Finite Group Databasebeta

← Group #309248

Character table — Group #309248

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122222222444444888888888888888888888888881616161616161616161616163232
order12222222444444444488884444444444448888888888888844444488888844
χ111111111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-111111111111111-1-1-1-1-1-111-1-1-1-1-1-1
χ3111111111111111111111111-1-111-1-11111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-111
χ4111111111111111111111111-1-111-1-1-1-1-1-1111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1
χ51111111111111111111111-1-111-1-111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ61111111111111111111111-1-111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111
χ71111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111111111-1-1-1-111-1-11111-1-1
χ81111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111111111-1-1-1-1-1-1-1-111
χ9111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-11111-1-1-1-111-1-11-1-1-111-1-11-1
χ10111111111111111111-1-1-1-111111111-1-111-1-1-1-1-1-11111-1-1-1-1-1-111-11-1-1-1-111-11
χ11111111111111111111-1-1-1-111-1-111-1-111-1-1-1-1-1-1-1-1-1-1-1-11111-1-1111-111-1-1111-1
χ12111111111111111111-1-1-1-111-1-111-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111-1-1-111111-1-1-11
χ13111111111111111111-1-1-1-1-1-111-1-11111-1-1-1-11111-1-1-1-1111111-1-11-1-1-1-1-111-11
χ14111111111111111111-1-1-1-1-1-111-1-111-1-111-1-11111-1-1-1-11111-1-111-11-1-111-1-11-1
χ15111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-111111111-1-1-1-1-1-1111-11111-1-1-11
χ16111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-111111111-1-1-1-111-1-1-1111-1-1111-1
χ172222222222-2-2-2-222-2-200002222-2-2-2-2000000000022-2-2000000000000000000
χ182222222222-2-2-2-222-2-2000022-2-2-2-2220000000000-2-222000000000000000000
χ192222222222-2-2-2-222-2-20000-2-22222-2-20000000000-2-222000000000000000000
χ202222222222-2-2-2-222-2-20000-2-2-2-22222000000000022-2-2000000000000000000
χ2122222222-2-22222-2-2-2-22222000000002222-2-20000000000000000-2-200000000
χ2222222222-2-22222-2-2-2-2222200000000-2-2-2-2-2-200000000000000002200000000
χ2322222222-2-22222-2-2-2-2-2-2-2-20000000022-2-2220000000000000000-2200000000
χ2422222222-2-22222-2-2-2-2-2-2-2-200000000-2-2222200000000000000002-200000000
χ2522-2-222-2-22222-2-2-2-22-222-2-20000000000002-20000000000002-22-20000000000
χ2622-2-222-2-22222-2-2-2-22-222-2-20000000000002-2000000000000-22-220000000000
χ2722-2-222-2-22222-2-2-2-22-2-2-222000000000000-220000000000002-2-220000000000
χ2822-2-222-2-22222-2-2-2-22-2-2-222000000000000-22000000000000-222-20000000000
χ2922-2-222-2-2-2-222-2-222-2222-2-2002i−2i002i−2i0000-220000000000000000002i−2i000000
χ3022-2-222-2-2-2-222-2-222-2222-2-200−2i2i00−2i2i0000-22000000000000000000−2i2i000000
χ3122-2-222-2-2-2-222-2-222-22-2-222002i−2i002i−2i00002-2000000000000000000−2i2i000000
χ3222-2-222-2-2-2-222-2-222-22-2-22200−2i2i00−2i2i00002-20000000000000000002i−2i000000
χ3322-2-222-2-2-2-2-2-222222-20000002i−2i00−2i2i00000022-2-200002i2i−2i−2i00000000000000
χ3422-2-222-2-2-2-2-2-222222-20000002i−2i00−2i2i000000-2-2220000−2i−2i2i2i00000000000000
χ3522-2-222-2-2-2-2-2-222222-2000000−2i2i002i−2i00000022-2-20000−2i−2i2i2i00000000000000
χ3622-2-222-2-2-2-2-2-222222-2000000−2i2i002i−2i000000-2-22200002i2i−2i−2i00000000000000
χ372-22-22-22-2002-22-200002i−2i2i−2i000000002-22i−2i000000i2−i2i2−i22−22−200000000i2−i22−200
χ382-22-22-22-2002-22-200002i−2i2i−2i000000002-22i−2i000000−i2i2−i2i2−22−2200000000−i2i2−2200
χ392-22-22-22-2002-22-200002i−2i2i−2i00000000-22−2i2i000000i2−i2i2−i22−22−200000000−i2i2−2200
χ402-22-22-22-2002-22-200002i−2i2i−2i00000000-22−2i2i000000−i2i2−i2i2−22−2200000000i2−i22−200
χ412-22-22-22-2002-22-20000−2i2i−2i2i000000002-2−2i2i000000i2−i2i2−i2−22−2200000000i2−i2−2200
χ422-22-22-22-2002-22-20000−2i2i−2i2i000000002-2−2i2i000000−i2i2−i2i22−22−200000000−i2i22−200
χ432-22-22-22-2002-22-20000−2i2i−2i2i00000000-222i−2i000000i2−i2i2−i2−22−2200000000−i2i22−200
χ442-22-22-22-2002-22-20000−2i2i−2i2i00000000-222i−2i000000−i2i2−i2i22−22−200000000i2−i2−2200
χ4544444444-4-4-4-4-4-4-4-44400000000000000000000000000000000000000000000
χ4644-4-444-4-444-4-444-4-4-4400000000000000000000000000000000000000000000
χ474-444-44-4-44-400004-40000000000000000000022−2222−220000000000000000000000
χ484-444-44-4-44-400004-400000000000000000000−2222−22220000000000000000000000
χ494-444-44-4-4-440000-440000004-400000000000000000000000000000000000000
χ504-444-44-4-4-440000-44000000-4400000000000000000000000000000000000000
χ514-44-44-44-400-44-44000000000000000000000000002i2−2i2−2i22i2000000000000000000
χ524-44-44-44-400-44-4400000000000000000000000000−2i22i22i2−2i2000000000000000000
χ534-4-444-4-44004-4-4400004i−4i−4i4i0000000000000000000000000000000000000000
χ544-4-444-4-44004-4-440000−4i4i4i−4i0000000000000000000000000000000000000000
χ554-4-444-4-4400-444-40000000000000000000000000000002i2−2i2−2i22i200000000000000
χ564-4-444-4-4400-444-4000000000000000000000000000000−2i22i22i2−2i200000000000000
χ574-4-4-4-44444-40000-4400000000004-40000000000000000000000000000000000
χ584-4-4-4-44444-40000-440000000000-440000000000000000000000000000000000
χ594-4-4-4-4444-4400004-40000000000000000000022−22−22220000000000000000000000
χ604-4-4-4-4444-4400004-400000000000000000000−222222−220000000000000000000000
χ61888-8-8-8-88000000000000000000000000000000000000000000000000000000
χ6288-88-8-88-8000000000000000000000000000000000000000000000000000000

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