Finite Group Databasebeta

← Group #315539

Character table — Group #315539

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size11111111222222224444444444888888888888888888888888161616161616161632323232
order12222222444444444488888888444444448888888888888888444488884444
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-111-1-111111111-1-1-1-1111111-1-1-1-111-1-1-1-1
χ311111111111111111111111111-1-111-1-1111111-1-1-1-111111111-1-11111-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-11111
χ51111111111111111111111-1-1-1-11111111111-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-11-1-11
χ61111111111111111111111-1-1-1-111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-111-1
χ71111111111111111111111-1-1-1-1-1-111-1-11111-1-111111111-1-1-1-1-1-1-1-1-1-111-111-1
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-11111111-1-11
χ9111111111111111111-1-1-1-1111111111111-1-1111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111
χ10111111111111111111-1-1-1-1111111-1-111-1-1-1-11111111111-1-1-1-1-1-1-1-111-1-111-1-1
χ11111111111111111111-1-1-1-11111-1-111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111-1-1
χ12111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-111-1-11111-1-111
χ13111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-11111-11-11
χ14111111111111111111-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-111-1-1111-11-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-11111-1-1-1-1111111-1-111-1-11-11-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111111111111-1-1-1-1-11-11
χ172222222222-2-22-2-22-2-200002222002200-2-200-2-200000000000000-2200000000
χ182222222222-2-22-2-22-2-20000222200-2-2002200-2-2000000000000002-200000000
χ192222222222-2-22-2-22-2-20000-2-2-2-2002200-2-20022000000000000002-200000000
χ202222222222-2-22-2-22-2-20000-2-2-2-200-2-20022002200000000000000-2200000000
χ2122222222-2-222-222-2-2-2222200002200-2-200-2-2000000000000002-20000000000
χ2222222222-2-222-222-2-2-222220000-2-2002200-2-200000000000000-220000000000
χ2322222222-2-222-222-2-2-2-2-2-2-200002200-2-2002200000000000000-220000000000
χ2422222222-2-222-222-2-2-2-2-2-2-20000-2-200220022000000000000002-20000000000
χ252-22-222-2-22-2-2-2222-2-222i2i−2i−2i0000000000002i−2i0022-2-2000000000000002i−2i0000
χ262-22-222-2-22-2-2-2222-2-222i2i−2i−2i0000000000002i−2i00-2-22200000000000000−2i2i0000
χ272-22-222-2-22-2-2-2222-2-22−2i−2i2i2i000000000000−2i2i0022-2-200000000000000−2i2i0000
χ282-22-222-2-22-2-2-2222-2-22−2i−2i2i2i000000000000−2i2i00-2-222000000000000002i−2i0000
χ292-22-222-2-2-2222-2-2-22-22000022-2-200000000002-200002i2i−2i−2i000000002i−2i000000
χ302-22-222-2-2-2222-2-2-22-22000022-2-200000000002-20000−2i−2i2i2i00000000−2i2i000000
χ312-22-222-2-2-2222-2-2-22-220000-2-2220000000000-2200002i2i−2i−2i00000000−2i2i000000
χ322-22-222-2-2-2222-2-2-22-220000-2-2220000000000-220000−2i−2i2i2i000000002i−2i000000
χ332-22-222-2-2-22-2-2-22222-22i2i−2i−2i22-2-200000000−2i2i-22000000002i2i−2i−2i000000000000
χ342-22-222-2-2-22-2-2-22222-22i2i−2i−2i-2-22200000000−2i2i2-200000000−2i−2i2i2i000000000000
χ352-22-222-2-2-22-2-2-22222-2−2i−2i2i2i22-2-2000000002i−2i-2200000000−2i−2i2i2i000000000000
χ362-22-222-2-2-22-2-2-22222-2−2i−2i2i2i-2-222000000002i−2i2-2000000002i2i−2i−2i000000000000
χ3744444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000
χ38444-4-4-44-44-400-40040000000000000000000000000022−2222−220000000000000000
χ39444-4-4-44-44-400-400400000000000000000000000000−2222−22220000000000000000
χ40444-4-4-44-4-4400400-40000000000004-400000000000000000000000000000000
χ41444-4-4-44-4-4400400-4000000000000-4400000000000000000000000000000000
χ4244-444-4-4-4004-404-40000000000000000000000022−2222−2200000000000000000000
χ4344-444-4-4-4004-404-400000000000000000000000−2222−222200000000000000000000
χ4444-444-4-4-400-440-44000000000004-40000000000000000000000000000000000
χ4544-444-4-4-400-440-4400000000000-440000000000000000000000000000000000
χ4644-4-4-44-4400000000002i2−2i22i2−2i22i2−2i22i2−2i2000000000000000000002-22-2000000000000
χ4744-4-4-44-4400000000002i2−2i22i2−2i2−2i22i2−2i22i200000000000000000000-22-22000000000000
χ4844-4-4-44-440000000000−2i22i2−2i22i22i2−2i22i2−2i200000000000000000000-22-22000000000000
χ4944-4-4-44-440000000000−2i22i2−2i22i2−2i22i2−2i22i2000000000000000000002-22-2000000000000
χ504-444-4-4-444400-400-400000000000000004-40000000000000000000000000000
χ514-444-4-4-444400-400-40000000000000000-440000000000000000000000000000
χ524-444-4-4-44-4-4004004000000000000000000000000002i2−2i2−2i22i20000000000000000
χ534-444-4-4-44-4-400400400000000000000000000000000−2i22i22i2−2i20000000000000000
χ544-44-444-4-44-4444-4-4-44-400000000000000000000000000000000000000000000
χ554-4-44-444-4000000000022−22−22222i2−2i2−2i22i200000000000000000000−2i2i2i−2i000000000000
χ564-4-44-444-4000000000022−22−2222−2i22i22i2−2i2000000000000000000002i−2i−2i2i000000000000
χ574-4-44-444-40000000000−222222−222i2−2i2−2i22i2000000000000000000002i−2i−2i2i000000000000
χ584-4-44-444-40000000000−222222−22−2i22i22i2−2i200000000000000000000−2i2i2i−2i000000000000
χ594-4-4-44-444004-40-440000000000000004-4000000000000000000000000000000
χ604-4-4-44-444004-40-44000000000000000-44000000000000000000000000000000
χ614-4-4-44-44400-4404-40000000000000000000000022−22−222200000000000000000000
χ624-4-4-44-44400-4404-400000000000000000000000−222222−2200000000000000000000

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