Finite Group Databasebeta

← Group #337289

Character table — Group #337289

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59
size11111111222222224444448888888888888888888888161616161616161616161616323232
order12222222444444444488882244444488888888888888244444888888444
χ111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-111-1-1-1-11111-1-1-1-111-1-1-11-1-1-1-1-1-111-1
χ311111111111111111111111111-1-11111111111111111-1-11-1-1-1-1-1-1-111-1-1-1
χ411111111111111111111111111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-111-11111-1-1-1-11
χ51111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-11
χ61111111111111111111111-1-1-1-111-1-1111111-1-1-1-1111111-1-1-111111-1-1-1-1-1
χ71111111111111111111111-1-1-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-111111111-1
χ81111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-1-111-1-1-1-1-1-1-1111
χ9111111111111111111-1-1-1-111111111-1-11111-1-1-1-1-1-1-1-11-1111-111-1-1-1-1-11-1
χ10111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-111111-1-1-1-1-1-1-11111-111
χ11111111111111111111-1-1-1-11111-1-111-1-11111-1-1-1-1-1-1-1-1-111-1-11-1-111-1-11-11
χ12111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-11-111111-1-1111-1-1
χ13111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1111111111-1111-1-1-111-1-11-1-1
χ14111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-11-1-1-1-1-111-1-1111-11
χ15111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-111-1-1111-1-1-1-1-111
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-11-1111-1-11111-11-1
χ172222222222-22-2-2-22-2-2222200002200-2-2000000000000-2-20002000000000
χ182222222222-22-2-2-22-2-222220000-2-200-2-200000000000022000-2000000000
χ192222222222-22-2-2-22-2-2-2-2-2-20000220022000000000000-22000-2000000000
χ202222222222-22-2-2-22-2-2-2-2-2-20000-2-200220000000000002-20002000000000
χ2122222222-2-22-2222-2-2-2000022-2-200220022-2-20000000000-2000000000000
χ2222222222-2-22-2222-2-2-2000022-2-200-2-200-2-22200000000002000000000000
χ2322222222-2-22-2222-2-2-20000-2-222002200-2-2220000000000-2000000000000
χ2422222222-2-22-2222-2-2-20000-2-22200-2-20022-2-200000000002000000000000
χ252-2222-2-2-2-2-2-2222-222-200000000000000000022-2-200000002i−2i0002i−2i00000
χ262-2222-2-2-2-2-2-2222-222-200000000000000000022-2-20000000−2i2i000−2i2i00000
χ272-2222-2-2-2-2-2-2222-222-2000000000000000000-2-22200000002i−2i000−2i2i00000
χ282-2222-2-2-2-2-2-2222-222-2000000000000000000-2-2220000000−2i2i0002i−2i00000
χ292-22-2-22-2200202-2-200022−2−2002i−2i002-22−2002i−2ii2−i2i2−i2i2i2−i2−i200000000002−2000
χ302-22-2-22-2200202-2-200022−2−2002i−2i00-222−200−2i2ii2−i2i2−i2−i2−i2i2i20000000000−22000
χ312-22-2-22-2200202-2-200022−2−200−2i2i002-22−200−2i2i−i2i2−i2i2−i2−i2i2i200000000002−2000
χ322-22-2-22-2200202-2-200022−2−200−2i2i00-222−2002i−2i−i2i2−i2i2i2i2−i2−i20000000000−22000
χ332-22-2-22-2200202-2-2000−2−222002i−2i002-2−22002i−2i−i2i2−i2i2−i2−i2i2i20000000000−22000
χ342-22-2-22-2200202-2-2000−2−222002i−2i00-22−2200−2i2i−i2i2−i2i2i2i2−i2−i200000000002−2000
χ352-22-2-22-2200202-2-2000−2−22200−2i2i002-2−2200−2i2ii2−i2i2−i2i2i2−i2−i20000000000−22000
χ362-22-2-22-2200202-2-2000−2−22200−2i2i00-22−22002i−2ii2−i2i2−i2−i2−i2i2i200000000002−2000
χ3744444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000
χ38444-4-4-44-40040-44-400000004-400000000000000000000000000000000000
χ39444-4-4-44-40040-44-40000000-4400000000000000000000000000000000000
χ40444-4-4-44-400-404-440000000000000000000002i2−2i2−2i22i20000000000000000000
χ41444-4-4-44-400-404-44000000000000000000000−2i22i22i2−2i20000000000000000000
χ4244-44-44-4-44-404000-4000000000000000000000000000000000022−220000000
χ4344-44-44-4-44-404000-40000000000000000000000000000000000−22220000000
χ4444-44-44-4-4-440-4000400000000004i−4i0000000000000000000000000000000
χ4544-44-44-4-4-440-400040000000000−4i4i0000000000000000000000000000000
χ4644-4-44-4-4400000000002i2−2i22i2−2i2000000000022−220000002i−2i2i−2i000000000000000
χ4744-4-44-4-4400000000002i2−2i22i2−2i20000000000−2222000000−2i2i−2i2i000000000000000
χ4844-4-44-4-440000000000−2i22i2−2i22i2000000000022−22000000−2i2i−2i2i000000000000000
χ4944-4-44-4-440000000000−2i22i2−2i22i20000000000−22220000002i−2i2i−2i000000000000000
χ504-4444-4-4-4444-4-4-44-44-400000000000000000000000000000000000000000
χ514-4444-4-4-444-4-444-4-4-4400000000000000000000000000000000000000000
χ524-4444-4-4-4-4-444-4-444-4400000000000000000000000000000000000000000
χ534-44-4-44-4400-40-4440002222−22−2200000000−2222000000000000000000000000000
χ544-44-4-44-4400-40-444000−22−2222220000000022−22000000000000000000000000000
χ554-4-44-4-4444-40-4000400000000000000000000000022−22−2222000000000000000
χ564-4-44-4-4444-40-40004000000000000000000000000−222222−22000000000000000
χ574-4-44-4-444-4404000-4004i−4i−4i4i0000000000000000000000000000000000000
χ584-4-44-4-444-4404000-400−4i4i4i−4i0000000000000000000000000000000000000
χ598-8-8-8888-8000000000000000000000000000000000000000000000000000

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