Finite Group Databasebeta

← Group #338804

Character table — Group #338804

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size1111111122222222444444444488888888888888888888888888881616161616161616323232
order12222222444444444488888888444444444444888888888888888844448888444
χ111111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-111-1-111-1-1-1-111111111111-1-1-1-1-111-1-1-1
χ311111111111111111111111111-1-1-1-11111-1-11111111111-1-1-1-11111-11-1-111-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111-1-1-1-11111-1-111-1-1-1-1111
χ51111111111111111111111-1-1-1-1111111-1-11111-1-1111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-111-1
χ61111111111111111111111-1-1-1-11111-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1111111-1-1-1-11
χ71111111111111111111111-1-1-1-1-1-1-1-111-1-1-1-111-1-11111111111-1-1-1-1-1-111-1-111-1-11
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-11-1-1111111-1
χ9111111111111111111-1-1-1-1111111-1-11111111111-1-1-1-1-1-11111-1-1-1-1-11-1-1-1-1-1-1-111
χ10111111111111111111-1-1-1-1111111-1-1-1-1-1-111-1-1111111-1-11111-1-1-1-1-1-11111-1-11-1-1
χ11111111111111111111-1-1-1-11111-1-1111111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111-1-1
χ12111111111111111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11-1-1-11111-111
χ13111111111111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111111-11-1
χ14111111111111111111-1-1-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-1-1-11111-11-1-1-1-1111-11
χ15111111111111111111-1-1-1-1-1-1-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1111111111-1-1-111-1-11-11
χ16111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-1111111111111-1-1-1-1-11-1
χ17222222222-22-2-222-2-2-22222000022220000-2-200000000-2-200000000-20000000000
χ18222222222-22-2-222-2-2-222220000-2-2-2-200002200000000-2-20000000020000000000
χ19222222222-22-2-222-2-2-2-2-2-2-2000022-2-20000-2-200000000220000000020000000000
χ20222222222-22-2-222-2-2-2-2-2-2-20000-2-222000022000000002200000000-20000000000
χ2122222222-22-222-2-22-2-200002222000022-2-200-2-2-2-20000000000000002000000000
χ2222222222-22-222-2-22-2-2000022220000-2-2220022-2-2000000000000000-2000000000
χ2322222222-22-222-2-22-2-20000-2-2-2-20000222200-2-222000000000000000-2000000000
χ2422222222-22-222-2-22-2-20000-2-2-2-20000-2-2-2-20022220000000000000002000000000
χ252222-2-2-2-220200-2-200022-2-222−2−22-22-2000000002−200000022−2−222−2−20000002−2000
χ262222-2-2-2-220200-2-200022-2-222−2−2-22-22000000002−2000000−2−22222−2−2000000−22000
χ272222-2-2-2-220200-2-200022-2-2−2−2222-22-200000000−22000000−2−222−2−222000000−22000
χ282222-2-2-2-220200-2-200022-2-2−2−222-22-2200000000−2200000022−2−2−2−2220000002−2000
χ292222-2-2-2-220200-2-2000-2-22222−2−22-2-22000000002−200000022−2−2−2−222000000−22000
χ302222-2-2-2-220200-2-2000-2-22222−2−2-222-2000000002−2000000−2−222−2−2220000002−2000
χ312222-2-2-2-220200-2-2000-2-222−2−2222-2-2200000000−22000000−2−22222−2−20000002−2000
χ322222-2-2-2-220200-2-2000-2-222−2−222-222-200000000−2200000022−2−222−2−2000000−22000
χ3322-2-2-222-20-202-2002002−22−22i−2i2i−2i0000002-2002i−2i00i2i2−i2−i22−20000i2−i2i2−i200002−200000
χ3422-2-2-222-20-202-2002002−22−22i−2i2i−2i000000-2200−2i2i00−i2−i2i2i22−20000i2−i2i2−i20000−2200000
χ3522-2-2-222-20-202-2002002−22−2−2i2i−2i2i0000002-200−2i2i00−i2−i2i2i22−20000−i2i2−i2i200002−200000
χ3622-2-2-222-20-202-2002002−22−2−2i2i−2i2i000000-22002i−2i00i2i2−i2−i22−20000−i2i2−i2i20000−2200000
χ3722-2-2-222-20-202-200200−22−222i−2i2i−2i0000002-2002i−2i00−i2−i2i2i2−220000−i2i2−i2i20000−2200000
χ3822-2-2-222-20-202-200200−22−222i−2i2i−2i000000-2200−2i2i00i2i2−i2−i2−220000−i2i2−i2i200002−200000
χ3922-2-2-222-20-202-200200−22−22−2i2i−2i2i0000002-200−2i2i00i2i2−i2−i2−220000i2−i2i2−i20000−2200000
χ4022-2-2-222-20-202-200200−22−22−2i2i−2i2i000000-22002i−2i00−i2−i2i2i2−220000i2−i2i2−i200002−200000
χ412-2-2222-2-2-222-2-2-222-2200000000000000000000002i−2i2i−2i002-22-20000002i−2i0000000
χ422-2-2222-2-2-222-2-2-222-2200000000000000000000002i−2i2i−2i00-22-22000000−2i2i0000000
χ432-2-2222-2-2-222-2-2-222-220000000000000000000000−2i2i−2i2i002-22-2000000−2i2i0000000
χ442-2-2222-2-2-222-2-2-222-220000000000000000000000−2i2i−2i2i00-22-220000002i−2i0000000
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000
χ464444-4-4-4-4-40-4004400000002222−22−22000000000000−22220000000000000000000000000
χ474444-4-4-4-4-40-400440000000−22−22222200000000000022−220000000000000000000000000
χ4844-4-44-4-44000000000022−22−22222i2−2i2−2i22i20000000000000000000000002i−2i−2i2i00000000000
χ4944-4-44-4-44000000000022−22−2222−2i22i22i2−2i2000000000000000000000000−2i2i2i−2i00000000000
χ5044-4-44-4-440000000000−222222−222i2−2i2−2i22i2000000000000000000000000−2i2i2i−2i00000000000
χ5144-4-44-4-440000000000−222222−22−2i22i22i2−2i20000000000000000000000002i−2i−2i2i00000000000
χ5244-4-4-444-4040-4400-40022−2222−220000000000000000000000−22220000000000000000000
χ5344-4-4-444-4040-4400-400−2222−2222000000000000000000000022−220000000000000000000
χ544-44-4-44-440404-400-4000000000000004i−4i000000000000000000000000000000000
χ554-44-4-44-440404-400-400000000000000−4i4i000000000000000000000000000000000
χ564-44-4-44-440-40-4400400000000000000000000000022−22−2222000000000000000000000
χ574-44-4-44-440-40-44004000000000000000000000000−222222−22000000000000000000000
χ584-4-4444-4-444-4-4-44-444-400000000000000000000000000000000000000000000000
χ594-4-4444-4-44-4-4444-4-4-4400000000000000000000000000000000000000000000000
χ604-4-4444-4-4-4-4444-44-44-400000000000000000000000000000000000000000000000
χ614-4-44-4-44440-400-4400000000000000000004-400000000000000000000000000000
χ624-4-44-4-44440-400-440000000000000000000-4400000000000000000000000000000
χ634-4-44-4-444-404004-4000000000000000000000000000000022−22−2222000000000000000
χ644-4-44-4-444-404004-40000000000000000000000000000000−222222−22000000000000000
χ658-88-88-88-8000000000000000000000000000000000000000000000000000000000

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