Finite Group Databasebeta

← Group #288331

Character table — Group #288331

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122222222444444888888888888888888888888881616161616161616161616163232
order12222222444444444488882244444444448888888888888844444488888824
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111-1-1-1-11111-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111
χ3111111111111111111111111-1-1-1-111111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1
χ4111111111111111111111111-1-1-1-1-1-1-1-11111-1-11111-1-1-1-1-1-1-1-11111-1-11111-1-1
χ51111111111111111111111-1-111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ61111111111111111111111-1-11111-1-1-1-1-1-11111-1-1-1-111111111-1-1-1-1-1-11111-1-1
χ71111111111111111111111-1-1-1-1-1-11111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-1111111-1-11111-1-1-1-1-1-111
χ9111111111111111111-1-1-1-11111-1-1111111-1-111-1-1-1-111-1-1-1-1-11-1-111-1-111-1-11-1
χ10111111111111111111-1-1-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1111-1-111-1-1111-1
χ11111111111111111111-1-1-1-111-1-111111111-1-111-1-1-1-111-1-1-1-11-111-1-1-1-1-1-111-11
χ12111111111111111111-1-1-1-111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-111111-1-1-1111111-1-1-11
χ13111111111111111111-1-1-1-1-1-111-1-11111-1-1-1-1-1-11111-1-11111-11-1-111-1-1-1-111-11
χ14111111111111111111-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1111-1-11111-1-1-11
χ15111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-11111-1-111111-111-1-1-1-111-1-11-1
χ16111111111111111111-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-11-1-1-11111-1-1111-1
χ172222222222-22-2-2-22-2-2000022000022-2-2-2-200220000-2-2000000000000000000
χ182222222222-22-2-2-22-2-20000220000-2-222-2-200-2-2000022000000000000000000
χ192222222222-22-2-2-22-2-20000-2-2000022-2-22200-2-2000022000000000000000000
χ202222222222-22-2-2-22-2-20000-2-20000-2-2222200220000-2-2000000000000000000
χ2122222222-2-22-2222-2-2-22222002222000000-2-2000000000000-2-2000000000000
χ2222222222-2-22-2222-2-2-2222200-2-2-2-2000000-2-200000000000022000000000000
χ2322222222-2-22-2222-2-2-2-2-2-2-20022-2-2000000220000000000002-2000000000000
χ2422222222-2-22-2222-2-2-2-2-2-2-200-2-22200000022000000000000-22000000000000
χ2522-2-2-2-222222-2-22-2-2-2200000000002i−2i2i−2i0000002i2i−2i−2i0022-2-200000000000000
χ2622-2-2-2-222222-2-22-2-2-2200000000002i−2i2i−2i000000−2i−2i2i2i00-2-22200000000000000
χ2722-2-2-2-222222-2-22-2-2-220000000000−2i2i−2i2i0000002i2i−2i−2i00-2-22200000000000000
χ2822-2-2-2-222222-2-22-2-2-220000000000−2i2i−2i2i000000−2i−2i2i2i0022-2-200000000000000
χ2922-2-2-2-22222-2-22-22-22-222-2-20000002i−2i−2i2i002-20000000000000000002i−2i000000
χ3022-2-2-2-22222-2-22-22-22-222-2-2000000−2i2i2i−2i002-2000000000000000000−2i2i000000
χ3122-2-2-2-22222-2-22-22-22-2-2-2220000002i−2i−2i2i00-22000000000000000000−2i2i000000
χ3222-2-2-2-22222-2-22-22-22-2-2-222000000−2i2i2i−2i00-220000000000000000002i−2i000000
χ3322-2-2-2-222-2-2-222-222-2222-2-2000000000000-22000000000000002-22-200000000
χ3422-2-2-2-222-2-2-222-222-2222-2-2000000000000-2200000000000000-22-2200000000
χ3522-2-2-2-222-2-2-222-222-22-2-2220000000000002-2000000000000002-2-2200000000
χ3622-2-2-2-222-2-2-222-222-22-2-2220000000000002-200000000000000-222-200000000
χ372-222-2-22-200-2022-20002i−2i2i−2i002-22i−2i00000000i2−i20000i2−i22−22−200000000i2−i22−200
χ382-222-2-22-200-2022-20002i−2i2i−2i002-22i−2i00000000−i2i20000−i2i2−22−2200000000−i2i2−2200
χ392-222-2-22-200-2022-20002i−2i2i−2i00-22−2i2i00000000i2−i20000i2−i22−22−200000000−i2i2−2200
χ402-222-2-22-200-2022-20002i−2i2i−2i00-22−2i2i00000000−i2i20000−i2i2−22−2200000000i2−i22−200
χ412-222-2-22-200-2022-2000−2i2i−2i2i002-2−2i2i00000000i2−i20000i2−i2−22−2200000000i2−i2−2200
χ422-222-2-22-200-2022-2000−2i2i−2i2i002-2−2i2i00000000−i2i20000−i2i22−22−200000000−i2i22−200
χ432-222-2-22-200-2022-2000−2i2i−2i2i00-222i−2i00000000i2−i20000i2−i2−22−2200000000−i2i22−200
χ442-222-2-22-200-2022-2000−2i2i−2i2i00-222i−2i00000000−i2i20000−i2i22−22−200000000i2−i2−2200
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000
χ46444-44-4-4-44-404000-4000000000000000000000022−2222−2200000000000000000000
χ47444-44-4-4-44-404000-40000000000000000000000−2222−222200000000000000000000
χ48444-44-4-4-4-440-4000400000000000000004i−4i0000000000000000000000000000
χ49444-44-4-4-4-440-400040000000000000000−4i4i0000000000000000000000000000
χ5044-44-44-4-44-40-4000400000000000000000000002i2−2i2−2i22i200000000000000000000
χ5144-44-44-4-44-40-400040000000000000000000000−2i22i22i2−2i200000000000000000000
χ5244-44-44-4-4-4404000-40000004-400000000000000000000000000000000000000
χ5344-44-44-4-4-4404000-4000000-4400000000000000000000000000000000000000
χ5444-4-4-4-444-4-444-44-444-400000000000000000000000000000000000000000000
χ554-444-4-44-40040-4-440000000000000000000002i2−2i20000−2i22i2000000000000000000
χ564-444-4-44-40040-4-44000000000000000000000−2i22i200002i2−2i2000000000000000000
χ574-4-4-4444-400404-4-40004i−4i−4i4i0000000000000000000000000000000000000000
χ584-4-4-4444-400404-4-4000−4i4i4i−4i0000000000000000000000000000000000000000
χ594-4-4-4444-400-40-4440000000000000000000000000000022−22−222200000000000000
χ604-4-4-4444-400-40-44400000000000000000000000000000−222222−2200000000000000
χ618-88-8-88-88000000000000000000000000000000000000000000000000000000
χ628-8-888-8-88000000000000000000000000000000000000000000000000000000

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