Finite Group Databasebeta

← Group #311571

Character table — Group #311571

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122222222444444888888888888888888888888881616161616161616161616163232
order12222222444444444488884444444444448888888888888844444488888844
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111
χ3111111111111111111111111-1-111-1-1111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1
χ4111111111111111111111111-1-111-1-1-1-1-1-111-1-11111-1-1-1-1-1-111-1-111-1-11111-1-1
χ51111111111111111111111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ61111111111111111111111-1-111-1-111-1-1-1-11111-1-1-1-1111111-1-111-1-1-1-11111-1-1
χ71111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111111111-1-111-1-1-1-1-1-111
χ9111111111111111111-1-1-1-1111111-1-11111-1-111-1-1-1-111-1-1-1-111-11-1-1-1-111-1-1-11
χ10111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-111111-1-111-11
χ11111111111111111111-1-1-1-111-1-111111111-1-111-1-1-1-111-1-1-1-1-1-11-111-1-1-1-1111-1
χ12111111111111111111-1-1-1-111-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111111-1-1-11111-1-11-1
χ13111111111111111111-1-1-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1111111-11-1-1-1-1-1-1111-1
χ14111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-11111111-1-11-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-11111-1-11111-1-11-111-1-111-1-1-11
χ16111111111111111111-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111111111-1-1-1-1111-1-1-111-1-111-11
χ172222222222-2-22-2-22-2-200002200-2-20022-2-200220000-2-2000000000000000000
χ182222222222-2-22-2-22-2-200002200-2-200-2-22200-2-2000022000000000000000000
χ192222222222-2-22-2-22-2-20000-2-200220022-2-200-2-2000022000000000000000000
χ202222222222-2-22-2-22-2-20000-2-2002200-2-22200220000-2-2000000000000000000
χ2122222222-2-222-222-2-2-22222002200220000-2-200000000000000-2-20000000000
χ2222222222-2-222-222-2-2-2222200-2-200-2-20000-2-200000000000000220000000000
χ2322222222-2-222-222-2-2-2-2-2-2-2002200-2-2000022000000000000002-20000000000
χ2422222222-2-222-222-2-2-2-2-2-2-200-2-2002200002200000000000000-220000000000
χ2522-22-2-2-222-2-2-2222-2-222i2i−2i−2i0000000000002i−2i0000000000002i−2i002-200000000
χ2622-22-2-2-222-2-2-2222-2-222i2i−2i−2i0000000000002i−2i000000000000−2i2i00-2200000000
χ2722-22-2-2-222-2-2-2222-2-22−2i−2i2i2i000000000000−2i2i0000000000002i−2i00-2200000000
χ2822-22-2-2-222-2-2-2222-2-22−2i−2i2i2i000000000000−2i2i000000000000−2i2i002-200000000
χ2922-22-2-2-22-2222-2-2-22-220000000000002i−2i2i−2i00002i2i−2i−2i0022-2-200000000000000
χ3022-22-2-2-22-2222-2-2-22-220000000000002i−2i2i−2i0000−2i−2i2i2i00-2-22200000000000000
χ3122-22-2-2-22-2222-2-2-22-22000000000000−2i2i−2i2i00002i2i−2i−2i00-2-22200000000000000
χ3222-22-2-2-22-2222-2-2-22-22000000000000−2i2i−2i2i0000−2i−2i2i2i0022-2-200000000000000
χ3322-22-2-2-22-22-2-2-22222-22i2i−2i−2i000000002i−2i−2i2i−2i2i0000000000000000002-2000000
χ3422-22-2-2-22-22-2-2-22222-22i2i−2i−2i00000000−2i2i2i−2i−2i2i000000000000000000-22000000
χ3522-22-2-2-22-22-2-2-22222-2−2i−2i2i2i000000002i−2i−2i2i2i−2i000000000000000000-22000000
χ3622-22-2-2-22-22-2-2-22222-2−2i−2i2i2i00000000−2i2i2i−2i2i−2i0000000000000000002-2000000
χ372-2-22-222-2002-202-20002i−2i2i−2i002-2002i−2i000000i2−i20000i2−i22−22−200000000i2−i22−200
χ382-2-22-222-2002-202-20002i−2i2i−2i002-2002i−2i000000−i2i20000−i2i2−22−2200000000−i2i2−2200
χ392-2-22-222-2002-202-20002i−2i2i−2i00-2200−2i2i000000i2−i20000i2−i22−22−200000000−i2i2−2200
χ402-2-22-222-2002-202-20002i−2i2i−2i00-2200−2i2i000000−i2i20000−i2i2−22−2200000000i2−i22−200
χ412-2-22-222-2002-202-2000−2i2i−2i2i002-200−2i2i000000i2−i20000i2−i2−22−2200000000i2−i2−2200
χ422-2-22-222-2002-202-2000−2i2i−2i2i002-200−2i2i000000−i2i20000−i2i22−22−200000000−i2i22−200
χ432-2-22-222-2002-202-2000−2i2i−2i2i00-22002i−2i000000i2−i20000i2−i2−22−2200000000−i2i22−200
χ442-2-22-222-2002-202-2000−2i2i−2i2i00-22002i−2i000000−i2i20000−i2i22−22−200000000i2−i2−2200
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000
χ46444-4-44-4-44-400-4004000000000000000000000022−2222−2200000000000000000000
χ47444-4-44-4-44-400-40040000000000000000000000−2222−222200000000000000000000
χ48444-4-44-4-4-4400400-40000004-400000000000000000000000000000000000000
χ49444-4-44-4-4-4400400-4000000-4400000000000000000000000000000000000000
χ5044-44-4-4-444-4444-4-4-44-400000000000000000000000000000000000000000000
χ5144-4-44-44-44400-400-400000000004-40000000000000000000000000000000000
χ5244-4-44-44-44400-400-40000000000-440000000000000000000000000000000000
χ5344-4-44-44-4-4-400400400000000000000000000002i2−2i2−2i22i200000000000000000000
χ5444-4-44-44-4-4-40040040000000000000000000000−2i22i22i2−2i200000000000000000000
χ554-4444-4-4-4004-40-440000000000000000000000000000022−22−222200000000000000
χ564-4444-4-4-4004-40-4400000000000000000000000000000−222222−2200000000000000
χ574-4444-4-4-400-4404-40004-4-440000000000000000000000000000000000000000
χ584-4444-4-4-400-4404-4000-444-40000000000000000000000000000000000000000
χ594-4-44-444-400-440-440000000000000000000002i2−2i20000−2i22i2000000000000000000
χ604-4-44-444-400-440-44000000000000000000000−2i22i200002i2−2i2000000000000000000
χ618-88-8-8-888000000000000000000000000000000000000000000000000000000
χ628-8-8-888-88000000000000000000000000000000000000000000000000000000

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