Finite Group Databasebeta

← Group #136384

Character table — Group #136384

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11112222222244444444488888888888888888161616161616161616161616161616163232
order12222244444444488888844444444816161616161616164444448888881616161688
χ111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-111-1-1-1-1-1-1
χ31111111111111111111111111-1-1-1-111111111111-1-1-1-11111-1-1-1-1-1-1-1-1
χ41111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1111111-1-1
χ6111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111-1-1-1-111
χ7111111111111111111111-1-1-1-1-1-1-1-1111111111-1-11111-1-1-1-1-1-1-1-1-1-111
χ8111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-1-1-111111111-1-11111-1-1
χ91111-1-1-11111-1-11-111-111-111-1-1ii−i−i-11111-1-1-1-11-1ii−i−i11-1-1i−iii−i−ii−i
χ101111-1-1-11111-1-11-111-111-111-1-1ii−i−i-1-1-1-1-111111-1ii−i−i-1-111i−i−i−iii−ii
χ111111-1-1-11111-1-11-111-111-111-1-1−i−iii-11111-1-1-1-11-1−i−iii11-1-1−ii−i−iii−ii
χ121111-1-1-11111-1-11-111-111-111-1-1−i−iii-1-1-1-1-111111-1−i−iii-1-111−iiii−i−ii−i
χ131111-1-1-11111-1-11-111-111-1-1-111ii−i−i-11111-1-1-1-1-11−i−iii-1-111i−iii−i−i−ii
χ141111-1-1-11111-1-11-111-111-1-1-111ii−i−i-1-1-1-1-11111-11−i−iii11-1-1i−i−i−iiii−i
χ151111-1-1-11111-1-11-111-111-1-1-111−i−iii-11111-1-1-1-1-11ii−i−i-1-111−ii−i−iiii−i
χ161111-1-1-11111-1-11-111-111-1-1-111−i−iii-1-1-1-1-11111-11ii−i−i11-1-1−iiii−i−i−ii
χ17222222222222222-2-2-2-2-2-200002222-2000000000000000000-2-2000000
χ18222222222222222-2-2-2-2-2-20000-2-2-2-2-200000000000000000022000000
χ19222222222-2-22-2-2-2222-2-2222220000-200000000-2-20000000000000000
χ20222222222-2-22-2-2-2222-2-22-2-2-2-20000-200000000220000000000000000
χ21222222222-2-22-2-2-2-2-2-222-200000000200000000002-22-2000000000000
χ22222222222-2-22-2-2-2-2-2-222-20000000020000000000-22-22000000000000
χ23222222-2-2-2-2-2-2-22200000000002-22-20i2i2−i2−i2i2i2−i2−i2000000000000i2−i2i2−i200
χ24222222-2-2-2-2-2-2-22200000000002-22-20−i2−i2i2i2−i2−i2i2i2000000000000−i2i2−i2i200
χ25222222-2-2-2-2-2-2-2220000000000-22-220i2i2−i2−i2i2i2−i2−i2000000000000−i2i2−i2i200
χ26222222-2-2-2-2-2-2-2220000000000-22-220−i2−i2i2i2−i2−i2i2i2000000000000i2−i2i2−i200
χ272222-2-22-2-2-2-2222-200000000002i−2i−2i2i0i2i2−i2−i2−i2−i2i2i2000000000000−222−200
χ282222-2-22-2-2-2-2222-200000000002i−2i−2i2i0−i2−i2i2i2i2i2−i2−i20000000000002−2−2200
χ292222-2-22-2-2-2-2222-20000000000−2i2i2i−2i0i2i2−i2−i2−i2−i2i2i20000000000002−2−2200
χ302222-2-22-2-2-2-2222-20000000000−2i2i2i−2i0−i2−i2i2i2i2i2−i2−i2000000000000−222−200
χ312222-2-2-22222-2-22-2-2-22-2-2200002i2i−2i−2i2000000000000000000−2i2i000000
χ322222-2-2-22222-2-22-2-2-22-2-220000−2i−2i2i2i20000000000000000002i−2i000000
χ332222-2-2-222-2-2-22-2222-2-2-2-222-2-20000200000000-220000000000000000
χ342222-2-2-222-2-2-22-2222-2-2-2-2-2-22200002000000002-20000000000000000
χ352222-2-2-222-2-2-22-22-2-2222200000000-200000000002i−2i−2i2i000000000000
χ362222-2-2-222-2-2-22-22-2-2222200000000-20000000000−2i2i2i−2i000000000000
χ372-22-22-2-22-20020002-2200-22i−2i2i−2i00000i2−i2i2−i2i2−i2i2−i20000002−22−200000000
χ382-22-22-2-22-20020002-2200-22i−2i2i−2i00000−i2i2−i2i2−i2i2−i2i2000000−22−2200000000
χ392-22-22-2-22-20020002-2200-2−2i2i−2i2i00000i2−i2i2−i2i2−i2i2−i2000000−22−2200000000
χ402-22-22-2-22-20020002-2200-2−2i2i−2i2i00000−i2i2−i2i2−i2i2−i2i20000002−22−200000000
χ412-22-2-2222-200-20002-2-20022i−2i−2i2i00000i2−i2i2−i2−i2i2−i2i20000002−2−2200000000
χ422-22-2-2222-200-20002-2-20022i−2i−2i2i00000−i2i2−i2i2i2−i2i2−i2000000−222−200000000
χ432-22-2-2222-200-20002-2-2002−2i2i2i−2i00000i2−i2i2−i2−i2i2−i2i2000000−222−200000000
χ442-22-2-2222-200-20002-2-2002−2i2i2i−2i00000−i2i2−i2i2i2−i2i2−i20000002−2−2200000000
χ45444444-4-4-444-44-4-400000000000000000000000000000000000000000
χ464444-4-44-4-4444-4-4400000000000000000000000000000000000000000
χ474-44-44-44-4400-40000000000000000002-2-222-2-22000000000000000000
χ484-44-44-44-4400-4000000000000000000-222-2-222-2000000000000000000
χ494-44-44-4-44-4004000-44-400400000000000000000000000000000000000
χ504-44-4-4444-400-4000-44400-400000000000000000000000000000000000
χ514-44-4-44-4-440040000000000000000002-2-22-222-2000000000000000000
χ524-44-4-44-4-44004000000000000000000-222-22-2-22000000000000000000
χ5388-8-8000008-8000000000000000000000000000000000000000000000
χ5488-8-800000-88000000000000000000000000000000000000000000000
χ558-8-88000000000000004i2−4i2000000000000000000000000000000000000
χ568-8-8800000000000000−4i24i2000000000000000000000000000000000000

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