Finite Group Databasebeta

← Group #313724

Character table — Group #313724

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size111111112222222244444444448888888888888888888816161616161616161616161616163232
order12222222444444444444448888222244888888888888884444444488888844
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111-1-11111-1-1-1-1-1-11-111-1111-1-1-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-111111111111111-11-1-11-1-1-111-1-1-1-1-1-1
χ41111111111111111111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111
χ51111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-111-1-1-1-1-11-1-11111-1-111-1-1-11
χ61111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1-111111-1-1111-1
χ71111111111111111111111-1-1-1-111-1-111-1-111-1-1-1-111-1-1-1-111111-1-1-1-1-1-1-1111-1
χ81111111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-111111-111-1-1-1-11111-1-1-11
χ911111111111111111-1-1-1-111111-1-111111111-1-1-1-11111111-1-1-1-11-1-1-1-11111-1-1
χ1011111111111111111-1-1-1-111111-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111-1-111-1-111-1-1-1-111
χ1111111111111111111-1-1-1-111111-1-1-1-1-1-11111-1-1-1-1111111-1-111-1-111-1-1-1-1-1-111
χ1211111111111111111-1-1-1-111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-11111-111111111-1-1
χ1311111111111111111-1-1-1-11-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-111-11-1-11111-1-11-1
χ1411111111111111111-1-1-1-11-1-1-1-1-1-111-1-1-1-1-1-11111-1-11111-111111-1-1-1-1-1-111-11
χ1511111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-111111111-1-1-1-11-1-1-1-1-11111-1-111-11
χ1611111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-11111-1-1111111-1-11-111-1-111-1-11-1
χ17222222222-22-22-22-2-20000-22222002222-2-2000000000000-20000-20000000000
χ18222222222-22-22-22-2-20000-2222200-2-2-2-2-2-20000000000002000020000000000
χ19222222222-22-22-22-2-20000-2-2-2-2-20022-2-22200000000000020000-20000000000
χ20222222222-22-22-22-2-20000-2-2-2-2-200-2-22222000000000000-2000020000000000
χ2122222222-22-22-22-22-22222-20000-2-2000000220000-2-200000200-200000000000
χ2222222222-22-22-22-22-22222-20000-2-2000000-2-200002200000-200200000000000
χ2322222222-22-22-22-22-2-2-2-2-2-2000022000000220000-2-200000-200200000000000
χ2422222222-22-22-22-22-2-2-2-2-2-2000022000000-2-200002200000200-200000000000
χ2522-2-2-2-22222-2-222-2-2-222-2-222i2i−2i−2i2-200002i−2i002i2i−2i−2i0000000000000000000000
χ2622-2-2-2-22222-2-222-2-2-222-2-22−2i−2i2i2i2-20000−2i2i00−2i−2i2i2i0000000000000000000000
χ2722-2-2-2-22222-2-222-2-2-2-2-22222i2i−2i−2i-2200002i−2i00−2i−2i2i2i0000000000000000000000
χ2822-2-2-2-22222-2-222-2-2-2-2-2222−2i−2i2i2i-220000−2i2i002i2i−2i−2i0000000000000000000000
χ2922-2-2-2-2222-2-222-2-2220000-22i2i−2i−2i000000−2i2i000000000000002i−2i002-200000000
χ3022-2-2-2-2222-2-222-2-2220000-22i2i−2i−2i000000−2i2i00000000000000−2i2i00-2200000000
χ3122-2-2-2-2222-2-222-2-2220000-2−2i−2i2i2i0000002i−2i000000000000002i−2i00-2200000000
χ3222-2-2-2-2222-2-222-2-2220000-2−2i−2i2i2i0000002i−2i00000000000000−2i2i002-200000000
χ3322-2-2-2-222-222-2-222-2222-2-2-20000-22000000000000002i2i−2i−2i000000002i−2i000000
χ3422-2-2-2-222-222-2-222-2222-2-2-20000-2200000000000000−2i−2i2i2i00000000−2i2i000000
χ3522-2-2-2-222-222-2-222-22-2-222-200002-2000000000000002i2i−2i−2i00000000−2i2i000000
χ3622-2-2-2-222-222-2-222-22-2-222-200002-200000000000000−2i−2i2i2i000000002i−2i000000
χ372-222-2-22-2-202020-200000002i−2i2i−2i002-22i−2i00i2−i20000i2−i22−22−20000000000i2−i22−200
χ382-222-2-22-2-202020-200000002i−2i2i−2i002-22i−2i00−i2i20000−i2i2−22−220000000000−i2i2−2200
χ392-222-2-22-2-202020-200000002i−2i2i−2i00-22−2i2i00i2−i20000i2−i22−22−20000000000−i2i2−2200
χ402-222-2-22-2-202020-200000002i−2i2i−2i00-22−2i2i00−i2i20000−i2i2−22−220000000000i2−i22−200
χ412-222-2-22-2-202020-20000000−2i2i−2i2i002-2−2i2i00i2−i20000i2−i2−22−220000000000i2−i2−2200
χ422-222-2-22-2-202020-20000000−2i2i−2i2i002-2−2i2i00−i2i20000−i2i22−22−20000000000−i2i22−200
χ432-222-2-22-2-202020-20000000−2i2i−2i2i00-222i−2i00i2−i20000i2−i2−22−220000000000−i2i22−200
χ442-222-2-22-2-202020-20000000−2i2i−2i2i00-222i−2i00−i2i20000−i2i22−22−20000000000i2−i2−2200
χ4544444444-4-4-4-4-4-4-4-44000040000000000000000000000000000000000000000
χ4644-4-4-4-444-4-444-4-444-4000040000000000000000000000000000000000000000
χ474-444-4-44-440-40-40400000000000000000002i2−2i20000−2i22i200000000000000000000
χ484-444-4-44-440-40-4040000000000000000000−2i22i200002i2−2i200000000000000000000
χ494-44-44-4-44040-40-40404i−4i4i−4i00000000000000000000000000000000000000000
χ504-44-44-4-44040-40-4040−4i4i−4i4i00000000000000000000000000000000000000000
χ514-44-44-4-440-404040-4000000000000000000002i2−2i22i2−2i20000000000000000000000
χ524-44-44-4-440-404040-400000000000000000000−2i22i2−2i22i20000000000000000000000
χ534-4-44-44-4404040-40-404i−4i−4i4i00000000000000000000000000000000000000000
χ544-4-44-44-4404040-40-40−4i4i4i−4i00000000000000000000000000000000000000000
χ554-4-44-44-440-40-404040000000000000000000022−22−22220000000000000000000000
χ564-4-44-44-440-40-4040400000000000000000000−222222−220000000000000000000000
χ574-4-4-4444-44040-40-40000000000000000000000000002i2−2i2−2i22i20000000000000000
χ584-4-4-4444-44040-40-4000000000000000000000000000−2i22i22i2−2i20000000000000000
χ594-4-4-4444-4-40-4040400000004-4-44000000000000000000000000000000000000
χ604-4-4-4444-4-40-404040000000-444-4000000000000000000000000000000000000
χ61888-8-88-8-8000000000000000000000000000000000000000000000000000000
χ6288-888-8-8-8000000000000000000000000000000000000000000000000000000

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