Finite Group Databasebeta

← Group #336752

Character table — Group #336752

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62C63C64C65
size1111111122222222444444444488888888888888888888888888881616161616161616323232
order12222222444444444488888888444444444444888888888888888844448888444
χ111111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-1-1-111111111-1-1-1-111111-1-1-111-1-1-1-1-1
χ311111111111111111111111111-1-1-1-1-1-111111111-1-1-1-11111111111-11-1-1-1-111-1-1-1
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
χ51111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-11111-1-111-11-1
χ61111111111111111111111-1-1-1-1111111-1-11111-1-1-1-1-1-1111111-1-1-1-11-1-1-1-1-1-1-11-11
χ71111111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-11-1-111111-11
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111111111-1-1-1-1-1-11111-1-1-11-1
χ9111111111111111111-1-1-1-1111111-1-111111111111111-1-1-1-1-1-1-1-1-1-1-11-1-1-1-1-1-111-1
χ10111111111111111111-1-1-1-1111111-1-111-1-1-1-1-1-1111111-1-11111-1-1-1-1-1-111-1-111-1-11
χ11111111111111111111-1-1-1-11111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11
χ12111111111111111111-1-1-1-11111-1-111-1-1-1-1-1-1-1-111-1-1-1-1-1-11111-1-1-1-11-1-1-1111111-1
χ13111111111111111111-1-1-1-1-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-111111111-11-1-111-1-1-111
χ14111111111111111111-1-1-1-1-1-1-1-111-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-11111-1-11111111-1-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-111-1-111-1-1-1-1-1-11111-1-1111111111111-1-1-1-11-1-1
χ16111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-11111-1-11111-1-1-1-1-1-111111-1-1-1-1-111-111
χ172222222222-22-2-2-22-2-2222200002222-2-2000000000000-2-200000000-20000000000
χ182222222222-22-2-2-22-2-222220000-2-2-2-222000000000000-2-20000000020000000000
χ192222222222-22-2-2-22-2-2-2-2-2-2000022-2-2-2-2000000000000220000000020000000000
χ202222222222-22-2-2-22-2-2-2-2-2-20000-2-222220000000000002200000000-20000000000
χ2122222222-2-22-2222-2-2-2000022220000002222-2-2-2-2000000000000000-2000000000
χ2222222222-2-22-2222-2-2-200002222000000-2-2-2-222-2-20000000000000002000000000
χ2322222222-2-22-2222-2-2-20000-2-2-2-200000022-2-22222000000000000000-2000000000
χ2422222222-2-22-2222-2-2-20000-2-2-2-2000000-2-222-2-2220000000000000002000000000
χ252222-2-2-2-22-202000-20022-2-222−2−22-22-2000000002−222−2−200000022−2−200002−200000
χ262222-2-2-2-22-202000-20022-2-222−2−2-22-22000000002−2−2−22200000022−2−20000−2200000
χ272222-2-2-2-22-202000-20022-2-2−2−2222-22-200000000−22−2−222000000−2−2220000−2200000
χ282222-2-2-2-22-202000-20022-2-2−2−222-22-2200000000−2222−2−2000000−2−22200002−200000
χ292222-2-2-2-22-202000-200-2-22222−2−22-2-22000000002−222−2−2000000−2−2220000−2200000
χ302222-2-2-2-22-202000-200-2-22222−2−2-222-2000000002−2−2−222000000−2−22200002−200000
χ312222-2-2-2-22-202000-200-2-222−2−2222-2-2200000000−22−2−22200000022−2−200002−200000
χ322222-2-2-2-22-202000-200-2-222−2−222-222-200000000−2222−2−200000022−2−20000−2200000
χ3322-2-2-2-22200202-2-20002−22−22-22-20000002i−2i2i−2i000000002−2i2i2−i2−i22−22−2000000i2−i2000
χ3422-2-2-2-22200202-2-20002−22−22-22-2000000−2i2i−2i2i000000002−2−i2−i2i2i22−22−2000000−i2i2000
χ3522-2-2-2-22200202-2-20002−22−2-22-220000002i−2i−2i2i000000002−2−i2−i2i2i2−22−22000000i2−i2000
χ3622-2-2-2-22200202-2-20002−22−2-22-22000000−2i2i2i−2i000000002−2i2i2−i2−i2−22−22000000−i2i2000
χ3722-2-2-2-22200202-2-2000−22−222-22-20000002i−2i2i−2i00000000−22−i2−i2i2i2−22−22000000−i2i2000
χ3822-2-2-2-22200202-2-2000−22−222-22-2000000−2i2i−2i2i00000000−22i2i2−i2−i2−22−22000000i2−i2000
χ3922-2-2-2-22200202-2-2000−22−22-22-220000002i−2i−2i2i00000000−22i2i2−i2−i22−22−2000000−i2i2000
χ4022-2-2-2-22200202-2-2000−22−22-22-22000000−2i2i2i−2i00000000−22−i2−i2i2i22−22−2000000i2−i2000
χ412-2-22-222-2-2-2-2222-222-200000000000000000000002i−2i2i−2i002-22-20000002i−2i0000000
χ422-2-22-222-2-2-2-2222-222-200000000000000000000002i−2i2i−2i00-22-22000000−2i2i0000000
χ432-2-22-222-2-2-2-2222-222-20000000000000000000000−2i2i−2i2i002-22-2000000−2i2i0000000
χ442-2-22-222-2-2-2-2222-222-20000000000000000000000−2i2i−2i2i00-22-220000002i−2i0000000
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000000
χ464444-4-4-4-4-440-400040000002222−22−22000000000000−22220000000000000000000000000
χ474444-4-4-4-4-440-40004000000−22−22222200000000000022−220000000000000000000000000
χ4844-4-444-4-4000000000022−22−222222−22−22220000000000000000000000002-2-2200000000000
χ4944-4-444-4-4000000000022−22−2222−222222−22000000000000000000000000-222-200000000000
χ5044-4-444-4-40000000000−222222−2222−22−2222000000000000000000000000-222-200000000000
χ5144-4-444-4-40000000000−222222−22−222222−220000000000000000000000002-2-2200000000000
χ5244-4-4-4-44400-40-44400022−2222−220000000000000000000000−22220000000000000000000
χ5344-4-4-4-44400-40-444000−2222−2222000000000000000000000022−220000000000000000000
χ544-44-44-44-40040-44-40000000000000000000004-4000000000000000000000000000
χ554-44-44-44-40040-44-4000000000000000000000-44000000000000000000000000000
χ564-44-44-44-400-404-4400000000000000000000000000000002i2−2i2−2i22i2000000000000000
χ574-44-44-44-400-404-440000000000000000000000000000000−2i22i22i2−2i2000000000000000
χ584-4-444-4-444-40-40004000000000000004-4000000000000000000000000000000000
χ594-4-444-4-444-40-4000400000000000000-44000000000000000000000000000000000
χ604-4-444-4-44-4404000-40000000000000000000000002i2−2i2−2i22i2000000000000000000000
χ614-4-444-4-44-4404000-4000000000000000000000000−2i22i22i2−2i2000000000000000000000
χ624-4-44-444-4444-4-4-44-44-400000000000000000000000000000000000000000000000
χ634-4-44-444-444-4-444-4-4-4400000000000000000000000000000000000000000000000
χ644-4-44-444-4-4-444-4-444-4400000000000000000000000000000000000000000000000
χ658-88-8-88-88000000000000000000000000000000000000000000000000000000000

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