Finite Group Databasebeta

← Group #295708

Character table — Group #295708

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122222222444444888888888888888888888888881616161616161616161616163232
order12222222444444444444444444444444888888888888888824444444888844
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ31111111111111111111111111111-1-1-1-111111111-1-1-1-1-1-1-1-1-11-1-11-1-1-1-1-1-1-111
χ41111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111111111-11-1-11-1-1-11111-1-1
χ5111111111111111111111111-1-1-1-1111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1
χ6111111111111111111111111-1-1-1-11111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11-1-1111111
χ7111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1
χ8111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1-1-111
χ91111111111111111-1-1-1-111-1-111-1-111111111-1-1-1-11111-1-1-1-1-1-1111-1-1-111-1-11-1
χ101111111111111111-1-1-1-111-1-111-1-11111-1-1-1-11111-1-1-1-11111-1-1111-1-1-1-1-111-11
χ111111111111111111-1-1-1-111-1-111-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111-1-1-11111-1-1111-1
χ121111111111111111-1-1-1-111-1-111-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11-1-1-1111111-1-1-11
χ131111111111111111-1-1-1-111-1-1-1-11111111111-1-1-1-11111-1-1-1-1-11-1-1-1-111-1-111-11
χ141111111111111111-1-1-1-111-1-1-1-1111111-1-1-1-11111-1-1-1-11111-11-1-1-1-11111-1-11-1
χ151111111111111111-1-1-1-111-1-1-1-111-1-1-1-11111-1-1-1-1-1-1-1-111111111-11-1-111-1-1-11
χ161111111111111111-1-1-1-111-1-1-1-111-1-1-1-1-1-1-1-111111111-1-1-1-11111-11-1-1-1-1111-1
χ172222222222-2-222-2-222-2-2-2-22-2000022-2-2000000000000000020000-200000000
χ182222222222-2-222-2-222-2-2-2-22-20000-2-2220000000000000000-20000200000000
χ192222222222-2-222-2-2-2-222-2-2-22000022-2-20000000000000000-20000200000000
χ202222222222-2-222-2-2-2-222-2-2-220000-2-222000000000000000020000-200000000
χ2122222222-2-222-2-2222222-2-2-2-22222000000000000000000000-200-2000000000
χ2222222222-2-222-2-2222222-2-2-2-2-2-2-2-20000000000000000000002002000000000
χ2322222222-2-222-2-222-2-2-2-2-2-22222-2-2000000000000000000000200-2000000000
χ2422222222-2-222-2-222-2-2-2-2-2-222-2-222000000000000000000000-2002000000000
χ2522222222-2-2-2-2-2-2-2-222-2-222-22000000000000000000000000002-2002-2000000
χ2622222222-2-2-2-2-2-2-2-222-2-222-2200000000000000000000000000-2200-22000000
χ2722222222-2-2-2-2-2-2-2-2-2-222222-2000000000000000000000000002-200-22000000
χ2822222222-2-2-2-2-2-2-2-2-2-222222-200000000000000000000000000-22002-2000000
χ29222-2-22-2-2-2-22-2222-200002-20000002i−2i2i−2i000022-2-200002i2i−2i−2i00000000000000
χ30222-2-22-2-2-2-22-2222-200002-20000002i−2i2i−2i0000-2-2220000−2i−2i2i2i00000000000000
χ31222-2-22-2-2-2-22-2222-200002-2000000−2i2i−2i2i000022-2-20000−2i−2i2i2i00000000000000
χ32222-2-22-2-2-2-22-2222-200002-2000000−2i2i−2i2i0000-2-22200002i2i−2i−2i00000000000000
χ33222-2-22-2-2-2-2-2222-220000-220000002i−2i−2i2i22-2-200002i2i−2i−2i000000000000000000
χ34222-2-22-2-2-2-2-2222-220000-220000002i−2i−2i2i-2-2220000−2i−2i2i2i000000000000000000
χ35222-2-22-2-2-2-2-2222-220000-22000000−2i2i2i−2i22-2-20000−2i−2i2i2i000000000000000000
χ36222-2-22-2-2-2-2-2222-220000-22000000−2i2i2i−2i-2-22200002i2i−2i−2i000000000000000000
χ372-2-2222-2-2002-200-222i−2i2i−2i00002-22i−2i000000000000i2−i2i2−i22−22−200000000i2−i22−200
χ382-2-2222-2-2002-200-222i−2i2i−2i00002-22i−2i000000000000−i2i2−i2i2−22−2200000000−i2i2−2200
χ392-2-2222-2-2002-200-222i−2i2i−2i0000-22−2i2i000000000000i2−i2i2−i22−22−200000000−i2i2−2200
χ402-2-2222-2-2002-200-222i−2i2i−2i0000-22−2i2i000000000000−i2i2−i2i2−22−2200000000i2−i22−200
χ412-2-2222-2-2002-200-22−2i2i−2i2i00002-2−2i2i000000000000i2−i2i2−i2−22−2200000000i2−i2−2200
χ422-2-2222-2-2002-200-22−2i2i−2i2i00002-2−2i2i000000000000−i2i2−i2i22−22−200000000−i2i22−200
χ432-2-2222-2-2002-200-22−2i2i−2i2i0000-222i−2i000000000000i2−i2i2−i2−22−2200000000−i2i22−200
χ442-2-2222-2-2002-200-22−2i2i−2i2i0000-222i−2i000000000000−i2i2−i2i22−22−200000000i2−i2−2200
χ45444-4-44-4-4444-4-4-44-40000-440000000000000000000000000000000000000000
χ46444-4-44-4-444-44-4-4-4400004-40000000000000000000000000000000000000000
χ474-444-4-44-44-4004-400000000000000000000002i2−2i22i2−2i20000000000000000000000
χ484-444-4-44-44-4004-40000000000000000000000−2i22i2−2i22i20000000000000000000000
χ494-444-4-44-4-4400-440000000000000000002i2−2i22i2−2i200000000000000000000000000
χ504-444-4-44-4-4400-44000000000000000000−2i22i2−2i22i200000000000000000000000000
χ514-44-44-4-444-400-440000000000000000002i2−2i2−2i22i200000000000000000000000000
χ524-44-44-4-444-400-44000000000000000000−2i22i22i2−2i200000000000000000000000000
χ534-44-44-4-44-44004-400000000000000000000002i2−2i2−2i22i20000000000000000000000
χ544-44-44-4-44-44004-40000000000000000000000−2i22i22i2−2i20000000000000000000000
χ554-4-4444-4-400-44004-44i−4i−4i4i000000000000000000000000000000000000000000
χ564-4-4444-4-400-44004-4−4i4i4i−4i000000000000000000000000000000000000000000
χ574-4-4-4-4444004400-4-400000000000000000000000000002i2−2i2−2i22i200000000000000
χ584-4-4-4-4444004400-4-40000000000000000000000000000−2i22i22i2−2i200000000000000
χ594-4-4-4-444400-4-4004400000000000000000000000022−22−2222000000000000000000
χ604-4-4-4-444400-4-40044000000000000000000000000−222222−22000000000000000000
χ6188-88-8-8-88000000000000000000000000000000000000000000000000000000
χ6288-8-88-88-8000000000000000000000000000000000000000000000000000000

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