Finite Group Databasebeta

← Group #312702

Character table — Group #312702

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size111111112222222244444444448888888888888888888816161616161616161616161616163232
order12222222444444444444448888224444888888888888884444444488888844
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1111111-1-1-1-1-1-11-111111-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-11111111111111111-11-1-1-1-1-11-1-111-1-1-1-1
χ411111111111111111111111111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111
χ51111111111111111111111-1-1-1-111-1-11111-1-1-1-1-1-111-1-1-1-11111-1-1-1111-1-1-1-11-1
χ61111111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-111111-111-1-1-1-1-1-11111-11
χ71111111111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1-1-1-11-1-11111-1-1-1-111-11
χ81111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111-11111-1-11-1
χ91111111111111111-1-1-1-11111111111-1-111-1-1-1-1111111111-1-1-11-1-1-111-1-111-1-1
χ101111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-111-1-11-1-11-1-111-1-111
χ111111111111111111-1-1-1-1111111-1-1-1-1-1-111-1-1-1-111111111-1-111-111-1-1-1-1-1-1-111
χ121111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1111-1111111111-1-1
χ131111111111111111-1-1-1-111-1-1-1-111-1-1-1-1111111-1-111-1-1-1-11-1-1-1-111-11111-1-1-11
χ141111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-11111-1-1-1-1111111-1-1-1111-1-1-1-1111-1
χ151111111111111111-1-1-1-111-1-1-1-1-1-111-1-1111111-1-111-1-1-1-1-1-1111-1-1-1-1-111111-1
χ161111111111111111-1-1-1-111-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-11111-1-1111-1-1-1-1-11
χ17222222222-22-22-22-20000-2-22222222200000000-2-2000000-2000-200000000000
χ18222222222-22-22-22-20000-2-22222-2-2-2-200000000-2-20000002000200000000000
χ19222222222-22-22-22-20000-2-2-2-2-2-222-2-20000000022000000-2000200000000000
χ20222222222-22-22-22-20000-2-2-2-2-2-2-2-22200000000220000002000-200000000000
χ2122222222-22-22-22-222222-2-200000000-2-222000000-2-200000200000-200000000
χ2222222222-22-22-22-222222-2-200000000-2-2-2-20000002200000-200000200000000
χ2322222222-22-22-22-22-2-2-2-2-2-2000000002222000000-2-200000-200000200000000
χ2422222222-22-22-22-22-2-2-2-2-2-20000000022-2-20000002200000200000-200000000
χ252222-2-2-2-22020-20-2000000022-2-22-22-2002−20000002−222−2−2000000002−2002−200
χ262222-2-2-2-22020-20-2000000022-2-22-22-200−22000000−22−2−22200000000−2200−2200
χ272222-2-2-2-22020-20-2000000022-2-2-22-22002−20000002−222−2−200000000−2200−2200
χ282222-2-2-2-22020-20-2000000022-2-2-22-2200−22000000−22−2−222000000002−2002−200
χ292222-2-2-2-22020-20-20000000-2-2222-2-22002−20000002−2−2−222000000002−200−2200
χ302222-2-2-2-22020-20-20000000-2-2222-2-2200−22000000−2222−2−200000000−22002−200
χ312222-2-2-2-22020-20-20000000-2-222-222-2002−20000002−2−2−22200000000−22002−200
χ322222-2-2-2-22020-20-20000000-2-222-222-200−22000000−2222−2−2000000002−200−2200
χ332-22-22-2-2222-2-222-2-22i2i−2i−2i-222i−2i2i−2i00002i−2i0022-2-22i−2i0000000000000000000000
χ342-22-22-2-2222-2-222-2-22i2i−2i−2i-22−2i2i−2i2i00002i−2i00-2-222−2i2i0000000000000000000000
χ352-22-22-2-2222-2-222-2-2−2i−2i2i2i-222i−2i2i−2i0000−2i2i00-2-2222i−2i0000000000000000000000
χ362-22-22-2-2222-2-222-2-2−2i−2i2i2i-22−2i2i−2i2i0000−2i2i0022-2-2−2i2i0000000000000000000000
χ372-22-22-2-222-2-222-2-2200002-22i−2i2i−2i000000000000−2i2i000000002i−2i02-2000000000
χ382-22-22-2-222-2-222-2-2200002-22i−2i2i−2i000000000000−2i2i00000000−2i2i0-22000000000
χ392-22-22-2-222-2-222-2-2200002-2−2i2i−2i2i0000000000002i−2i000000002i−2i0-22000000000
χ402-22-22-2-222-2-222-2-2200002-2−2i2i−2i2i0000000000002i−2i00000000−2i2i02-2000000000
χ412-22-22-2-22-222-2-222-22i2i−2i−2i2-200000000−2i2i00000000002i−2i2i−2i00000000002-20000
χ422-22-22-2-22-222-2-222-22i2i−2i−2i2-200000000−2i2i0000000000−2i2i−2i2i0000000000-220000
χ432-22-22-2-22-222-2-222-2−2i−2i2i2i2-2000000002i−2i00000000002i−2i2i−2i0000000000-220000
χ442-22-22-2-22-222-2-222-2−2i−2i2i2i2-2000000002i−2i0000000000−2i2i−2i2i00000000002-20000
χ4544444444-4-4-4-4-4-4-4-40000440000000000000000000000000000000000000000
χ464444-4-4-4-4-40-404040000000000000000022−22000000−222200000000000000000000
χ474444-4-4-4-4-40-4040400000000000000000−222200000022−2200000000000000000000
χ4844-4-444-4-404040-40-44-44-4000000000000000000000000000000000000000000
χ4944-4-444-4-404040-40-4-44-44000000000000000000000000000000000000000000
χ5044-4-444-4-40-40-404040000000000000000002i2−2i22i2−2i2000000000000000000000000
χ5144-4-444-4-40-40-40404000000000000000000−2i22i2−2i22i2000000000000000000000000
χ524-44-44-4-44-4-444-4-4440000-440000000000000000000000000000000000000000
χ534-44-4-444-440-40-40400000004i−4i−4i4i000000000000000000000000000000000000
χ544-44-4-444-440-40-4040000000−4i4i4i−4i000000000000000000000000000000000000
χ554-44-4-444-4-404040-40000000000000000000000000002i2−2i2−2i22i20000000000000000
χ564-44-4-444-4-404040-4000000000000000000000000000−2i22i22i2−2i20000000000000000
χ574-4-444-44-4040-40-4044i−4i−4i4i000000000000000000000000000000000000000000
χ584-4-444-44-4040-40-404−4i4i4i−4i000000000000000000000000000000000000000000
χ594-4-444-44-40-404040-40000000000000000002i2−2i2−2i22i2000000000000000000000000
χ604-4-444-44-40-404040-4000000000000000000−2i22i22i2−2i2000000000000000000000000
χ6188-8-8-8-888000000000000000000000000000000000000000000000000000000
χ628-8-88-88-88000000000000000000000000000000000000000000000000000000

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