4-44000000000000000000000000000000000000000000
χ604-4-44-44-440-40-40404-444-4000000000000000000000000000000000000000000
χ6188-8-8-8-888000000000000000000000000000000000000000000000000000000
χ628-8-8-8888-8000000000000000000000000000000000000000000000000000000

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