Finite Group Databasebeta

← Group #271165

Character table — Group #271165

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size1111111122222222444444888888888888888888888888881616161616161616161616163232
order12222222444444442244442222444444888888888888888824444444888844
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1
χ3111111111111111111111111-1-11111-1-111111111-1-1-1-1-1-1-1-1-11-1-11-1-1-1-1-1-1-111
χ4111111111111111111111111-1-11111-1-1-1-1-1-1-1-1-1-111111111-11-1-11-1-1-11111-1-1
χ51111111111111111111111-1-1111-1-111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1
χ61111111111111111111111-1-1111-1-1111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11-1-1-1-11-1-1111111
χ71111111111111111111111-1-1-1-11-1-11-1-111111111-1-1-1-1-1-1-1-1-1-111-1-1111111-1-1
χ81111111111111111111111-1-1-1-11-1-11-1-1-1-1-1-1-1-1-1-111111111-1-111-1-111-1-1-1-111
χ91111111111111111-1-11-1-111111-1-1-1-1111111-1-1-1-11111-1-1-1-1-1-1-1-11-11111-1-11-1
χ101111111111111111-1-11-1-111111-1-1-1-111-1-1-1-11111-1-1-1-11111-1-1-1-11-111-1-111-11
χ111111111111111111-1-11-1-1111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-111111-11111-1-1-1-1111-1
χ121111111111111111-1-11-1-1111-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-11-11111-1-111-1-1-11
χ131111111111111111-1-11-1-11-1-111-111-1111111-1-1-1-11111-1-1-1-1-1111-1-1-1-1-1-111-11
χ141111111111111111-1-11-1-11-1-111-111-111-1-1-1-11111-1-1-1-11111-1111-1-1-1-111-1-11-1
χ151111111111111111-1-11-1-11-1-1-1-1-111-1-1-11111-1-1-1-1-1-1-1-1111111-1-1-111111-1-1-11
χ161111111111111111-1-11-1-11-1-1-1-1-111-1-1-1-1-1-1-111111111-1-1-1-111-1-1-1111-1-1111-1
χ172222222222-2-2-222-222-2-2-2-20022-2002-2-20000000000000000-20000200000000
χ182222222222-2-2-222-222-2-2-2-200-2-2-200222000000000000000020000-200000000
χ192222222222-2-2-222-2-2-2-222-20022200-2-2-2000000000000000020000-200000000
χ202222222222-2-2-222-2-2-2-222-200-2-2200-2220000000000000000-20000200000000
χ2122222222-2-2222-2-2222-222-22200-222-20000000000000000000-200-2000000000
χ2222222222-2-2222-2-2222-222-2-2-200-2-2-2-200000000000000000002002000000000
χ2322222222-2-2222-2-22-2-2-2-2-2-222002-2-220000000000000000000200-2000000000
χ2422222222-2-2222-2-22-2-2-2-2-2-2-2-20022220000000000000000000-2002000000000
χ2522222222-2-2-2-2-2-2-2-2222-2-220000200-2000000000000000000002-2002-2000000
χ2622222222-2-2-2-2-2-2-2-2222-2-220000200-200000000000000000000-2200-22000000
χ2722222222-2-2-2-2-2-2-2-2-2-222220000-2002000000000000000000002-200-22000000
χ2822222222-2-2-2-2-2-2-2-2-2-222220000-200200000000000000000000-22002-2000000
χ2922-2-22-2-220022-200-22-202-202-20002-200000000000i2i2−i2−i2i2i2−i2−i200000000i2−i2i2−i200
χ3022-2-22-2-220022-200-22-202-202-20002-200000000000−i2−i2i2i2−i2−i2i2i200000000−i2i2−i2i200
χ3122-2-22-2-220022-200-22-202-20-22000-2200000000000i2i2−i2−i2i2i2−i2−i200000000−i2i2−i2i200
χ3222-2-22-2-220022-200-22-202-20-22000-2200000000000−i2−i2i2i2−i2−i2i2i200000000i2−i2i2−i200
χ3322-2-22-2-220022-200-2-220-2202-2000-2200000000000i2i2−i2−i2−i2−i2i2i200000000i2−i2−i2i200
χ3422-2-22-2-220022-200-2-220-2202-2000-2200000000000−i2−i2i2i2i2i2−i2−i200000000−i2i2i2−i200
χ3522-2-22-2-220022-200-2-220-220-220002-200000000000i2i2−i2−i2−i2−i2i2i200000000−i2i2i2−i200
χ3622-2-22-2-220022-200-2-220-220-220002-200000000000−i2−i2i2i2i2i2−i2−i200000000i2−i2−i2i200
χ372-2-22-2-2222-22-222-2-200200-2002-200002-22i2i−2i−2i00002i−2i2i−2i000000000000000000
χ382-2-22-2-2222-22-222-2-200200-2002-200002-2−2i−2i2i2i0000−2i2i−2i2i000000000000000000
χ392-2-22-2-2222-22-222-2-200200-200-220000-222i2i−2i−2i0000−2i2i−2i2i000000000000000000
χ402-2-22-2-2222-22-222-2-200200-200-220000-22−2i−2i2i2i00002i−2i2i−2i000000000000000000
χ412-2-22-2-2222-2-22-22-2200-2002002-20000-22000022-2-200002-22-200000000000000
χ422-2-22-2-2222-2-22-22-2200-2002002-20000-220000-2-2220000-22-2200000000000000
χ432-2-22-2-2222-2-22-22-2200-200200-2200002-2000022-2-20000-22-2200000000000000
χ442-2-22-2-2222-2-22-22-2200-200200-2200002-20000-2-22200002-22-200000000000000
χ45444-4-4-44-444000-4-400000000000000000000022−2222−220000000000000000000000
χ46444-4-4-44-444000-4-4000000000000000000000−2222−22220000000000000000000000
χ47444-4-4-44-4-4-400044000000000000000002i2−2i22i2−2i200000000000000000000000000
χ48444-4-4-44-4-4-40004400000000000000000−2i22i2−2i22i200000000000000000000000000
χ4944-4-44-4-4400-4-440044-40-4400000000000000000000000000000000000000000
χ5044-4-44-4-4400-4-44004-4404-400000000000000000000000000000000000000000
χ514-44-4-44-44004-4-400400000000000000000000000022−22−2222000000000000000000
χ524-44-4-44-44004-4-4004000000000000000000000000−222222−22000000000000000000
χ534-44-4-44-4400-44400-400000000000000000000000000002i2−2i2−2i22i200000000000000
χ544-44-4-44-4400-44400-40000000000000000000000000000−2i22i22i2−2i200000000000000
χ554-4-44-4-444-444-44-44-400-40040000000000000000000000000000000000000000
χ564-4-44-4-444-44-44-4-44400400-40000000000000000000000000000000000000000
χ574-4-4-4444-44-4000-4400000000000000000000022−22−22220000000000000000000000
χ584-4-4-4444-44-4000-44000000000000000000000−222222−220000000000000000000000
χ594-4-4-4444-4-440004-40000000000000000022−22−222200000000000000000000000000
χ604-4-4-4444-4-440004-400000000000000000−222222−2200000000000000000000000000
χ6188-88-88-8-8000000000000000000000000000000000000000000000000000000
χ628-8888-8-8-8000000000000000000000000000000000000000000000000000000

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