Finite Group Databasebeta

← Group #340209

Character table — Group #340209

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size11111111222222224444448888888888888888888888161616161616161616161616323232
order12222222444444444488882244444488888888888888244444888888444
χ111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111-1-11111-1-11111-1-1-1-1-1-111-11-1-1-1-1-1-1-1-111-1
χ3111111111111111111111111-1-1111111111111111111-1-11-1-1-111-1-1-1-1-1-1-1
χ4111111111111111111111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-1-1-111-1-11111-1-11
χ51111111111111111111111-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-11
χ61111111111111111111111-1-111-1-1-1-11111-1-1-1-111111111-11-1-1-1-11111-1-1-1
χ71111111111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-111111111-1
χ81111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1111
χ9111111111111111111-1-1-1-111111111-1-111-1-1-1-111-1-1-1-1-111-111-1-111-1-1-11-1
χ10111111111111111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-11111-11-1-1-1-111-1-111-111
χ11111111111111111111-1-1-1-111-1-11111-1-111-1-1-1-111-1-1-1-11-111-1-1-1-1-1-1111-11
χ12111111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111-1-11111111-1-11-1-1
χ13111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-11111-1-11111-111-111-1-1-1-1111-1-1
χ14111111111111111111-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1-11-1-1-1-11111-1-11-11
χ15111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-111111-111-1-1-1-111-1-1-111
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11-1-111111-1-111-11-1
χ172222222222-2-22-22-2-2-2222200220000-2-2000000000000-2-20200000000000
χ182222222222-2-22-22-2-2-2222200-2-20000-2-2000000000000220-200000000000
χ192222222222-2-22-22-2-2-2-2-2-2-200220000220000000000002-20-200000000000
χ202222222222-2-22-22-2-2-2-2-2-2-200-2-2000022000000000000-220200000000000
χ2122222222-2-222-22-22-2-20000220022-2-200220000-2-2000000-2000000000000
χ2222222222-2-222-22-22-2-200002200-2-2-2-200-2-20000220000002000000000000
χ2322222222-2-222-22-22-2-20000-2-200222200-2-2000022000000-2000000000000
χ2422222222-2-222-22-22-2-20000-2-200-2-22200220000-2-20000002000000000000
χ252-22-2-2-222-2-2-2-222222-2000000000000000022-2-200000000002-200002-2000
χ262-22-2-2-222-2-2-2-222222-2000000000000000022-2-20000000000-220000-22000
χ272-22-2-2-222-2-2-2-222222-20000000000000000-2-22200000000002-20000-22000
χ282-22-2-2-222-2-2-2-222222-20000000000000000-2-2220000000000-2200002-2000
χ292-2-222-2-22002-2020-20022−2−200002-22i−2i2−200i2−i2i2−i22i−2ii2i2−i2−i20000002−20000000
χ302-2-222-2-22002-2020-20022−2−200002-2−2i2i2−200−i2i2−i2i2−2i2i−i2−i2i2i20000002−20000000
χ312-2-222-2-22002-2020-20022−2−20000-222i−2i2−200i2−i2i2−i2−2i2i−i2−i2i2i2000000−220000000
χ322-2-222-2-22002-2020-20022−2−20000-22−2i2i2−200−i2i2−i2i22i−2ii2i2−i2−i2000000−220000000
χ332-2-222-2-22002-2020-200−2−22200002-22i−2i−2200−i2i2−i2i22i−2i−i2−i2i2i2000000−220000000
χ342-2-222-2-22002-2020-200−2−22200002-2−2i2i−2200i2−i2i2−i2−2i2ii2i2−i2−i2000000−220000000
χ352-2-222-2-22002-2020-200−2−2220000-222i−2i−2200−i2i2−i2i2−2i2ii2i2−i2−i20000002−20000000
χ362-2-222-2-22002-2020-200−2−2220000-22−2i2i−2200i2−i2i2−i22i−2i−i2−i2i2i20000002−20000000
χ3744444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000
χ38444-44-4-4-4000000000022−2222−22000000000022−220000002-22-2000000000000000
χ39444-44-4-4-4000000000022−2222−220000000000−2222000000-22-22000000000000000
χ40444-44-4-4-40000000000−2222−2222000000000022−22000000-22-22000000000000000
χ41444-44-4-4-40000000000−2222−22220000000000−22220000002-22-2000000000000000
χ4244-44-4-44-44-40040-40000000004-4000000000000000000000000000000000
χ4344-44-4-44-44-40040-4000000000-44000000000000000000000000000000000
χ4444-44-4-44-4-4400-40400000000000000000000000000000000000002i2−2i200000
χ4544-44-4-44-4-4400-4040000000000000000000000000000000000000−2i22i200000
χ4644-4-4-44-44004-40-4040000004-400000000000000000000000000000000000
χ4744-4-4-44-44004-40-404000000-4400000000000000000000000000000000000
χ4844-4-4-44-4400-44040-40000000000000000002i2−2i2−2i22i2000000000000000000000
χ4944-4-4-44-4400-44040-4000000000000000000−2i22i22i2−2i2000000000000000000000
χ504-44-4-4-4444444-4-4-4-44-400000000000000000000000000000000000000000
χ514-44-4-4-44444-4-4-44-44-4400000000000000000000000000000000000000000
χ524-44-4-4-444-4-4444-44-4-4400000000000000000000000000000000000000000
χ534-4-444-4-4400-440-404002222−22−2200000000−2222000000000000000000000000000
χ544-4-444-4-4400-440-40400−22−2222220000000022−22000000000000000000000000000
χ554-4-4-4444-44-400-4040004-4-440000000000000000000000000000000000000
χ564-4-4-4444-44-400-404000-444-40000000000000000000000000000000000000
χ574-4-4-4444-4-440040-400000000000000000000000002i2−2i2−2i22i2000000000000000
χ584-4-4-4444-4-440040-40000000000000000000000000−2i22i22i2−2i2000000000000000
χ598-888-88-8-8000000000000000000000000000000000000000000000000000

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