Finite Group Databasebeta

← Group #136371

Character table — Group #136371

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size11112222222244444444488888888888888888161616161616161616161616161616163232
order12222244444444488888822448888816161616161616164444888888881616161644
χ111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111-1-1-1-1-1-1-1-11111-1-1-1-11111-1-1-1-1-1-1
χ311111111111111111111111111-1-1-1-11111111111-1-11111-1-1-1-1-1-1-1-1-1-1
χ411111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1-1-1-1-1-1-1111111
χ5111111111111111111111-1-1-1-11111111111111-1-111-1-1-1-1-1-1-1-11111-1-1
χ6111111111111111111111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-111
χ7111111111111111111111-1-1-1-11-1-1-1-111111111-1-1-1-1-1-1-1-11111-1-1-1-111
χ8111111111111111111111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1111111111111-1-1
χ91111-1-11-1111-11-1-111-111-111-1-1-1ii−i−i1111-1-1-1-11-1i−i11-1-1ii−i−iii−i−ii−i
χ101111-1-11-1111-11-1-111-111-111-1-1-1ii−i−i-1-1-1-111111-1i−i-1-111ii−i−i−i−iii−ii
χ111111-1-11-1111-11-1-111-111-111-1-1-1−i−iii1111-1-1-1-11-1−ii11-1-1−i−iii−i−iii−ii
χ121111-1-11-1111-11-1-111-111-111-1-1-1−i−iii-1-1-1-111111-1−ii-1-111−i−iiiii−i−ii−i
χ131111-1-11-1111-11-1-111-111-1-1-111-1ii−i−i1111-1-1-1-1-11i−i-1-111−i−iiiii−i−i−ii
χ141111-1-11-1111-11-1-111-111-1-1-111-1ii−i−i-1-1-1-11111-11i−i11-1-1−i−iii−i−iiii−i
χ151111-1-11-1111-11-1-111-111-1-1-111-1−i−iii1111-1-1-1-1-11−ii-1-111ii−i−i−i−iiii−i
χ161111-1-11-1111-11-1-111-111-1-1-111-1−i−iii-1-1-1-11111-11−ii11-1-1ii−i−iii−i−i−ii
χ17222222222222222-2-2-2-2-2-20000-222220000000000-2-200000000000000
χ18222222222222222-2-2-2-2-2-20000-2-2-2-2-200000000002200000000000000
χ19222222-2222-22-2-2-2222-2-222222-2000000000000-2-20000000000000000
χ20222222-2222-22-2-2-2222-2-22-2-2-2-2-2000000000000220000000000000000
χ21222222-2222-22-2-2-2-2-2-222-200002000000000000000000002-22-2000000
χ22222222-2222-22-2-2-2-2-2-222-20000200000000000000000000-22-22000000
χ23222222-2-2-2-2-2-222-2000000000002i−2i2i−2ii2i2−i2−i2i2i2−i2−i20000000000002−22−200
χ24222222-2-2-2-2-2-222-2000000000002i−2i2i−2i−i2−i2i2i2−i2−i2i2i2000000000000−22−2200
χ25222222-2-2-2-2-2-222-200000000000−2i2i−2i2ii2i2−i2−i2i2i2−i2−i2000000000000−22−2200
χ26222222-2-2-2-2-2-222-200000000000−2i2i−2i2i−i2−i2i2i2−i2−i2i2i20000000000002−22−200
χ272222-2-22-2222-22-2-2-2-22-2-22000022i2i−2i−2i0000000000−2i2i00000000000000
χ282222-2-22-2222-22-2-2-2-22-2-2200002−2i−2i2i2i00000000002i−2i00000000000000
χ292222-2-2-22-2-2-222-22000000000002-2-22i2i2−i2−i2−i2−i2i2i2000000000000−i2i2i2−i200
χ302222-2-2-22-2-2-222-22000000000002-2-22−i2−i2i2i2i2i2−i2−i2000000000000i2−i2−i2i200
χ312222-2-2-22-2-2-222-2200000000000-222-2i2i2−i2−i2−i2−i2i2i2000000000000i2−i2−i2i200
χ322222-2-2-22-2-2-222-2200000000000-222-2−i2−i2i2i2i2i2−i2−i2000000000000−i2i2i2−i200
χ332222-2-2-2-222-2-2-22222-2-2-2-222-2-22000000000000-220000000000000000
χ342222-2-2-2-222-2-2-22222-2-2-2-2-2-22220000000000002-20000000000000000
χ352222-2-2-2-222-2-2-222-2-222220000-2000000000000000000002i−2i−2i2i000000
χ362222-2-2-2-222-2-2-222-2-222220000-200000000000000000000−2i2i2i−2i000000
χ3722-2-22-20-22-2020002-2200-22-22-200000i2−i2i2−i2i2−i2i2−i20000i2−i2i2−i20000000000
χ3822-2-22-20-22-2020002-2200-22-22-200000−i2i2−i2i2−i2i2−i2i20000−i2i2−i2i20000000000
χ3922-2-22-20-22-2020002-2200-2-22-2200000i2−i2i2−i2i2−i2i2−i20000−i2i2−i2i20000000000
χ4022-2-22-20-22-2020002-2200-2-22-2200000−i2i2−i2i2−i2i2−i2i20000i2−i2i2−i20000000000
χ4122-2-2-22022-20-20002-2-20022-2-2200000i2−i2i2−i2−i2i2−i2i20000i2−i2−i2i20000000000
χ4222-2-2-22022-20-20002-2-20022-2-2200000−i2i2−i2i2i2−i2i2−i20000−i2i2i2−i20000000000
χ4322-2-2-22022-20-20002-2-2002-222-200000i2−i2i2−i2−i2i2−i2i20000−i2i2i2−i20000000000
χ4422-2-2-22022-20-20002-2-2002-222-200000−i2i2−i2i2i2−i2i2−i20000i2−i2−i2i20000000000
χ454444444-4-4-44-4-4-4400000000000000000000000000000000000000000
χ464444-4-444-4-444-44-400000000000000000000000000000000000000000
χ4744-4-44-404-440-40000000000000000002-2-222-2-22000000000000000000
χ4844-4-44-404-440-4000000000000000000-222-2-222-2000000000000000000
χ4944-4-44-40-44-404000-44-400400000000000000000000000000000000000
χ5044-4-4-44044-40-4000-44400-400000000000000000000000000000000000
χ5144-4-4-440-4-44040000000000000000002-2-22-222-2000000000000000000
χ5244-4-4-440-4-4404000000000000000000-222-22-2-22000000000000000000
χ538-88-8000000000000004i2−4i2000000000000000000000000000000000000
χ548-88-800000000000000−4i24i2000000000000000000000000000000000000
χ558-8-88008000-8000000000000000000000000000000000000000000000
χ568-8-8800-80008000000000000000000000000000000000000000000000

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