Finite Group Databasebeta

← Group #316639

Character table — Group #316639

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122222222444444444488888888888888881616161616161616161616161616161616161616
order12222222444444442244448888444444888888888822222444448888888888
χ111111111111111111111111111111111111111111111111111111111111111
χ21111111111111111111111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-1
χ31111111111111111111111111111-1-1-1-11111-1-1-1-111-11111-11111-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111-1-1-1-11111-1-1-1-111-1-1-1-1-1-1-1-1-1-11111-1-11111
χ51111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-111-1-1
χ61111111111111111111111-1-1-1-1111111-1-1-1-1-1-1-1-1-1-11-1-1-1-111111-1-111-1-1-1-111
χ71111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-11111-1-1-1-1-1-1-11111-1-111
χ81111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1111111-1-11111-1-1
χ91111111111111111-1-111-1-11111-1-1111111-1-11111-1-1-111-1-1-111-1-111-1-1-1-1-1-111
χ101111111111111111-1-111-1-11111-1-1111111-1-11111-1-1-1-1-111-1-1-111-1-111-1-111-1-1
χ111111111111111111-1-111-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-1111-1-1111-1-1-1-1111111-1-1
χ121111111111111111-1-111-1-11111-1-1-1-1-1-111-1-1-1-1-1-1-1-11-1-1111-1-11111-1-111-1-111
χ131111111111111111-1-111-1-1-1-1-1-1-1-11111-1-111-1-1-1-111-111-1-1-1-1-111111111-1-1-1-1
χ141111111111111111-1-111-1-1-1-1-1-1-1-11111-1-111-1-1-1-111-1-1-111-111-1-1-1-1-1-1111111
χ151111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111111-1-11-1-111-1-1-1-1-1-11111
χ161111111111111111-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111-1-111111-1-11111-1-1-1-1-1-1
χ17222222222-222-2-22-222-2-2-2-200002-222-2-2000000000020000-200000000000000
χ18222222222-222-2-22-222-2-2-2-200002-2-2-2220000000000-20000200000000000000
χ19222222222-222-2-22-2-2-2-2-2220000-2222-2-20000000000-20000200000000000000
χ20222222222-222-2-22-2-2-2-2-2220000-22-2-222000000000020000-200000000000000
χ2122222222-22-2-222-2222-2-2222222-2-20000-2-2-2-200002200000000000000000000
χ2222222222-22-2-222-2222-2-222-2-2-2-2-2-2000022220000-2-200000000000000000000
χ2322222222-22-2-222-22-2-2-2-2-2-22222220000-2-2220000-2-200000000000000000000
χ2422222222-22-2-222-22-2-2-2-2-2-2-2-2-2-222000022-2-200002200000000000000000000
χ2522222222-2-2-2-2-2-2-2-22222-2-20000-22000000002i2i−2i−2i00000000000000002i−2i0000
χ2622222222-2-2-2-2-2-2-2-22222-2-20000-2200000000−2i−2i2i2i0000000000000000−2i2i0000
χ2722222222-2-2-2-2-2-2-2-2-2-2222200002-2000000002i2i−2i−2i0000000000000000−2i2i0000
χ2822222222-2-2-2-2-2-2-2-2-2-2222200002-200000000−2i−2i2i2i00000000000000002i−2i0000
χ29222-2-22-2-202002-20-22-2002-22i2i−2i−2i000000000000002i−2i00000000002−2i2−i2002−2i2−i2
χ30222-2-22-2-202002-20-22-2002-22i2i−2i−2i000000000000002i−2i0000000000−22−i2i200−22−i2i2
χ31222-2-22-2-202002-20-22-2002-2−2i−2i2i2i00000000000000−2i2i00000000002−2−i2i2002−2−i2i2
χ32222-2-22-2-202002-20-22-2002-2−2i−2i2i2i00000000000000−2i2i0000000000−22i2−i200−22i2−i2
χ33222-2-22-2-202002-20-2-2200-222i2i−2i−2i00000000000000−2i2i00000000002−2−i2i200−22i2−i2
χ34222-2-22-2-202002-20-2-2200-222i2i−2i−2i00000000000000−2i2i0000000000−22i2−i2002−2−i2i2
χ35222-2-22-2-202002-20-2-2200-22−2i−2i2i2i000000000000002i−2i00000000002−2i2−i200−22−i2i2
χ36222-2-22-2-202002-20-2-2200-22−2i−2i2i2i000000000000002i−2i0000000000−22−i2i2002−2i2−i2
χ372-2-2222-2-222-2-2-222-2002-2002i−2i2i−2i0000002i−2i0000000002-20002i−2i000000000000
χ382-2-2222-2-222-2-2-222-2002-2002i−2i2i−2i0000002i−2i000000000-22000−2i2i000000000000
χ392-2-2222-2-222-2-2-222-2002-200−2i2i−2i2i000000−2i2i0000000002-2000−2i2i000000000000
χ402-2-2222-2-222-2-2-222-2002-200−2i2i−2i2i000000−2i2i000000000-220002i−2i000000000000
χ412-2-2222-2-2-2222-22-2-200-22002i−2i2i−2i000000−2i2i000000000002-20002i−2i0000000000
χ422-2-2222-2-2-2222-22-2-200-22002i−2i2i−2i000000−2i2i00000000000-22000−2i2i0000000000
χ432-2-2222-2-2-2222-22-2-200-2200−2i2i−2i2i0000002i−2i000000000002-2000−2i2i0000000000
χ442-2-2222-2-2-2222-22-2-200-2200−2i2i−2i2i0000002i−2i00000000000-220002i−2i0000000000
χ45444-4-44-4-40-400-44044-400-440000000000000000000000000000000000000000
χ46444-4-44-4-40-400-4404-44004-40000000000000000000000000000000000000000
χ4744-44-4-44-4404-400-40000000000000004i−4i000000000000000000000000000000
χ4844-44-4-44-4404-400-4000000000000000−4i4i000000000000000000000000000000
χ4944-44-4-44-4-40-4400400000000000004-400000000000000000000000000000000
χ5044-44-4-44-4-40-440040000000000000-4400000000000000000000000000000000
χ514-444-4-4-4440-4400-40000000000000000000002i2−2i22i2−2i20000000000000000000000
χ524-444-4-4-4440-4400-4000000000000000000000−2i22i2−2i22i20000000000000000000000
χ534-444-4-4-44-404-400400000000000000000000022−22−22220000000000000000000000
χ544-444-4-4-44-404-4004000000000000000000000−222222−220000000000000000000000
χ554-4-4444-4-44-4-4-44-44400-44000000000000000000000000000000000000000000
χ564-4-4444-4-4-4-4444-4-44004-4000000000000000000000000000000000000000000
χ574-4-4-4-44440400-4-4040000004-4-44000000000000000000000000000000000000
χ584-4-4-4-44440400-4-404000000-444-4000000000000000000000000000000000000
χ594-4-4-4-44440-400440-40000000000000000004-400000000000000000000000000
χ604-4-4-4-44440-400440-4000000000000000000-4400000000000000000000000000
χ6188-8-88-8-88000000000000000000000000000000000000000000000000000000
χ628-88-88-88-8000000000000000000000000000000000000000000000000000000

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