Finite Group Databasebeta

← Group #312709

Character table — Group #312709

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size111111112222222244444444448888888888888888888816161616161616161616161616163232
order12222222444444444444448888224444888888888888884444444488888844
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1111111-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-111111111111111111-1-1-1-1-1-11-1-111-1-1-1-1
χ411111111111111111111111111-1-1-1-111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-11111
χ51111111111111111111111-1-1-1-111-1-11111-1-1-1-1-1-111-1-1-1-1111-11-1-1111-1-1-1-11-1
χ61111111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-11111-111-11-1-1-1-1-11111-11
χ71111111111111111111111-1-1-1-1-1-1111111-1-1-1-1-1-111-1-1-1-11-1-11-1111-1-1-1-111-11
χ81111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-11111-1-1-11-111-11111-1-11-1
χ911111111111111111-1-1-1-1111111111-1-111-1-1-1-111111111-1-1-111-1-1-111-1-111-1-1
χ1011111111111111111-1-1-1-1111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11-1-111-1-11-1-111-1-111
χ1111111111111111111-1-1-1-111111-1-1-1-1-1-111-1-1-1-111111111-111-1-111-1-1-1-1-1-1-111
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111-1-1111111111-1-1
χ1311111111111111111-1-1-1-11-1-1-1-111-1-1-1-1111111-1-111-1-1-1-1-1-1-1-1111-11111-1-1-11
χ1411111111111111111-1-1-1-11-1-1-1-111-1-1-1-1-1-11111-1-1-1-111111-1-1-11111-1-1-1-1111-1
χ1511111111111111111-1-1-1-11-1-1-1-1-1-111-1-1111111-1-111-1-1-1-1-1111-1-1-1-1-1-111111-1
χ1611111111111111111-1-1-1-11-1-1-1-1-1-111-1-1-1-11111-1-1-1-111111111-1-1-1111-1-1-1-1-11
χ17222222222-22-22-22-2-20000-22222222200000000-2-2000000000-2-200000000000
χ18222222222-22-22-22-2-20000-22222-2-2-2-200000000-2-20000000002200000000000
χ19222222222-22-22-22-2-20000-2-2-2-2-222-2-200000000220000000002-200000000000
χ20222222222-22-22-22-2-20000-2-2-2-2-2-2-2220000000022000000000-2200000000000
χ2122222222-22-22-22-22-22222-200000000-2-222000000-2-200002000000-200000000
χ2222222222-22-22-22-22-22222-200000000-2-2-2-2000000220000-2000000200000000
χ2322222222-22-22-22-22-2-2-2-2-2-2000000002222000000-2-20000-2000000200000000
χ2422222222-22-22-22-22-2-2-2-2-2-20000000022-2-20000002200002000000-200000000
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
χ332-22-22-2-2222-2-222-2-2-22i2i−2i−2i22i−2i2i−2i00002i−2i0022-2-22i−2i0000000000000000000000
χ342-22-22-2-2222-2-222-2-2-22i2i−2i−2i2−2i2i−2i2i00002i−2i00-2-222−2i2i0000000000000000000000
χ352-22-22-2-2222-2-222-2-2-2−2i−2i2i2i22i−2i2i−2i0000−2i2i00-2-2222i−2i0000000000000000000000
χ362-22-22-2-2222-2-222-2-2-2−2i−2i2i2i2−2i2i−2i2i0000−2i2i0022-2-2−2i2i0000000000000000000000
χ372-22-22-2-222-2-222-2-2220000-22i−2i2i−2i000000000000−2i2i00000002i−2i002-2000000000
χ382-22-22-2-222-2-222-2-2220000-22i−2i2i−2i000000000000−2i2i0000000−2i2i00-22000000000
χ392-22-22-2-222-2-222-2-2220000-2−2i2i−2i2i0000000000002i−2i00000002i−2i00-22000000000
χ402-22-22-2-222-2-222-2-2220000-2−2i2i−2i2i0000000000002i−2i0000000−2i2i002-2000000000
χ412-22-22-2-22-222-2-222-222i2i−2i−2i-200000000−2i2i00000000002i−2i2i−2i00000000002-20000
χ422-22-22-2-22-222-2-222-222i2i−2i−2i-200000000−2i2i0000000000−2i2i−2i2i0000000000-220000
χ432-22-22-2-22-222-2-222-22−2i−2i2i2i-2000000002i−2i00000000002i−2i2i−2i0000000000-220000
χ442-22-22-2-22-222-2-222-22−2i−2i2i2i-2000000002i−2i0000000000−2i2i−2i2i00000000002-20000
χ4544444444-4-4-4-4-4-4-4-44000040000000000000000000000000000000000000000
χ464444-4-4-4-4-40-404040000000000000000022−22000000−222200000000000000000000
χ474444-4-4-4-4-40-4040400000000000000000−222200000022−2200000000000000000000
χ4844-4-4-44-4404040-40-404i−4i4i−4i00000000000000000000000000000000000000000
χ4944-4-4-44-4404040-40-40−4i4i−4i4i00000000000000000000000000000000000000000
χ5044-4-4-44-440-40-4040400000000000000000022−2222−22000000000000000000000000
χ5144-4-4-44-440-40-40404000000000000000000−2222−2222000000000000000000000000
χ524-44-44-4-44-4-444-4-444-4000040000000000000000000000000000000000000000
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
χ574-4-44-4-444040-40-40404-4-4400000000000000000000000000000000000000000
χ584-4-44-4-444040-40-4040-444-400000000000000000000000000000000000000000
χ594-4-44-4-4440-404040-400000000000000000022−22−2222000000000000000000000000
χ604-4-44-4-4440-404040-4000000000000000000−222222−22000000000000000000000000
χ6188-8-88-88-8000000000000000000000000000000000000000000000000000000
χ628-8-8888-8-8000000000000000000000000000000000000000000000000000000

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