Finite Group Databasebeta

← Group #136552

Character table — Group #136552

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
χ31111111111111111111111111-1-1-1-1111111111-1-1-1-1111111-1-1-1-1-1-1-1-1
χ41111111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1111111
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
χ7111111111111111111111-1-1-1-1-1-1-1-11111111111111-1-1-1-1-1-1-1-1-1-1-1-111
χ8111111111111111111111-1-1-1-1-1-1-1-11-1-1-1-1-1-1-1-11111-1-11111-1-11111-1-1
χ91111-1-1-11111-11-1-11-1-1-1-11ii−i−iii−i−i1iiii−i−i−i−i11-1-1i−i11-1-1i−i11-1-1i−i
χ101111-1-1-11111-11-1-11-1-1-1-11ii−i−iii−i−i1−i−i−i−iiiii11-1-1i−i-1-111i−i-1-111−ii
χ111111-1-1-11111-11-1-11-1-1-1-11ii−i−i−i−iii1iiii−i−i−i−i-1-111i−i11-1-1−ii-1-111−ii
χ121111-1-1-11111-11-1-11-1-1-1-11ii−i−i−i−iii1−i−i−i−iiiii-1-111i−i-1-111−ii11-1-1i−i
χ131111-1-1-11111-11-1-11-1-1-1-11−i−iiiii−i−i1iiii−i−i−i−i-1-111−ii-1-111i−i11-1-1−ii
χ141111-1-1-11111-11-1-11-1-1-1-11−i−iiiii−i−i1−i−i−i−iiiii-1-111−ii11-1-1i−i-1-111i−i
χ151111-1-1-11111-11-1-11-1-1-1-11−i−iii−i−iii1iiii−i−i−i−i11-1-1−ii-1-111−ii-1-111i−i
χ161111-1-1-11111-11-1-11-1-1-1-11−i−iii−i−iii1−i−i−i−iiiii11-1-1−ii11-1-1−ii11-1-1−ii
χ17222222222222222-2-2-2-2-2-200002222-2000000000000000000-2-2000000
χ18222222222222222-2-2-2-2-2-20000-2-2-2-2-200000000000000000022000000
χ19222222222-2-22-2-2-2222-2-2222220000-2000000000000-2-2000000000000
χ20222222222-2-22-2-2-2222-2-22-2-2-2-20000-200000000000022000000000000
χ21222222222-2-22-2-2-2-2-2-222-2000000002000000002-22-200000000000000
χ22222222222-2-22-2-2-2-2-2-222-200000000200000000-22-2200000000000000
χ23222222-2-2-2-2-2-222-200000000002-22-20i2i2−i2−i2i2i2−i2−i2000000000000i2−i2i2−i200
χ24222222-2-2-2-2-2-222-200000000002-22-20−i2−i2i2i2−i2−i2i2i2000000000000−i2i2−i2i200
χ25222222-2-2-2-2-2-222-20000000000-22-220i2i2−i2−i2i2i2−i2−i2000000000000−i2i2−i2i200
χ26222222-2-2-2-2-2-222-20000000000-22-220−i2−i2i2i2−i2−i2i2i2000000000000i2−i2i2−i200
χ272222-2-22-2-2-2-222-2200000000002i−2i−2i2i022−2−2−2−222000000000000−i2i2i2−i200
χ282222-2-22-2-2-2-222-2200000000002i−2i−2i2i0−2−22222−2−2000000000000i2−i2−i2i200
χ292222-2-22-2-2-2-222-220000000000−2i2i2i−2i022−2−2−2−222000000000000i2−i2−i2i200
χ302222-2-22-2-2-2-222-220000000000−2i2i2i−2i0−2−22222−2−2000000000000−i2i2i2−i200
χ312222-2-2-22222-22-2-2-22222-200002i2i−2i−2i-2000000000000000000−2i2i000000
χ322222-2-2-22222-22-2-2-22222-20000−2i−2i2i2i-20000000000000000002i−2i000000
χ332222-2-2-222-2-2-2-2222-2-22222i2i−2i−2i0000-2000000000000−2i2i000000000000
χ342222-2-2-222-2-2-2-2222-2-2222−2i−2i2i2i0000-20000000000002i−2i000000000000
χ352222-2-2-222-2-2-2-222-222-2-2-2000000002000000002-2-2200000000000000
χ362222-2-2-222-2-2-2-222-222-2-2-200000000200000000-222-200000000000000
χ3722-2-22-222-200-200022-200-22-22-2000002−22−22−22−20000002−22−200000000
χ3822-2-22-222-200-200022-200-22-22-200000−22−22−22−22000000−22−2200000000
χ3922-2-22-222-200-200022-200-2-22-22000002−22−22−22−2000000−22−2200000000
χ4022-2-22-222-200-200022-200-2-22-2200000−22−22−22−220000002−22−200000000
χ4122-2-2-22-22-20020002-2200-22i−2i−2i2i00000i2−i2i2−i2−i2i2−i2i20000002−2−2200000000
χ4222-2-2-22-22-20020002-2200-22i−2i−2i2i00000−i2i2−i2i2i2−i2i2−i2000000−222−200000000
χ4322-2-2-22-22-20020002-2200-2−2i2i2i−2i00000i2−i2i2−i2−i2i2−i2i2000000−222−200000000
χ4422-2-2-22-22-20020002-2200-2−2i2i2i−2i00000−i2i2−i2i2i2−i2i2−i20000002−2−2200000000
χ45444444-4-4-444-4-4-4400000000000000000000000000000000000000000
χ464444-4-44-4-4444-44-400000000000000000000000000000000000000000
χ4744-4-44-444-400-4000-4-4400400000000000000000000000000000000000
χ4844-4-44-4-4-440040000000000000000002i−2i−2i2i2i−2i−2i2i000000000000000000
χ4944-4-44-4-4-44004000000000000000000−2i2i2i−2i−2i2i2i−2i000000000000000000
χ5044-4-4-444-4400-40000000000000000002-2-22-222-2000000000000000000
χ5144-4-4-444-4400-4000000000000000000-222-22-2-22000000000000000000
χ5244-4-4-44-44-4004000-44-400400000000000000000000000000000000000
χ538-88-80000000000000042−42000000000000000000000000000000000000
χ548-88-800000000000000−4242000000000000000000000000000000000000
χ558-8-88000008-8000000000000000000000000000000000000000000000
χ568-8-8800000-88000000000000000000000000000000000000000000000

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